xref: /libCEED/interface/ceed-preconditioning.c (revision daaf13a462f999a7d367f3df68e0e3c34270722c)
1 // Copyright (c) 2017-2024, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
3 //
4 // SPDX-License-Identifier: BSD-2-Clause
5 //
6 // This file is part of CEED:  http://github.com/ceed
7 
8 #include <ceed-impl.h>
9 #include <ceed.h>
10 #include <ceed/backend.h>
11 #include <assert.h>
12 #include <math.h>
13 #include <stdbool.h>
14 #include <stdio.h>
15 #include <string.h>
16 
17 /// @file
18 /// Implementation of CeedOperator preconditioning interfaces
19 
20 /// ----------------------------------------------------------------------------
21 /// CeedOperator Library Internal Preconditioning Functions
22 /// ----------------------------------------------------------------------------
23 /// @addtogroup CeedOperatorDeveloper
24 /// @{
25 
26 /**
27   @brief Duplicate a `CeedQFunction` with a reference `Ceed` to fallback for advanced `CeedOperator` functionality
28 
29   @param[in]  fallback_ceed `Ceed` on which to create fallback `CeedQFunction`
30   @param[in]  qf            `CeedQFunction` to create fallback for
31   @param[out] qf_fallback   Fallback `CeedQFunction`
32 
33   @return An error code: 0 - success, otherwise - failure
34 
35   @ref Developer
36 **/
37 static int CeedQFunctionCreateFallback(Ceed fallback_ceed, CeedQFunction qf, CeedQFunction *qf_fallback) {
38   char               *source_path_with_name = NULL;
39   CeedInt             num_input_fields, num_output_fields;
40   Ceed                ceed;
41   CeedQFunctionField *input_fields, *output_fields;
42 
43   // Check if NULL qf passed in
44   if (!qf) return CEED_ERROR_SUCCESS;
45 
46   CeedCall(CeedQFunctionGetCeed(qf, &ceed));
47   CeedDebug256(ceed, 1, "---------- CeedOperator Fallback ----------\n");
48   CeedDebug(ceed, "Creating fallback CeedQFunction\n");
49 
50   if (qf->source_path) {
51     size_t path_len = strlen(qf->source_path), name_len = strlen(qf->kernel_name);
52     CeedCall(CeedCalloc(path_len + name_len + 2, &source_path_with_name));
53     memcpy(source_path_with_name, qf->source_path, path_len);
54     memcpy(&source_path_with_name[path_len], ":", 1);
55     memcpy(&source_path_with_name[path_len + 1], qf->kernel_name, name_len);
56   } else {
57     CeedCall(CeedCalloc(1, &source_path_with_name));
58   }
59 
60   {
61     CeedInt           vec_length;
62     CeedQFunctionUser f;
63 
64     CeedCall(CeedQFunctionGetVectorLength(qf, &vec_length));
65     CeedCall(CeedQFunctionGetUserFunction(qf, &f));
66     CeedCall(CeedQFunctionCreateInterior(fallback_ceed, vec_length, f, source_path_with_name, qf_fallback));
67   }
68   {
69     CeedQFunctionContext ctx;
70 
71     CeedCall(CeedQFunctionGetContext(qf, &ctx));
72     CeedCall(CeedQFunctionSetContext(*qf_fallback, ctx));
73   }
74   CeedCall(CeedQFunctionGetFields(qf, &num_input_fields, &input_fields, &num_output_fields, &output_fields));
75   for (CeedInt i = 0; i < num_input_fields; i++) {
76     const char  *field_name;
77     CeedInt      size;
78     CeedEvalMode eval_mode;
79 
80     CeedCall(CeedQFunctionFieldGetData(input_fields[i], &field_name, &size, &eval_mode));
81     CeedCall(CeedQFunctionAddInput(*qf_fallback, field_name, size, eval_mode));
82   }
83   for (CeedInt i = 0; i < num_output_fields; i++) {
84     const char  *field_name;
85     CeedInt      size;
86     CeedEvalMode eval_mode;
87 
88     CeedCall(CeedQFunctionFieldGetData(output_fields[i], &field_name, &size, &eval_mode));
89     CeedCall(CeedQFunctionAddOutput(*qf_fallback, field_name, size, eval_mode));
90   }
91   CeedCall(CeedFree(&source_path_with_name));
92   return CEED_ERROR_SUCCESS;
93 }
94 
95 /**
96   @brief Duplicate a `CeedOperator` with a reference `Ceed` to fallback for advanced `CeedOperator` functionality
97 
98   @param[in,out] op `CeedOperator` to create fallback for
99 
100   @return An error code: 0 - success, otherwise - failure
101 
102   @ref Developer
103 **/
104 static int CeedOperatorCreateFallback(CeedOperator op) {
105   bool         is_composite;
106   Ceed         ceed, ceed_fallback;
107   CeedOperator op_fallback;
108 
109   // Check not already created
110   if (op->op_fallback) return CEED_ERROR_SUCCESS;
111 
112   // Fallback Ceed
113   CeedCall(CeedOperatorGetCeed(op, &ceed));
114   CeedCall(CeedGetOperatorFallbackCeed(ceed, &ceed_fallback));
115   if (!ceed_fallback) return CEED_ERROR_SUCCESS;
116 
117   CeedDebug256(ceed, 1, "---------- CeedOperator Fallback ----------\n");
118   CeedDebug(ceed, "Creating fallback CeedOperator\n");
119 
120   // Clone Op
121   CeedCall(CeedOperatorIsComposite(op, &is_composite));
122   if (is_composite) {
123     CeedInt       num_suboperators;
124     CeedOperator *sub_operators;
125 
126     CeedCall(CeedCompositeOperatorCreate(ceed_fallback, &op_fallback));
127     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
128     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
129     for (CeedInt i = 0; i < num_suboperators; i++) {
130       CeedOperator op_sub_fallback;
131 
132       CeedCall(CeedOperatorGetFallback(sub_operators[i], &op_sub_fallback));
133       CeedCall(CeedCompositeOperatorAddSub(op_fallback, op_sub_fallback));
134     }
135   } else {
136     CeedInt            num_input_fields, num_output_fields;
137     CeedQFunction      qf_fallback = NULL, dqf_fallback = NULL, dqfT_fallback = NULL;
138     CeedOperatorField *input_fields, *output_fields;
139 
140     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->qf, &qf_fallback));
141     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->dqf, &dqf_fallback));
142     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->dqfT, &dqfT_fallback));
143     CeedCall(CeedOperatorCreate(ceed_fallback, qf_fallback, dqf_fallback, dqfT_fallback, &op_fallback));
144     CeedCall(CeedOperatorGetFields(op, &num_input_fields, &input_fields, &num_output_fields, &output_fields));
145     for (CeedInt i = 0; i < num_input_fields; i++) {
146       const char         *field_name;
147       CeedVector          vec;
148       CeedElemRestriction rstr;
149       CeedBasis           basis;
150 
151       CeedCall(CeedOperatorFieldGetData(input_fields[i], &field_name, &rstr, &basis, &vec));
152       CeedCall(CeedOperatorSetField(op_fallback, field_name, rstr, basis, vec));
153       CeedCall(CeedVectorDestroy(&vec));
154       CeedCall(CeedElemRestrictionDestroy(&rstr));
155       CeedCall(CeedBasisDestroy(&basis));
156     }
157     for (CeedInt i = 0; i < num_output_fields; i++) {
158       const char         *field_name;
159       CeedVector          vec;
160       CeedElemRestriction rstr;
161       CeedBasis           basis;
162 
163       CeedCall(CeedOperatorFieldGetData(output_fields[i], &field_name, &rstr, &basis, &vec));
164       CeedCall(CeedOperatorSetField(op_fallback, field_name, rstr, basis, vec));
165       CeedCall(CeedVectorDestroy(&vec));
166       CeedCall(CeedElemRestrictionDestroy(&rstr));
167       CeedCall(CeedBasisDestroy(&basis));
168     }
169     {
170       CeedQFunctionAssemblyData data;
171 
172       CeedCall(CeedOperatorGetQFunctionAssemblyData(op, &data));
173       CeedCall(CeedQFunctionAssemblyDataReferenceCopy(data, &op_fallback->qf_assembled));
174     }
175     // Cleanup
176     CeedCall(CeedQFunctionDestroy(&qf_fallback));
177     CeedCall(CeedQFunctionDestroy(&dqf_fallback));
178     CeedCall(CeedQFunctionDestroy(&dqfT_fallback));
179   }
180   CeedCall(CeedOperatorSetName(op_fallback, op->name));
181   CeedCall(CeedOperatorCheckReady(op_fallback));
182   // Note: No ref-counting here so we don't get caught in a reference loop.
183   //       The op holds the only reference to op_fallback and is responsible for deleting itself and op_fallback.
184   op->op_fallback                 = op_fallback;
185   op_fallback->op_fallback_parent = op;
186   return CEED_ERROR_SUCCESS;
187 }
188 
189 /**
190   @brief Core logic for assembling operator diagonal or point block diagonal
191 
192   @param[in]  op             `CeedOperator` to assemble diagonal or point block diagonal
193   @param[in]  request        Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
194   @param[in]  is_point_block Boolean flag to assemble diagonal or point block diagonal
195   @param[out] assembled      `CeedVector` to store assembled diagonal
196 
197   @return An error code: 0 - success, otherwise - failure
198 
199   @ref Developer
200 **/
201 static inline int CeedSingleOperatorLinearAssembleAddDiagonal_Mesh(CeedOperator op, CeedRequest *request, const bool is_point_block,
202                                                                    CeedVector assembled) {
203   Ceed ceed;
204   bool is_composite;
205 
206   CeedCall(CeedOperatorGetCeed(op, &ceed));
207   CeedCall(CeedOperatorIsComposite(op, &is_composite));
208   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
209 
210   // Assemble QFunction
211   CeedInt             layout_qf[3];
212   const CeedScalar   *assembled_qf_array;
213   CeedVector          assembled_qf        = NULL;
214   CeedElemRestriction assembled_elem_rstr = NULL;
215 
216   CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled_qf, &assembled_elem_rstr, request));
217   CeedCall(CeedElemRestrictionGetELayout(assembled_elem_rstr, layout_qf));
218   CeedCall(CeedElemRestrictionDestroy(&assembled_elem_rstr));
219   CeedCall(CeedVectorGetArrayRead(assembled_qf, CEED_MEM_HOST, &assembled_qf_array));
220 
221   // Get assembly data
222   const CeedEvalMode     **eval_modes_in, **eval_modes_out;
223   CeedInt                  num_active_bases_in, *num_eval_modes_in, num_active_bases_out, *num_eval_modes_out;
224   CeedSize               **eval_mode_offsets_in, **eval_mode_offsets_out, num_output_components;
225   CeedBasis               *active_bases_in, *active_bases_out;
226   CeedElemRestriction     *active_elem_rstrs_in, *active_elem_rstrs_out;
227   CeedOperatorAssemblyData data;
228 
229   CeedCall(CeedOperatorGetOperatorAssemblyData(op, &data));
230   CeedCall(CeedOperatorAssemblyDataGetEvalModes(data, &num_active_bases_in, &num_eval_modes_in, &eval_modes_in, &eval_mode_offsets_in,
231                                                 &num_active_bases_out, &num_eval_modes_out, &eval_modes_out, &eval_mode_offsets_out,
232                                                 &num_output_components));
233   CeedCall(CeedOperatorAssemblyDataGetBases(data, NULL, &active_bases_in, NULL, NULL, &active_bases_out, NULL));
234   CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, NULL, &active_elem_rstrs_in, NULL, &active_elem_rstrs_out));
235 
236   // Loop over all active bases (find matching input/output pairs)
237   for (CeedInt b = 0; b < CeedIntMin(num_active_bases_in, num_active_bases_out); b++) {
238     CeedInt             b_in, b_out, num_elem, num_nodes, num_qpts, num_comp;
239     bool                has_eval_none = false;
240     CeedScalar         *elem_diag_array, *identity = NULL;
241     CeedVector          elem_diag;
242     CeedElemRestriction diag_elem_rstr;
243 
244     if (num_active_bases_in <= num_active_bases_out) {
245       b_in = b;
246       for (b_out = 0; b_out < num_active_bases_out; b_out++) {
247         if (active_bases_in[b_in] == active_bases_out[b_out]) {
248           break;
249         }
250       }
251       if (b_out == num_active_bases_out) {
252         continue;
253       }  // No matching output basis found
254     } else {
255       b_out = b;
256       for (b_in = 0; b_in < num_active_bases_in; b_in++) {
257         if (active_bases_in[b_in] == active_bases_out[b_out]) {
258           break;
259         }
260       }
261       if (b_in == num_active_bases_in) {
262         continue;
263       }  // No matching output basis found
264     }
265     CeedCheck(active_elem_rstrs_in[b_in] == active_elem_rstrs_out[b_out], ceed, CEED_ERROR_UNSUPPORTED,
266               "Cannot assemble operator diagonal with different input and output active element restrictions");
267 
268     // Assemble point block diagonal restriction, if needed
269     if (is_point_block) {
270       CeedCall(CeedOperatorCreateActivePointBlockRestriction(active_elem_rstrs_in[b_in], &diag_elem_rstr));
271     } else {
272       CeedCall(CeedElemRestrictionCreateUnsignedCopy(active_elem_rstrs_in[b_in], &diag_elem_rstr));
273     }
274 
275     // Create diagonal vector
276     CeedCall(CeedElemRestrictionCreateVector(diag_elem_rstr, NULL, &elem_diag));
277 
278     // Assemble element operator diagonals
279     CeedCall(CeedVectorSetValue(elem_diag, 0.0));
280     CeedCall(CeedVectorGetArray(elem_diag, CEED_MEM_HOST, &elem_diag_array));
281     CeedCall(CeedElemRestrictionGetNumElements(diag_elem_rstr, &num_elem));
282     CeedCall(CeedBasisGetNumNodes(active_bases_in[b_in], &num_nodes));
283     CeedCall(CeedBasisGetNumComponents(active_bases_in[b_in], &num_comp));
284     if (active_bases_in[b_in] == CEED_BASIS_NONE) num_qpts = num_nodes;
285     else CeedCall(CeedBasisGetNumQuadraturePoints(active_bases_in[b_in], &num_qpts));
286 
287     // Construct identity matrix for basis if required
288     for (CeedInt i = 0; i < num_eval_modes_in[b_in]; i++) {
289       has_eval_none = has_eval_none || (eval_modes_in[b_in][i] == CEED_EVAL_NONE);
290     }
291     for (CeedInt i = 0; i < num_eval_modes_out[b_out]; i++) {
292       has_eval_none = has_eval_none || (eval_modes_out[b_out][i] == CEED_EVAL_NONE);
293     }
294     if (has_eval_none) {
295       CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
296       for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) identity[i * num_nodes + i] = 1.0;
297     }
298 
299     // Compute the diagonal of B^T D B
300     // Each element
301     for (CeedSize e = 0; e < num_elem; e++) {
302       // Each basis eval mode pair
303       CeedInt      d_out              = 0, q_comp_out;
304       CeedEvalMode eval_mode_out_prev = CEED_EVAL_NONE;
305 
306       for (CeedInt e_out = 0; e_out < num_eval_modes_out[b_out]; e_out++) {
307         CeedInt           d_in              = 0, q_comp_in;
308         const CeedScalar *B_t               = NULL;
309         CeedEvalMode      eval_mode_in_prev = CEED_EVAL_NONE;
310 
311         CeedCall(CeedOperatorGetBasisPointer(active_bases_out[b_out], eval_modes_out[b_out][e_out], identity, &B_t));
312         CeedCall(CeedBasisGetNumQuadratureComponents(active_bases_out[b_out], eval_modes_out[b_out][e_out], &q_comp_out));
313         if (q_comp_out > 1) {
314           if (e_out == 0 || eval_modes_out[b_out][e_out] != eval_mode_out_prev) d_out = 0;
315           else B_t = &B_t[(++d_out) * num_qpts * num_nodes];
316         }
317         eval_mode_out_prev = eval_modes_out[b_out][e_out];
318 
319         for (CeedInt e_in = 0; e_in < num_eval_modes_in[b_in]; e_in++) {
320           const CeedScalar *B = NULL;
321 
322           CeedCall(CeedOperatorGetBasisPointer(active_bases_in[b_in], eval_modes_in[b_in][e_in], identity, &B));
323           CeedCall(CeedBasisGetNumQuadratureComponents(active_bases_in[b_in], eval_modes_in[b_in][e_in], &q_comp_in));
324           if (q_comp_in > 1) {
325             if (e_in == 0 || eval_modes_in[b_in][e_in] != eval_mode_in_prev) d_in = 0;
326             else B = &B[(++d_in) * num_qpts * num_nodes];
327           }
328           eval_mode_in_prev = eval_modes_in[b_in][e_in];
329 
330           // Each component
331           for (CeedInt c_out = 0; c_out < num_comp; c_out++) {
332             // Each qpt/node pair
333             for (CeedInt q = 0; q < num_qpts; q++) {
334               if (is_point_block) {
335                 // Point Block Diagonal
336                 for (CeedInt c_in = 0; c_in < num_comp; c_in++) {
337                   const CeedSize c_offset =
338                       (eval_mode_offsets_in[b_in][e_in] + c_in) * num_output_components + eval_mode_offsets_out[b_out][e_out] + c_out;
339                   const CeedScalar qf_value = assembled_qf_array[q * layout_qf[0] + c_offset * layout_qf[1] + e * layout_qf[2]];
340 
341                   for (CeedInt n = 0; n < num_nodes; n++) {
342                     elem_diag_array[((e * num_comp + c_out) * num_comp + c_in) * num_nodes + n] +=
343                         B_t[q * num_nodes + n] * qf_value * B[q * num_nodes + n];
344                   }
345                 }
346               } else {
347                 // Diagonal Only
348                 const CeedInt c_offset =
349                     (eval_mode_offsets_in[b_in][e_in] + c_out) * num_output_components + eval_mode_offsets_out[b_out][e_out] + c_out;
350                 const CeedScalar qf_value = assembled_qf_array[q * layout_qf[0] + c_offset * layout_qf[1] + e * layout_qf[2]];
351 
352                 for (CeedInt n = 0; n < num_nodes; n++) {
353                   elem_diag_array[(e * num_comp + c_out) * num_nodes + n] += B_t[q * num_nodes + n] * qf_value * B[q * num_nodes + n];
354                 }
355               }
356             }
357           }
358         }
359       }
360     }
361     CeedCall(CeedVectorRestoreArray(elem_diag, &elem_diag_array));
362 
363     // Assemble local operator diagonal
364     CeedCall(CeedElemRestrictionApply(diag_elem_rstr, CEED_TRANSPOSE, elem_diag, assembled, request));
365 
366     // Cleanup
367     CeedCall(CeedElemRestrictionDestroy(&diag_elem_rstr));
368     CeedCall(CeedVectorDestroy(&elem_diag));
369     CeedCall(CeedFree(&identity));
370   }
371   CeedCall(CeedVectorRestoreArrayRead(assembled_qf, &assembled_qf_array));
372   CeedCall(CeedVectorDestroy(&assembled_qf));
373   return CEED_ERROR_SUCCESS;
374 }
375 
376 /**
377   @brief Core logic for assembling operator diagonal or point block diagonal
378 
379   @param[in]  op             `CeedOperator` to assemble diagonal or point block diagonal
380   @param[in]  request        Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
381   @param[in]  is_point_block Boolean flag to assemble diagonal or point block diagonal
382   @param[out] assembled      `CeedVector` to store assembled diagonal
383 
384   @return An error code: 0 - success, otherwise - failure
385 
386   @ref Developer
387 **/
388 static inline int CeedSingleOperatorLinearAssembleAddDiagonal(CeedOperator op, CeedRequest *request, const bool is_point_block,
389                                                               CeedVector assembled) {
390   Ceed ceed;
391   bool is_at_points;
392 
393   CeedCall(CeedOperatorGetCeed(op, &ceed));
394   CeedCall(CeedOperatorIsAtPoints(op, &is_at_points));
395   CeedCheck(!is_at_points, ceed, CEED_ERROR_UNSUPPORTED, "AtPoints operator not supported");
396   CeedCall(CeedSingleOperatorLinearAssembleAddDiagonal_Mesh(op, request, is_point_block, assembled));
397   return CEED_ERROR_SUCCESS;
398 }
399 
400 /**
401   @brief Core logic for assembling composite operator diagonal
402 
403   @param[in]  op             `CeedOperator` to assemble point block diagonal
404   @param[in]  request        Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
405   @param[in]  is_point_block Boolean flag to assemble diagonal or point block diagonal
406   @param[out] assembled      `CeedVector` to store assembled diagonal
407 
408   @return An error code: 0 - success, otherwise - failure
409 
410   @ref Developer
411 **/
412 static inline int CeedCompositeOperatorLinearAssembleAddDiagonal(CeedOperator op, CeedRequest *request, const bool is_point_block,
413                                                                  CeedVector assembled) {
414   CeedInt       num_sub;
415   CeedOperator *suboperators;
416 
417   CeedCall(CeedCompositeOperatorGetNumSub(op, &num_sub));
418   CeedCall(CeedCompositeOperatorGetSubList(op, &suboperators));
419   for (CeedInt i = 0; i < num_sub; i++) {
420     if (is_point_block) {
421       CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(suboperators[i], assembled, request));
422     } else {
423       CeedCall(CeedOperatorLinearAssembleAddDiagonal(suboperators[i], assembled, request));
424     }
425   }
426   return CEED_ERROR_SUCCESS;
427 }
428 
429 /**
430   @brief Build nonzero pattern for non-composite CeedOperator`.
431 
432   Users should generally use @ref CeedOperatorLinearAssembleSymbolic().
433 
434   @param[in]  op     `CeedOperator` to assemble nonzero pattern
435   @param[in]  offset Offset for number of entries
436   @param[out] rows   Row number for each entry
437   @param[out] cols   Column number for each entry
438 
439   @return An error code: 0 - success, otherwise - failure
440 
441   @ref Developer
442 **/
443 static int CeedSingleOperatorAssembleSymbolic(CeedOperator op, CeedInt offset, CeedInt *rows, CeedInt *cols) {
444   Ceed                ceed;
445   bool                is_composite;
446   CeedSize            num_nodes_in, num_nodes_out, local_num_entries, count = 0;
447   CeedInt             num_elem_in, elem_size_in, num_comp_in, layout_er_in[3];
448   CeedInt             num_elem_out, elem_size_out, num_comp_out, layout_er_out[3];
449   CeedScalar         *array;
450   const CeedScalar   *elem_dof_a_in, *elem_dof_a_out;
451   CeedVector          index_vec_in, index_vec_out, elem_dof_in, elem_dof_out;
452   CeedElemRestriction elem_rstr_in, elem_rstr_out, index_elem_rstr_in, index_elem_rstr_out;
453 
454   CeedCall(CeedOperatorGetCeed(op, &ceed));
455   CeedCall(CeedOperatorIsComposite(op, &is_composite));
456   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
457 
458   CeedCall(CeedOperatorGetActiveVectorLengths(op, &num_nodes_in, &num_nodes_out));
459   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &elem_rstr_in, &elem_rstr_out));
460   CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_in, &num_elem_in));
461   CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_in, &elem_size_in));
462   CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_in, &num_comp_in));
463   CeedCall(CeedElemRestrictionGetELayout(elem_rstr_in, layout_er_in));
464 
465   // Determine elem_dof relation for input
466   CeedCall(CeedVectorCreate(ceed, num_nodes_in, &index_vec_in));
467   CeedCall(CeedVectorGetArrayWrite(index_vec_in, CEED_MEM_HOST, &array));
468   for (CeedSize i = 0; i < num_nodes_in; i++) array[i] = i;
469   CeedCall(CeedVectorRestoreArray(index_vec_in, &array));
470   CeedCall(CeedVectorCreate(ceed, num_elem_in * elem_size_in * num_comp_in, &elem_dof_in));
471   CeedCall(CeedVectorSetValue(elem_dof_in, 0.0));
472   CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr_in, &index_elem_rstr_in));
473   CeedCall(CeedElemRestrictionApply(index_elem_rstr_in, CEED_NOTRANSPOSE, index_vec_in, elem_dof_in, CEED_REQUEST_IMMEDIATE));
474   CeedCall(CeedVectorGetArrayRead(elem_dof_in, CEED_MEM_HOST, &elem_dof_a_in));
475   CeedCall(CeedVectorDestroy(&index_vec_in));
476   CeedCall(CeedElemRestrictionDestroy(&index_elem_rstr_in));
477 
478   if (elem_rstr_in != elem_rstr_out) {
479     CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_out, &num_elem_out));
480     CeedCheck(num_elem_in == num_elem_out, ceed, CEED_ERROR_UNSUPPORTED,
481               "Active input and output operator restrictions must have the same number of elements."
482               " Input has %" CeedInt_FMT " elements; output has %" CeedInt_FMT "elements.",
483               num_elem_in, num_elem_out);
484     CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_out, &elem_size_out));
485     CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_out, &num_comp_out));
486     CeedCall(CeedElemRestrictionGetELayout(elem_rstr_out, layout_er_out));
487 
488     // Determine elem_dof relation for output
489     CeedCall(CeedVectorCreate(ceed, num_nodes_out, &index_vec_out));
490     CeedCall(CeedVectorGetArrayWrite(index_vec_out, CEED_MEM_HOST, &array));
491     for (CeedSize i = 0; i < num_nodes_out; i++) array[i] = i;
492     CeedCall(CeedVectorRestoreArray(index_vec_out, &array));
493     CeedCall(CeedVectorCreate(ceed, num_elem_out * elem_size_out * num_comp_out, &elem_dof_out));
494     CeedCall(CeedVectorSetValue(elem_dof_out, 0.0));
495     CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr_out, &index_elem_rstr_out));
496     CeedCall(CeedElemRestrictionApply(index_elem_rstr_out, CEED_NOTRANSPOSE, index_vec_out, elem_dof_out, CEED_REQUEST_IMMEDIATE));
497     CeedCall(CeedVectorGetArrayRead(elem_dof_out, CEED_MEM_HOST, &elem_dof_a_out));
498     CeedCall(CeedVectorDestroy(&index_vec_out));
499     CeedCall(CeedElemRestrictionDestroy(&index_elem_rstr_out));
500   } else {
501     num_elem_out     = num_elem_in;
502     elem_size_out    = elem_size_in;
503     num_comp_out     = num_comp_in;
504     layout_er_out[0] = layout_er_in[0];
505     layout_er_out[1] = layout_er_in[1];
506     layout_er_out[2] = layout_er_in[2];
507     elem_dof_a_out   = elem_dof_a_in;
508   }
509   local_num_entries = (CeedSize)elem_size_out * num_comp_out * elem_size_in * num_comp_in * num_elem_in;
510 
511   // Determine i, j locations for element matrices
512   for (CeedInt e = 0; e < num_elem_in; e++) {
513     for (CeedInt comp_in = 0; comp_in < num_comp_in; comp_in++) {
514       for (CeedInt comp_out = 0; comp_out < num_comp_out; comp_out++) {
515         for (CeedInt i = 0; i < elem_size_out; i++) {
516           for (CeedInt j = 0; j < elem_size_in; j++) {
517             const CeedInt elem_dof_index_row = i * layout_er_out[0] + comp_out * layout_er_out[1] + e * layout_er_out[2];
518             const CeedInt elem_dof_index_col = j * layout_er_in[0] + comp_in * layout_er_in[1] + e * layout_er_in[2];
519             const CeedInt row                = elem_dof_a_out[elem_dof_index_row];
520             const CeedInt col                = elem_dof_a_in[elem_dof_index_col];
521 
522             rows[offset + count] = row;
523             cols[offset + count] = col;
524             count++;
525           }
526         }
527       }
528     }
529   }
530   CeedCheck(count == local_num_entries, ceed, CEED_ERROR_MAJOR, "Error computing assembled entries");
531   CeedCall(CeedVectorRestoreArrayRead(elem_dof_in, &elem_dof_a_in));
532   CeedCall(CeedVectorDestroy(&elem_dof_in));
533   if (elem_rstr_in != elem_rstr_out) {
534     CeedCall(CeedVectorRestoreArrayRead(elem_dof_out, &elem_dof_a_out));
535     CeedCall(CeedVectorDestroy(&elem_dof_out));
536   }
537   CeedCall(CeedElemRestrictionDestroy(&elem_rstr_in));
538   CeedCall(CeedElemRestrictionDestroy(&elem_rstr_out));
539   return CEED_ERROR_SUCCESS;
540 }
541 
542 /**
543   @brief Assemble nonzero entries for non-composite `CeedOperator`.
544 
545   Users should generally use @ref CeedOperatorLinearAssemble().
546 
547   @param[in]  op     `CeedOperator` to assemble
548   @param[in]  offset Offset for number of entries
549   @param[out] values Values to assemble into matrix
550 
551   @return An error code: 0 - success, otherwise - failure
552 
553   @ref Developer
554 **/
555 static int CeedSingleOperatorAssemble(CeedOperator op, CeedInt offset, CeedVector values) {
556   Ceed ceed;
557   bool is_composite;
558 
559   CeedCall(CeedOperatorGetCeed(op, &ceed));
560   CeedCall(CeedOperatorIsComposite(op, &is_composite));
561   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
562 
563   // Early exit for empty operator
564   {
565     CeedInt num_elem = 0;
566 
567     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
568     if (num_elem == 0) return CEED_ERROR_SUCCESS;
569   }
570 
571   if (op->LinearAssembleSingle) {
572     // Backend version
573     CeedCall(op->LinearAssembleSingle(op, offset, values));
574     return CEED_ERROR_SUCCESS;
575   } else {
576     // Operator fallback
577     CeedOperator op_fallback;
578 
579     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
580     if (op_fallback) {
581       CeedCall(CeedSingleOperatorAssemble(op_fallback, offset, values));
582       return CEED_ERROR_SUCCESS;
583     }
584   }
585 
586   // Assemble QFunction
587   CeedInt             layout_qf[3];
588   const CeedScalar   *assembled_qf_array;
589   CeedVector          assembled_qf        = NULL;
590   CeedElemRestriction assembled_elem_rstr = NULL;
591 
592   CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled_qf, &assembled_elem_rstr, CEED_REQUEST_IMMEDIATE));
593   CeedCall(CeedElemRestrictionGetELayout(assembled_elem_rstr, layout_qf));
594   CeedCall(CeedElemRestrictionDestroy(&assembled_elem_rstr));
595   CeedCall(CeedVectorGetArrayRead(assembled_qf, CEED_MEM_HOST, &assembled_qf_array));
596 
597   // Get assembly data
598   CeedInt                  num_elem_in, elem_size_in, num_comp_in, num_qpts_in;
599   CeedInt                  num_elem_out, elem_size_out, num_comp_out, num_qpts_out;
600   CeedSize                 local_num_entries, count = 0;
601   const CeedEvalMode     **eval_modes_in, **eval_modes_out;
602   CeedInt                  num_active_bases_in, *num_eval_modes_in, num_active_bases_out, *num_eval_modes_out;
603   CeedBasis               *active_bases_in, *active_bases_out, basis_in, basis_out;
604   const CeedScalar       **B_mats_in, **B_mats_out, *B_mat_in, *B_mat_out;
605   CeedElemRestriction      elem_rstr_in, elem_rstr_out;
606   CeedRestrictionType      elem_rstr_type_in, elem_rstr_type_out;
607   const bool              *elem_rstr_orients_in = NULL, *elem_rstr_orients_out = NULL;
608   const CeedInt8          *elem_rstr_curl_orients_in = NULL, *elem_rstr_curl_orients_out = NULL;
609   CeedOperatorAssemblyData data;
610 
611   CeedCall(CeedOperatorGetOperatorAssemblyData(op, &data));
612   CeedCall(CeedOperatorAssemblyDataGetEvalModes(data, &num_active_bases_in, &num_eval_modes_in, &eval_modes_in, NULL, &num_active_bases_out,
613                                                 &num_eval_modes_out, &eval_modes_out, NULL, NULL));
614 
615   CeedCheck(num_active_bases_in == 1 && num_active_bases_out == 1, ceed, CEED_ERROR_UNSUPPORTED,
616             "Cannot assemble operator with multiple active bases");
617   CeedCheck(num_eval_modes_in[0] > 0 && num_eval_modes_out[0] > 0, ceed, CEED_ERROR_UNSUPPORTED, "Cannot assemble operator without inputs/outputs");
618 
619   CeedCall(CeedOperatorAssemblyDataGetBases(data, NULL, &active_bases_in, &B_mats_in, NULL, &active_bases_out, &B_mats_out));
620   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &elem_rstr_in, &elem_rstr_out));
621   basis_in  = active_bases_in[0];
622   basis_out = active_bases_out[0];
623   B_mat_in  = B_mats_in[0];
624   B_mat_out = B_mats_out[0];
625 
626   CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_in, &num_elem_in));
627   CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_in, &elem_size_in));
628   CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_in, &num_comp_in));
629   if (basis_in == CEED_BASIS_NONE) num_qpts_in = elem_size_in;
630   else CeedCall(CeedBasisGetNumQuadraturePoints(basis_in, &num_qpts_in));
631 
632   CeedCall(CeedElemRestrictionGetType(elem_rstr_in, &elem_rstr_type_in));
633   if (elem_rstr_type_in == CEED_RESTRICTION_ORIENTED) {
634     CeedCall(CeedElemRestrictionGetOrientations(elem_rstr_in, CEED_MEM_HOST, &elem_rstr_orients_in));
635   } else if (elem_rstr_type_in == CEED_RESTRICTION_CURL_ORIENTED) {
636     CeedCall(CeedElemRestrictionGetCurlOrientations(elem_rstr_in, CEED_MEM_HOST, &elem_rstr_curl_orients_in));
637   }
638 
639   if (elem_rstr_in != elem_rstr_out) {
640     CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_out, &num_elem_out));
641     CeedCheck(num_elem_in == num_elem_out, ceed, CEED_ERROR_UNSUPPORTED,
642               "Active input and output operator restrictions must have the same number of elements."
643               " Input has %" CeedInt_FMT " elements; output has %" CeedInt_FMT "elements.",
644               num_elem_in, num_elem_out);
645     CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_out, &elem_size_out));
646     CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_out, &num_comp_out));
647     if (basis_out == CEED_BASIS_NONE) num_qpts_out = elem_size_out;
648     else CeedCall(CeedBasisGetNumQuadraturePoints(basis_out, &num_qpts_out));
649     CeedCheck(num_qpts_in == num_qpts_out, ceed, CEED_ERROR_UNSUPPORTED,
650               "Active input and output bases must have the same number of quadrature points."
651               " Input has %" CeedInt_FMT " points; output has %" CeedInt_FMT "points.",
652               num_qpts_in, num_qpts_out);
653 
654     CeedCall(CeedElemRestrictionGetType(elem_rstr_out, &elem_rstr_type_out));
655     if (elem_rstr_type_out == CEED_RESTRICTION_ORIENTED) {
656       CeedCall(CeedElemRestrictionGetOrientations(elem_rstr_out, CEED_MEM_HOST, &elem_rstr_orients_out));
657     } else if (elem_rstr_type_out == CEED_RESTRICTION_CURL_ORIENTED) {
658       CeedCall(CeedElemRestrictionGetCurlOrientations(elem_rstr_out, CEED_MEM_HOST, &elem_rstr_curl_orients_out));
659     }
660   } else {
661     num_elem_out  = num_elem_in;
662     elem_size_out = elem_size_in;
663     num_comp_out  = num_comp_in;
664     num_qpts_out  = num_qpts_in;
665 
666     elem_rstr_orients_out      = elem_rstr_orients_in;
667     elem_rstr_curl_orients_out = elem_rstr_curl_orients_in;
668   }
669   local_num_entries = (CeedSize)elem_size_out * num_comp_out * elem_size_in * num_comp_in * num_elem_in;
670 
671   // Loop over elements and put in data structure
672   // We store B_mat_in, B_mat_out, BTD, elem_mat in row-major order
673   CeedTensorContract contract;
674   CeedScalar        *vals, *BTD_mat = NULL, *elem_mat = NULL, *elem_mat_b = NULL;
675 
676   CeedCall(CeedBasisGetTensorContract(basis_in, &contract));
677   CeedCall(CeedCalloc(elem_size_out * num_qpts_in * num_eval_modes_in[0], &BTD_mat));
678   CeedCall(CeedCalloc(elem_size_out * elem_size_in, &elem_mat));
679   if (elem_rstr_curl_orients_in || elem_rstr_curl_orients_out) CeedCall(CeedCalloc(elem_size_out * elem_size_in, &elem_mat_b));
680 
681   CeedCall(CeedVectorGetArray(values, CEED_MEM_HOST, &vals));
682   for (CeedSize e = 0; e < num_elem_in; e++) {
683     for (CeedInt comp_in = 0; comp_in < num_comp_in; comp_in++) {
684       for (CeedInt comp_out = 0; comp_out < num_comp_out; comp_out++) {
685         // Compute B^T*D
686         for (CeedSize n = 0; n < elem_size_out; n++) {
687           for (CeedSize q = 0; q < num_qpts_in; q++) {
688             for (CeedInt e_in = 0; e_in < num_eval_modes_in[0]; e_in++) {
689               const CeedSize btd_index = n * (num_qpts_in * num_eval_modes_in[0]) + q * num_eval_modes_in[0] + e_in;
690               CeedScalar     sum       = 0.0;
691 
692               for (CeedInt e_out = 0; e_out < num_eval_modes_out[0]; e_out++) {
693                 const CeedSize b_out_index     = (q * num_eval_modes_out[0] + e_out) * elem_size_out + n;
694                 const CeedSize eval_mode_index = ((e_in * num_comp_in + comp_in) * num_eval_modes_out[0] + e_out) * num_comp_out + comp_out;
695                 const CeedSize qf_index        = q * layout_qf[0] + eval_mode_index * layout_qf[1] + e * layout_qf[2];
696 
697                 sum += B_mat_out[b_out_index] * assembled_qf_array[qf_index];
698               }
699               BTD_mat[btd_index] = sum;
700             }
701           }
702         }
703 
704         // Form element matrix itself (for each block component)
705         if (contract) {
706           CeedCall(CeedTensorContractApply(contract, 1, num_qpts_in * num_eval_modes_in[0], elem_size_in, elem_size_out, BTD_mat, CEED_NOTRANSPOSE,
707                                            false, B_mat_in, elem_mat));
708         } else {
709           CeedCall(CeedMatrixMatrixMultiply(ceed, BTD_mat, B_mat_in, elem_mat, elem_size_out, elem_size_in, num_qpts_in * num_eval_modes_in[0]));
710         }
711 
712         // Transform the element matrix if required
713         if (elem_rstr_orients_out) {
714           const bool *elem_orients = &elem_rstr_orients_out[e * elem_size_out];
715 
716           for (CeedInt i = 0; i < elem_size_out; i++) {
717             const double orient = elem_orients[i] ? -1.0 : 1.0;
718 
719             for (CeedInt j = 0; j < elem_size_in; j++) {
720               elem_mat[i * elem_size_in + j] *= orient;
721             }
722           }
723         } else if (elem_rstr_curl_orients_out) {
724           const CeedInt8 *elem_curl_orients = &elem_rstr_curl_orients_out[e * 3 * elem_size_out];
725 
726           // T^T*(B^T*D*B)
727           memcpy(elem_mat_b, elem_mat, elem_size_out * elem_size_in * sizeof(CeedScalar));
728           for (CeedInt i = 0; i < elem_size_out; i++) {
729             for (CeedInt j = 0; j < elem_size_in; j++) {
730               elem_mat[i * elem_size_in + j] = elem_mat_b[i * elem_size_in + j] * elem_curl_orients[3 * i + 1] +
731                                                (i > 0 ? elem_mat_b[(i - 1) * elem_size_in + j] * elem_curl_orients[3 * i - 1] : 0.0) +
732                                                (i < elem_size_out - 1 ? elem_mat_b[(i + 1) * elem_size_in + j] * elem_curl_orients[3 * i + 3] : 0.0);
733             }
734           }
735         }
736         if (elem_rstr_orients_in) {
737           const bool *elem_orients = &elem_rstr_orients_in[e * elem_size_in];
738 
739           for (CeedInt i = 0; i < elem_size_out; i++) {
740             for (CeedInt j = 0; j < elem_size_in; j++) {
741               elem_mat[i * elem_size_in + j] *= elem_orients[j] ? -1.0 : 1.0;
742             }
743           }
744         } else if (elem_rstr_curl_orients_in) {
745           const CeedInt8 *elem_curl_orients = &elem_rstr_curl_orients_in[e * 3 * elem_size_in];
746 
747           // (B^T*D*B)*T
748           memcpy(elem_mat_b, elem_mat, elem_size_out * elem_size_in * sizeof(CeedScalar));
749           for (CeedInt i = 0; i < elem_size_out; i++) {
750             for (CeedInt j = 0; j < elem_size_in; j++) {
751               elem_mat[i * elem_size_in + j] = elem_mat_b[i * elem_size_in + j] * elem_curl_orients[3 * j + 1] +
752                                                (j > 0 ? elem_mat_b[i * elem_size_in + j - 1] * elem_curl_orients[3 * j - 1] : 0.0) +
753                                                (j < elem_size_in - 1 ? elem_mat_b[i * elem_size_in + j + 1] * elem_curl_orients[3 * j + 3] : 0.0);
754             }
755           }
756         }
757 
758         // Put element matrix in coordinate data structure
759         for (CeedInt i = 0; i < elem_size_out; i++) {
760           for (CeedInt j = 0; j < elem_size_in; j++) {
761             vals[offset + count] = elem_mat[i * elem_size_in + j];
762             count++;
763           }
764         }
765       }
766     }
767   }
768   CeedCheck(count == local_num_entries, ceed, CEED_ERROR_MAJOR, "Error computing entries");
769   CeedCall(CeedVectorRestoreArray(values, &vals));
770 
771   // Cleanup
772   CeedCall(CeedFree(&BTD_mat));
773   CeedCall(CeedFree(&elem_mat));
774   CeedCall(CeedFree(&elem_mat_b));
775   if (elem_rstr_type_in == CEED_RESTRICTION_ORIENTED) {
776     CeedCall(CeedElemRestrictionRestoreOrientations(elem_rstr_in, &elem_rstr_orients_in));
777   } else if (elem_rstr_type_in == CEED_RESTRICTION_CURL_ORIENTED) {
778     CeedCall(CeedElemRestrictionRestoreCurlOrientations(elem_rstr_in, &elem_rstr_curl_orients_in));
779   }
780   if (elem_rstr_in != elem_rstr_out) {
781     if (elem_rstr_type_out == CEED_RESTRICTION_ORIENTED) {
782       CeedCall(CeedElemRestrictionRestoreOrientations(elem_rstr_out, &elem_rstr_orients_out));
783     } else if (elem_rstr_type_out == CEED_RESTRICTION_CURL_ORIENTED) {
784       CeedCall(CeedElemRestrictionRestoreCurlOrientations(elem_rstr_out, &elem_rstr_curl_orients_out));
785     }
786   }
787   CeedCall(CeedVectorRestoreArrayRead(assembled_qf, &assembled_qf_array));
788   CeedCall(CeedVectorDestroy(&assembled_qf));
789   CeedCall(CeedElemRestrictionDestroy(&elem_rstr_in));
790   CeedCall(CeedElemRestrictionDestroy(&elem_rstr_out));
791   return CEED_ERROR_SUCCESS;
792 }
793 
794 /**
795   @brief Count number of entries for assembled `CeedOperator`
796 
797   @param[in]  op          `CeedOperator` to assemble
798   @param[out] num_entries Number of entries in assembled representation
799 
800   @return An error code: 0 - success, otherwise - failure
801 
802   @ref Utility
803 **/
804 static int CeedSingleOperatorAssemblyCountEntries(CeedOperator op, CeedSize *num_entries) {
805   bool                is_composite;
806   CeedInt             num_elem_in, elem_size_in, num_comp_in, num_elem_out, elem_size_out, num_comp_out;
807   Ceed                ceed;
808   CeedElemRestriction rstr_in, rstr_out;
809 
810   CeedCall(CeedOperatorGetCeed(op, &ceed));
811   CeedCall(CeedOperatorIsComposite(op, &is_composite));
812   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
813 
814   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &rstr_in, &rstr_out));
815   CeedCall(CeedElemRestrictionGetNumElements(rstr_in, &num_elem_in));
816   CeedCall(CeedElemRestrictionGetElementSize(rstr_in, &elem_size_in));
817   CeedCall(CeedElemRestrictionGetNumComponents(rstr_in, &num_comp_in));
818   if (rstr_in != rstr_out) {
819     CeedCall(CeedElemRestrictionGetNumElements(rstr_out, &num_elem_out));
820     CeedCheck(num_elem_in == num_elem_out, ceed, CEED_ERROR_UNSUPPORTED,
821               "Active input and output operator restrictions must have the same number of elements."
822               " Input has %" CeedInt_FMT " elements; output has %" CeedInt_FMT "elements.",
823               num_elem_in, num_elem_out);
824     CeedCall(CeedElemRestrictionGetElementSize(rstr_out, &elem_size_out));
825     CeedCall(CeedElemRestrictionGetNumComponents(rstr_out, &num_comp_out));
826   } else {
827     num_elem_out  = num_elem_in;
828     elem_size_out = elem_size_in;
829     num_comp_out  = num_comp_in;
830   }
831   CeedCall(CeedElemRestrictionDestroy(&rstr_in));
832   CeedCall(CeedElemRestrictionDestroy(&rstr_out));
833   *num_entries = (CeedSize)elem_size_in * num_comp_in * elem_size_out * num_comp_out * num_elem_in;
834   return CEED_ERROR_SUCCESS;
835 }
836 
837 /**
838   @brief Common code for creating a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator`
839 
840   @param[in]  op_fine      Fine grid `CeedOperator`
841   @param[in]  p_mult_fine  L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
842   @param[in]  rstr_coarse  Coarse grid `CeedElemRestriction`
843   @param[in]  basis_coarse Coarse grid active vector `CeedBasis`
844   @param[in]  basis_c_to_f `CeedBasis` for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction operators
845   @param[out] op_coarse    Coarse grid `CeedOperator`
846   @param[out] op_prolong   Coarse to fine `CeedOperator`, or `NULL`
847   @param[out] op_restrict  Fine to coarse `CeedOperator`, or `NULL`
848 
849   @return An error code: 0 - success, otherwise - failure
850 
851   @ref Developer
852 **/
853 static int CeedSingleOperatorMultigridLevel(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
854                                             CeedBasis basis_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong, CeedOperator *op_restrict) {
855   bool                is_composite;
856   Ceed                ceed;
857   CeedInt             num_comp, num_input_fields, num_output_fields;
858   CeedVector          mult_vec         = NULL;
859   CeedElemRestriction rstr_p_mult_fine = NULL, rstr_fine = NULL;
860   CeedOperatorField  *input_fields, *output_fields;
861 
862   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
863 
864   // Check for composite operator
865   CeedCall(CeedOperatorIsComposite(op_fine, &is_composite));
866   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Automatic multigrid setup for composite operators not supported");
867 
868   // Coarse Grid
869   CeedCall(CeedOperatorCreate(ceed, op_fine->qf, op_fine->dqf, op_fine->dqfT, op_coarse));
870   CeedCall(CeedOperatorGetFields(op_fine, &num_input_fields, &input_fields, &num_output_fields, &output_fields));
871   // -- Clone input fields
872   for (CeedInt i = 0; i < num_input_fields; i++) {
873     const char         *field_name;
874     CeedVector          vec;
875     CeedElemRestriction rstr  = NULL;
876     CeedBasis           basis = NULL;
877 
878     CeedCall(CeedOperatorFieldGetName(input_fields[i], &field_name));
879     CeedCall(CeedOperatorFieldGetVector(input_fields[i], &vec));
880     if (vec == CEED_VECTOR_ACTIVE) {
881       CeedCall(CeedElemRestrictionReferenceCopy(rstr_coarse, &rstr));
882       CeedCall(CeedBasisReferenceCopy(basis_coarse, &basis));
883       if (!rstr_fine) CeedCall(CeedOperatorFieldGetElemRestriction(input_fields[i], &rstr_fine));
884     } else {
885       CeedCall(CeedOperatorFieldGetElemRestriction(input_fields[i], &rstr));
886       CeedCall(CeedOperatorFieldGetBasis(input_fields[i], &basis));
887     }
888     CeedCall(CeedOperatorSetField(*op_coarse, field_name, rstr, basis, vec));
889     CeedCall(CeedVectorDestroy(&vec));
890     CeedCall(CeedElemRestrictionDestroy(&rstr));
891     CeedCall(CeedBasisDestroy(&basis));
892   }
893   // -- Clone output fields
894   for (CeedInt i = 0; i < num_output_fields; i++) {
895     const char         *field_name;
896     CeedVector          vec;
897     CeedElemRestriction rstr  = NULL;
898     CeedBasis           basis = NULL;
899 
900     CeedCall(CeedOperatorFieldGetName(output_fields[i], &field_name));
901     CeedCall(CeedOperatorFieldGetVector(output_fields[i], &vec));
902     if (vec == CEED_VECTOR_ACTIVE) {
903       CeedCall(CeedElemRestrictionReferenceCopy(rstr_coarse, &rstr));
904       CeedCall(CeedBasisReferenceCopy(basis_coarse, &basis));
905       if (!rstr_fine) CeedCall(CeedOperatorFieldGetElemRestriction(output_fields[i], &rstr_fine));
906     } else {
907       CeedCall(CeedOperatorFieldGetElemRestriction(output_fields[i], &rstr));
908       CeedCall(CeedOperatorFieldGetBasis(output_fields[i], &basis));
909     }
910     CeedCall(CeedOperatorSetField(*op_coarse, field_name, rstr, basis, vec));
911     CeedCall(CeedVectorDestroy(&vec));
912     CeedCall(CeedElemRestrictionDestroy(&rstr));
913     CeedCall(CeedBasisDestroy(&basis));
914   }
915   // -- Clone QFunctionAssemblyData
916   {
917     CeedQFunctionAssemblyData fine_data;
918 
919     CeedCall(CeedOperatorGetQFunctionAssemblyData(op_fine, &fine_data));
920     CeedCall(CeedQFunctionAssemblyDataReferenceCopy(fine_data, &(*op_coarse)->qf_assembled));
921   }
922 
923   // Multiplicity vector
924   if (op_restrict || op_prolong) {
925     CeedVector          mult_e_vec;
926     CeedRestrictionType rstr_type;
927 
928     CeedCall(CeedElemRestrictionGetType(rstr_fine, &rstr_type));
929     CeedCheck(rstr_type != CEED_RESTRICTION_CURL_ORIENTED, ceed, CEED_ERROR_UNSUPPORTED,
930               "Element restrictions created with CeedElemRestrictionCreateCurlOriented are not supported");
931     CeedCheck(p_mult_fine, ceed, CEED_ERROR_INCOMPATIBLE, "Prolongation or restriction operator creation requires fine grid multiplicity vector");
932     CeedCall(CeedElemRestrictionCreateUnsignedCopy(rstr_fine, &rstr_p_mult_fine));
933     CeedCall(CeedElemRestrictionCreateVector(rstr_fine, &mult_vec, &mult_e_vec));
934     CeedCall(CeedVectorSetValue(mult_e_vec, 0.0));
935     CeedCall(CeedElemRestrictionApply(rstr_p_mult_fine, CEED_NOTRANSPOSE, p_mult_fine, mult_e_vec, CEED_REQUEST_IMMEDIATE));
936     CeedCall(CeedVectorSetValue(mult_vec, 0.0));
937     CeedCall(CeedElemRestrictionApply(rstr_p_mult_fine, CEED_TRANSPOSE, mult_e_vec, mult_vec, CEED_REQUEST_IMMEDIATE));
938     CeedCall(CeedVectorDestroy(&mult_e_vec));
939     CeedCall(CeedVectorReciprocal(mult_vec));
940   }
941 
942   // Clone name
943   bool   has_name = op_fine->name;
944   size_t name_len = op_fine->name ? strlen(op_fine->name) : 0;
945   CeedCall(CeedOperatorSetName(*op_coarse, op_fine->name));
946 
947   // Check that coarse to fine basis is provided if prolong/restrict operators are requested
948   CeedCheck(basis_c_to_f || (!op_restrict && !op_prolong), ceed, CEED_ERROR_INCOMPATIBLE,
949             "Prolongation or restriction operator creation requires coarse-to-fine basis");
950 
951   // Restriction/Prolongation Operators
952   CeedCall(CeedBasisGetNumComponents(basis_coarse, &num_comp));
953 
954   // Restriction
955   if (op_restrict) {
956     CeedInt             *num_comp_r_data;
957     CeedQFunctionContext ctx_r;
958     CeedQFunction        qf_restrict;
959 
960     CeedCall(CeedQFunctionCreateInteriorByName(ceed, "Scale", &qf_restrict));
961     CeedCall(CeedCalloc(1, &num_comp_r_data));
962     num_comp_r_data[0] = num_comp;
963     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_r));
964     CeedCall(CeedQFunctionContextSetData(ctx_r, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_r_data), num_comp_r_data));
965     CeedCall(CeedQFunctionSetContext(qf_restrict, ctx_r));
966     CeedCall(CeedQFunctionContextDestroy(&ctx_r));
967     CeedCall(CeedQFunctionAddInput(qf_restrict, "input", num_comp, CEED_EVAL_NONE));
968     CeedCall(CeedQFunctionAddInput(qf_restrict, "scale", num_comp, CEED_EVAL_NONE));
969     CeedCall(CeedQFunctionAddOutput(qf_restrict, "output", num_comp, CEED_EVAL_INTERP));
970     CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_restrict, num_comp));
971 
972     CeedCall(CeedOperatorCreate(ceed, qf_restrict, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, op_restrict));
973     CeedCall(CeedOperatorSetField(*op_restrict, "input", rstr_fine, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE));
974     CeedCall(CeedOperatorSetField(*op_restrict, "scale", rstr_p_mult_fine, CEED_BASIS_NONE, mult_vec));
975     CeedCall(CeedOperatorSetField(*op_restrict, "output", rstr_coarse, basis_c_to_f, CEED_VECTOR_ACTIVE));
976 
977     // Set name
978     char *restriction_name;
979 
980     CeedCall(CeedCalloc(17 + name_len, &restriction_name));
981     sprintf(restriction_name, "restriction%s%s", has_name ? " for " : "", has_name ? op_fine->name : "");
982     CeedCall(CeedOperatorSetName(*op_restrict, restriction_name));
983     CeedCall(CeedFree(&restriction_name));
984 
985     // Check
986     CeedCall(CeedOperatorCheckReady(*op_restrict));
987 
988     // Cleanup
989     CeedCall(CeedQFunctionDestroy(&qf_restrict));
990   }
991 
992   // Prolongation
993   if (op_prolong) {
994     CeedInt             *num_comp_p_data;
995     CeedQFunctionContext ctx_p;
996     CeedQFunction        qf_prolong;
997 
998     CeedCall(CeedQFunctionCreateInteriorByName(ceed, "Scale", &qf_prolong));
999     CeedCall(CeedCalloc(1, &num_comp_p_data));
1000     num_comp_p_data[0] = num_comp;
1001     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_p));
1002     CeedCall(CeedQFunctionContextSetData(ctx_p, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_p_data), num_comp_p_data));
1003     CeedCall(CeedQFunctionSetContext(qf_prolong, ctx_p));
1004     CeedCall(CeedQFunctionContextDestroy(&ctx_p));
1005     CeedCall(CeedQFunctionAddInput(qf_prolong, "input", num_comp, CEED_EVAL_INTERP));
1006     CeedCall(CeedQFunctionAddInput(qf_prolong, "scale", num_comp, CEED_EVAL_NONE));
1007     CeedCall(CeedQFunctionAddOutput(qf_prolong, "output", num_comp, CEED_EVAL_NONE));
1008     CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_prolong, num_comp));
1009 
1010     CeedCall(CeedOperatorCreate(ceed, qf_prolong, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, op_prolong));
1011     CeedCall(CeedOperatorSetField(*op_prolong, "input", rstr_coarse, basis_c_to_f, CEED_VECTOR_ACTIVE));
1012     CeedCall(CeedOperatorSetField(*op_prolong, "scale", rstr_p_mult_fine, CEED_BASIS_NONE, mult_vec));
1013     CeedCall(CeedOperatorSetField(*op_prolong, "output", rstr_fine, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE));
1014 
1015     // Set name
1016     char *prolongation_name;
1017 
1018     CeedCall(CeedCalloc(18 + name_len, &prolongation_name));
1019     sprintf(prolongation_name, "prolongation%s%s", has_name ? " for " : "", has_name ? op_fine->name : "");
1020     CeedCall(CeedOperatorSetName(*op_prolong, prolongation_name));
1021     CeedCall(CeedFree(&prolongation_name));
1022 
1023     // Check
1024     CeedCall(CeedOperatorCheckReady(*op_prolong));
1025 
1026     // Cleanup
1027     CeedCall(CeedQFunctionDestroy(&qf_prolong));
1028   }
1029 
1030   // Check
1031   CeedCall(CeedOperatorCheckReady(*op_coarse));
1032 
1033   // Cleanup
1034   CeedCall(CeedVectorDestroy(&mult_vec));
1035   CeedCall(CeedElemRestrictionDestroy(&rstr_fine));
1036   CeedCall(CeedElemRestrictionDestroy(&rstr_p_mult_fine));
1037   CeedCall(CeedBasisDestroy(&basis_c_to_f));
1038   return CEED_ERROR_SUCCESS;
1039 }
1040 
1041 /**
1042   @brief Build 1D mass matrix and Laplacian with perturbation
1043 
1044   @param[in]  interp_1d   Interpolation matrix in one dimension
1045   @param[in]  grad_1d     Gradient matrix in one dimension
1046   @param[in]  q_weight_1d Quadrature weights in one dimension
1047   @param[in]  P_1d        Number of basis nodes in one dimension
1048   @param[in]  Q_1d        Number of quadrature points in one dimension
1049   @param[in]  dim         Dimension of basis
1050   @param[out] mass        Assembled mass matrix in one dimension
1051   @param[out] laplace     Assembled perturbed Laplacian in one dimension
1052 
1053   @return An error code: 0 - success, otherwise - failure
1054 
1055   @ref Developer
1056 **/
1057 CeedPragmaOptimizeOff
1058 static int CeedBuildMassLaplace(const CeedScalar *interp_1d, const CeedScalar *grad_1d, const CeedScalar *q_weight_1d, CeedInt P_1d, CeedInt Q_1d,
1059                                 CeedInt dim, CeedScalar *mass, CeedScalar *laplace) {
1060   for (CeedInt i = 0; i < P_1d; i++) {
1061     for (CeedInt j = 0; j < P_1d; j++) {
1062       CeedScalar sum = 0.0;
1063       for (CeedInt k = 0; k < Q_1d; k++) sum += interp_1d[k * P_1d + i] * q_weight_1d[k] * interp_1d[k * P_1d + j];
1064       mass[i + j * P_1d] = sum;
1065     }
1066   }
1067   // -- Laplacian
1068   for (CeedInt i = 0; i < P_1d; i++) {
1069     for (CeedInt j = 0; j < P_1d; j++) {
1070       CeedScalar sum = 0.0;
1071 
1072       for (CeedInt k = 0; k < Q_1d; k++) sum += grad_1d[k * P_1d + i] * q_weight_1d[k] * grad_1d[k * P_1d + j];
1073       laplace[i + j * P_1d] = sum;
1074     }
1075   }
1076   CeedScalar perturbation = dim > 2 ? 1e-6 : 1e-4;
1077   for (CeedInt i = 0; i < P_1d; i++) laplace[i + P_1d * i] += perturbation;
1078   return CEED_ERROR_SUCCESS;
1079 }
1080 CeedPragmaOptimizeOn
1081 
1082 /// @}
1083 
1084 /// ----------------------------------------------------------------------------
1085 /// CeedOperator Backend API
1086 /// ----------------------------------------------------------------------------
1087 /// @addtogroup CeedOperatorBackend
1088 /// @{
1089 
1090 /**
1091   @brief Select correct basis matrix pointer based on @ref CeedEvalMode
1092 
1093   @param[in]  basis     `CeedBasis` from which to get the basis matrix
1094   @param[in]  eval_mode Current basis evaluation mode
1095   @param[in]  identity  Pointer to identity matrix
1096   @param[out] basis_ptr `CeedBasis` pointer to set
1097 
1098   @ref Backend
1099 **/
1100 int CeedOperatorGetBasisPointer(CeedBasis basis, CeedEvalMode eval_mode, const CeedScalar *identity, const CeedScalar **basis_ptr) {
1101   switch (eval_mode) {
1102     case CEED_EVAL_NONE:
1103       *basis_ptr = identity;
1104       break;
1105     case CEED_EVAL_INTERP:
1106       CeedCall(CeedBasisGetInterp(basis, basis_ptr));
1107       break;
1108     case CEED_EVAL_GRAD:
1109       CeedCall(CeedBasisGetGrad(basis, basis_ptr));
1110       break;
1111     case CEED_EVAL_DIV:
1112       CeedCall(CeedBasisGetDiv(basis, basis_ptr));
1113       break;
1114     case CEED_EVAL_CURL:
1115       CeedCall(CeedBasisGetCurl(basis, basis_ptr));
1116       break;
1117     case CEED_EVAL_WEIGHT:
1118       break;  // Caught by QF Assembly
1119   }
1120   assert(*basis_ptr != NULL);
1121   return CEED_ERROR_SUCCESS;
1122 }
1123 
1124 /**
1125   @brief Create point block restriction for active `CeedOperatorField`
1126 
1127   @param[in]  rstr             Original `CeedElemRestriction` for active field
1128   @param[out] point_block_rstr Address of the variable where the newly created `CeedElemRestriction` will be stored
1129 
1130   @return An error code: 0 - success, otherwise - failure
1131 
1132   @ref Backend
1133 **/
1134 int CeedOperatorCreateActivePointBlockRestriction(CeedElemRestriction rstr, CeedElemRestriction *point_block_rstr) {
1135   Ceed           ceed;
1136   CeedInt        num_elem, num_comp, shift, elem_size, comp_stride, *point_block_offsets;
1137   CeedSize       l_size;
1138   const CeedInt *offsets;
1139 
1140   CeedCall(CeedElemRestrictionGetCeed(rstr, &ceed));
1141   CeedCall(CeedElemRestrictionGetOffsets(rstr, CEED_MEM_HOST, &offsets));
1142 
1143   // Expand offsets
1144   CeedCall(CeedElemRestrictionGetNumElements(rstr, &num_elem));
1145   CeedCall(CeedElemRestrictionGetNumComponents(rstr, &num_comp));
1146   CeedCall(CeedElemRestrictionGetElementSize(rstr, &elem_size));
1147   CeedCall(CeedElemRestrictionGetCompStride(rstr, &comp_stride));
1148   CeedCall(CeedElemRestrictionGetLVectorSize(rstr, &l_size));
1149   shift = num_comp;
1150   if (comp_stride != 1) shift *= num_comp;
1151   CeedCall(CeedCalloc(num_elem * elem_size, &point_block_offsets));
1152   for (CeedInt i = 0; i < num_elem * elem_size; i++) {
1153     point_block_offsets[i] = offsets[i] * shift;
1154   }
1155 
1156   // Create new restriction
1157   CeedCall(CeedElemRestrictionCreate(ceed, num_elem, elem_size, num_comp * num_comp, 1, l_size * num_comp, CEED_MEM_HOST, CEED_OWN_POINTER,
1158                                      point_block_offsets, point_block_rstr));
1159 
1160   // Cleanup
1161   CeedCall(CeedElemRestrictionRestoreOffsets(rstr, &offsets));
1162   return CEED_ERROR_SUCCESS;
1163 }
1164 
1165 /**
1166   @brief Get `CeedQFunctionAssemblyData`
1167 
1168   @param[in]  op   `CeedOperator` to assemble
1169   @param[out] data `CeedQFunctionAssemblyData`
1170 
1171   @return An error code: 0 - success, otherwise - failure
1172 
1173   @ref Backend
1174 **/
1175 int CeedOperatorGetQFunctionAssemblyData(CeedOperator op, CeedQFunctionAssemblyData *data) {
1176   if (!op->qf_assembled) {
1177     CeedQFunctionAssemblyData data;
1178 
1179     CeedCall(CeedQFunctionAssemblyDataCreate(op->ceed, &data));
1180     op->qf_assembled = data;
1181   }
1182   *data = op->qf_assembled;
1183   return CEED_ERROR_SUCCESS;
1184 }
1185 
1186 /**
1187   @brief Create object holding `CeedQFunction` assembly data for `CeedOperator`
1188 
1189   @param[in]  ceed `Ceed` object used to create the `CeedQFunctionAssemblyData`
1190   @param[out] data Address of the variable where the newly created `CeedQFunctionAssemblyData` will be stored
1191 
1192   @return An error code: 0 - success, otherwise - failure
1193 
1194   @ref Backend
1195 **/
1196 int CeedQFunctionAssemblyDataCreate(Ceed ceed, CeedQFunctionAssemblyData *data) {
1197   CeedCall(CeedCalloc(1, data));
1198   (*data)->ref_count = 1;
1199   (*data)->ceed      = ceed;
1200   CeedCall(CeedReference(ceed));
1201   return CEED_ERROR_SUCCESS;
1202 }
1203 
1204 /**
1205   @brief Increment the reference counter for a `CeedQFunctionAssemblyData`
1206 
1207   @param[in,out] data `CeedQFunctionAssemblyData` to increment the reference counter
1208 
1209   @return An error code: 0 - success, otherwise - failure
1210 
1211   @ref Backend
1212 **/
1213 int CeedQFunctionAssemblyDataReference(CeedQFunctionAssemblyData data) {
1214   data->ref_count++;
1215   return CEED_ERROR_SUCCESS;
1216 }
1217 
1218 /**
1219   @brief Set re-use of `CeedQFunctionAssemblyData`
1220 
1221   @param[in,out] data       `CeedQFunctionAssemblyData` to mark for reuse
1222   @param[in]     reuse_data Boolean flag indicating data re-use
1223 
1224   @return An error code: 0 - success, otherwise - failure
1225 
1226   @ref Backend
1227 **/
1228 int CeedQFunctionAssemblyDataSetReuse(CeedQFunctionAssemblyData data, bool reuse_data) {
1229   data->reuse_data        = reuse_data;
1230   data->needs_data_update = true;
1231   return CEED_ERROR_SUCCESS;
1232 }
1233 
1234 /**
1235   @brief Mark `CeedQFunctionAssemblyData` as stale
1236 
1237   @param[in,out] data              `CeedQFunctionAssemblyData` to mark as stale
1238   @param[in]     needs_data_update Boolean flag indicating if update is needed or completed
1239 
1240   @return An error code: 0 - success, otherwise - failure
1241 
1242   @ref Backend
1243 **/
1244 int CeedQFunctionAssemblyDataSetUpdateNeeded(CeedQFunctionAssemblyData data, bool needs_data_update) {
1245   data->needs_data_update = needs_data_update;
1246   return CEED_ERROR_SUCCESS;
1247 }
1248 
1249 /**
1250   @brief Determine if `CeedQFunctionAssemblyData` needs update
1251 
1252   @param[in]  data             `CeedQFunctionAssemblyData` to mark as stale
1253   @param[out] is_update_needed Boolean flag indicating if re-assembly is required
1254 
1255   @return An error code: 0 - success, otherwise - failure
1256 
1257   @ref Backend
1258 **/
1259 int CeedQFunctionAssemblyDataIsUpdateNeeded(CeedQFunctionAssemblyData data, bool *is_update_needed) {
1260   *is_update_needed = !data->reuse_data || data->needs_data_update;
1261   return CEED_ERROR_SUCCESS;
1262 }
1263 
1264 /**
1265   @brief Copy the pointer to a `CeedQFunctionAssemblyData`.
1266 
1267   Both pointers should be destroyed with @ref CeedQFunctionAssemblyDataDestroy().
1268 
1269   Note: If the value of ` *data_copy` passed to this function is non-`NULL` , then it is assumed that ` *data_copy` is a pointer to a `CeedQFunctionAssemblyData`.
1270         This `CeedQFunctionAssemblyData` will be destroyed if ` *data_copy` is the only reference to this `CeedQFunctionAssemblyData`.
1271 
1272   @param[in]     data      `CeedQFunctionAssemblyData` to copy reference to
1273   @param[in,out] data_copy Variable to store copied reference
1274 
1275   @return An error code: 0 - success, otherwise - failure
1276 
1277   @ref Backend
1278 **/
1279 int CeedQFunctionAssemblyDataReferenceCopy(CeedQFunctionAssemblyData data, CeedQFunctionAssemblyData *data_copy) {
1280   CeedCall(CeedQFunctionAssemblyDataReference(data));
1281   CeedCall(CeedQFunctionAssemblyDataDestroy(data_copy));
1282   *data_copy = data;
1283   return CEED_ERROR_SUCCESS;
1284 }
1285 
1286 /**
1287   @brief Get setup status for internal objects for `CeedQFunctionAssemblyData`
1288 
1289   @param[in]  data     `CeedQFunctionAssemblyData` to retrieve status
1290   @param[out] is_setup Boolean flag for setup status
1291 
1292   @return An error code: 0 - success, otherwise - failure
1293 
1294   @ref Backend
1295 **/
1296 int CeedQFunctionAssemblyDataIsSetup(CeedQFunctionAssemblyData data, bool *is_setup) {
1297   *is_setup = data->is_setup;
1298   return CEED_ERROR_SUCCESS;
1299 }
1300 
1301 /**
1302   @brief Set internal objects for `CeedQFunctionAssemblyData`
1303 
1304   @param[in,out] data `CeedQFunctionAssemblyData` to set objects
1305   @param[in]     vec  `CeedVector` to store assembled `CeedQFunction` at quadrature points
1306   @param[in]     rstr `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1307 
1308   @return An error code: 0 - success, otherwise - failure
1309 
1310   @ref Backend
1311 **/
1312 int CeedQFunctionAssemblyDataSetObjects(CeedQFunctionAssemblyData data, CeedVector vec, CeedElemRestriction rstr) {
1313   CeedCall(CeedVectorReferenceCopy(vec, &data->vec));
1314   CeedCall(CeedElemRestrictionReferenceCopy(rstr, &data->rstr));
1315 
1316   data->is_setup = true;
1317   return CEED_ERROR_SUCCESS;
1318 }
1319 
1320 /**
1321   @brief Get internal objects for `CeedQFunctionAssemblyData`
1322 
1323   @param[in,out] data `CeedQFunctionAssemblyData` to set objects
1324   @param[out]    vec  `CeedVector` to store assembled `CeedQFunction` at quadrature points
1325   @param[out]    rstr `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1326 
1327   @return An error code: 0 - success, otherwise - failure
1328 
1329   @ref Backend
1330 **/
1331 int CeedQFunctionAssemblyDataGetObjects(CeedQFunctionAssemblyData data, CeedVector *vec, CeedElemRestriction *rstr) {
1332   CeedCheck(data->is_setup, data->ceed, CEED_ERROR_INCOMPLETE, "Internal objects not set; must call CeedQFunctionAssemblyDataSetObjects first.");
1333 
1334   CeedCall(CeedVectorReferenceCopy(data->vec, vec));
1335   CeedCall(CeedElemRestrictionReferenceCopy(data->rstr, rstr));
1336   return CEED_ERROR_SUCCESS;
1337 }
1338 
1339 /**
1340   @brief Destroy `CeedQFunctionAssemblyData`
1341 
1342   @param[in,out] data  `CeedQFunctionAssemblyData` to destroy
1343 
1344   @return An error code: 0 - success, otherwise - failure
1345 
1346   @ref Backend
1347 **/
1348 int CeedQFunctionAssemblyDataDestroy(CeedQFunctionAssemblyData *data) {
1349   if (!*data || --(*data)->ref_count > 0) {
1350     *data = NULL;
1351     return CEED_ERROR_SUCCESS;
1352   }
1353   CeedCall(CeedDestroy(&(*data)->ceed));
1354   CeedCall(CeedVectorDestroy(&(*data)->vec));
1355   CeedCall(CeedElemRestrictionDestroy(&(*data)->rstr));
1356 
1357   CeedCall(CeedFree(data));
1358   return CEED_ERROR_SUCCESS;
1359 }
1360 
1361 /**
1362   @brief Get `CeedOperatorAssemblyData`
1363 
1364   @param[in]  op   `CeedOperator` to assemble
1365   @param[out] data `CeedOperatorAssemblyData`
1366 
1367   @return An error code: 0 - success, otherwise - failure
1368 
1369   @ref Backend
1370 **/
1371 int CeedOperatorGetOperatorAssemblyData(CeedOperator op, CeedOperatorAssemblyData *data) {
1372   if (!op->op_assembled) {
1373     CeedOperatorAssemblyData data;
1374 
1375     CeedCall(CeedOperatorAssemblyDataCreate(op->ceed, op, &data));
1376     op->op_assembled = data;
1377   }
1378   *data = op->op_assembled;
1379   return CEED_ERROR_SUCCESS;
1380 }
1381 
1382 /**
1383   @brief Create object holding `CeedOperator` assembly data.
1384 
1385   The `CeedOperatorAssemblyData` holds an array with references to every active `CeedBasis` used in the `CeedOperator`.
1386   An array with references to the corresponding active `CeedElemRestriction` is also stored.
1387   For each active `CeedBasis, the `CeedOperatorAssemblyData` holds an array of all input and output @ref CeedEvalMode for this `CeedBasis`.
1388   The `CeedOperatorAssemblyData` holds an array of offsets for indexing into the assembled `CeedQFunction` arrays to the row representing each @ref CeedEvalMode.
1389   The number of input columns across all active bases for the assembled `CeedQFunction` is also stored.
1390   Lastly, the `CeedOperatorAssembly` data holds assembled matrices representing the full action of the `CeedBasis` for all @ref CeedEvalMode.
1391 
1392   @param[in]  ceed `Ceed` object used to create the `CeedOperatorAssemblyData`
1393   @param[in]  op   `CeedOperator` to be assembled
1394   @param[out] data Address of the variable where the newly created `CeedOperatorAssemblyData` will be stored
1395 
1396   @return An error code: 0 - success, otherwise - failure
1397 
1398   @ref Backend
1399 **/
1400 int CeedOperatorAssemblyDataCreate(Ceed ceed, CeedOperator op, CeedOperatorAssemblyData *data) {
1401   CeedInt             num_active_bases_in = 0, num_active_bases_out = 0, offset = 0;
1402   CeedInt             num_input_fields, *num_eval_modes_in = NULL, num_output_fields, *num_eval_modes_out = NULL;
1403   CeedSize          **eval_mode_offsets_in = NULL, **eval_mode_offsets_out = NULL;
1404   CeedEvalMode      **eval_modes_in = NULL, **eval_modes_out = NULL;
1405   CeedQFunctionField *qf_fields;
1406   CeedQFunction       qf;
1407   CeedOperatorField  *op_fields;
1408   bool                is_composite;
1409 
1410   CeedCall(CeedOperatorIsComposite(op, &is_composite));
1411   CeedCheck(!is_composite, ceed, CEED_ERROR_INCOMPATIBLE, "Can only create CeedOperator assembly data for non-composite operators.");
1412 
1413   // Allocate
1414   CeedCall(CeedCalloc(1, data));
1415   (*data)->ceed = ceed;
1416   CeedCall(CeedReference(ceed));
1417 
1418   // Build OperatorAssembly data
1419   CeedCall(CeedOperatorGetQFunction(op, &qf));
1420 
1421   // Determine active input basis
1422   CeedCall(CeedQFunctionGetFields(qf, &num_input_fields, &qf_fields, NULL, NULL));
1423   CeedCall(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
1424   for (CeedInt i = 0; i < num_input_fields; i++) {
1425     CeedVector vec;
1426 
1427     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
1428     if (vec == CEED_VECTOR_ACTIVE) {
1429       CeedInt      index = -1, num_comp, q_comp;
1430       CeedEvalMode eval_mode;
1431       CeedBasis    basis_in = NULL;
1432 
1433       CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis_in));
1434       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
1435       CeedCall(CeedBasisGetNumComponents(basis_in, &num_comp));
1436       CeedCall(CeedBasisGetNumQuadratureComponents(basis_in, eval_mode, &q_comp));
1437       for (CeedInt i = 0; i < num_active_bases_in; i++) {
1438         if ((*data)->active_bases_in[i] == basis_in) index = i;
1439       }
1440       if (index == -1) {
1441         CeedElemRestriction elem_rstr_in;
1442 
1443         index = num_active_bases_in;
1444         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->active_bases_in));
1445         (*data)->active_bases_in[num_active_bases_in] = NULL;
1446         CeedCall(CeedBasisReferenceCopy(basis_in, &(*data)->active_bases_in[num_active_bases_in]));
1447         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->active_elem_rstrs_in));
1448         (*data)->active_elem_rstrs_in[num_active_bases_in] = NULL;
1449         CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr_in));
1450         CeedCall(CeedElemRestrictionReferenceCopy(elem_rstr_in, &(*data)->active_elem_rstrs_in[num_active_bases_in]));
1451         CeedCall(CeedElemRestrictionDestroy(&elem_rstr_in));
1452         CeedCall(CeedRealloc(num_active_bases_in + 1, &num_eval_modes_in));
1453         num_eval_modes_in[index] = 0;
1454         CeedCall(CeedRealloc(num_active_bases_in + 1, &eval_modes_in));
1455         eval_modes_in[index] = NULL;
1456         CeedCall(CeedRealloc(num_active_bases_in + 1, &eval_mode_offsets_in));
1457         eval_mode_offsets_in[index] = NULL;
1458         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->assembled_bases_in));
1459         (*data)->assembled_bases_in[index] = NULL;
1460         num_active_bases_in++;
1461       }
1462       if (eval_mode != CEED_EVAL_WEIGHT) {
1463         // q_comp = 1 if CEED_EVAL_NONE, CEED_EVAL_WEIGHT caught by QF Assembly
1464         CeedCall(CeedRealloc(num_eval_modes_in[index] + q_comp, &eval_modes_in[index]));
1465         CeedCall(CeedRealloc(num_eval_modes_in[index] + q_comp, &eval_mode_offsets_in[index]));
1466         for (CeedInt d = 0; d < q_comp; d++) {
1467           eval_modes_in[index][num_eval_modes_in[index] + d]        = eval_mode;
1468           eval_mode_offsets_in[index][num_eval_modes_in[index] + d] = offset;
1469           offset += num_comp;
1470         }
1471         num_eval_modes_in[index] += q_comp;
1472       }
1473       CeedCall(CeedBasisDestroy(&basis_in));
1474     }
1475     CeedCall(CeedVectorDestroy(&vec));
1476   }
1477 
1478   // Determine active output basis
1479   CeedCall(CeedQFunctionGetFields(qf, NULL, NULL, &num_output_fields, &qf_fields));
1480   CeedCall(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
1481   offset = 0;
1482   for (CeedInt i = 0; i < num_output_fields; i++) {
1483     CeedVector vec;
1484 
1485     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
1486     if (vec == CEED_VECTOR_ACTIVE) {
1487       CeedInt      index = -1, num_comp, q_comp;
1488       CeedEvalMode eval_mode;
1489       CeedBasis    basis_out = NULL;
1490 
1491       CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis_out));
1492       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
1493       CeedCall(CeedBasisGetNumComponents(basis_out, &num_comp));
1494       CeedCall(CeedBasisGetNumQuadratureComponents(basis_out, eval_mode, &q_comp));
1495       for (CeedInt i = 0; i < num_active_bases_out; i++) {
1496         if ((*data)->active_bases_out[i] == basis_out) index = i;
1497       }
1498       if (index == -1) {
1499         CeedElemRestriction elem_rstr_out;
1500 
1501         index = num_active_bases_out;
1502         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->active_bases_out));
1503         (*data)->active_bases_out[num_active_bases_out] = NULL;
1504         CeedCall(CeedBasisReferenceCopy(basis_out, &(*data)->active_bases_out[num_active_bases_out]));
1505         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->active_elem_rstrs_out));
1506         (*data)->active_elem_rstrs_out[num_active_bases_out] = NULL;
1507         CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr_out));
1508         CeedCall(CeedElemRestrictionReferenceCopy(elem_rstr_out, &(*data)->active_elem_rstrs_out[num_active_bases_out]));
1509         CeedCall(CeedElemRestrictionDestroy(&elem_rstr_out));
1510         CeedCall(CeedRealloc(num_active_bases_out + 1, &num_eval_modes_out));
1511         num_eval_modes_out[index] = 0;
1512         CeedCall(CeedRealloc(num_active_bases_out + 1, &eval_modes_out));
1513         eval_modes_out[index] = NULL;
1514         CeedCall(CeedRealloc(num_active_bases_out + 1, &eval_mode_offsets_out));
1515         eval_mode_offsets_out[index] = NULL;
1516         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->assembled_bases_out));
1517         (*data)->assembled_bases_out[index] = NULL;
1518         num_active_bases_out++;
1519       }
1520       if (eval_mode != CEED_EVAL_WEIGHT) {
1521         // q_comp = 1 if CEED_EVAL_NONE, CEED_EVAL_WEIGHT caught by QF Assembly
1522         CeedCall(CeedRealloc(num_eval_modes_out[index] + q_comp, &eval_modes_out[index]));
1523         CeedCall(CeedRealloc(num_eval_modes_out[index] + q_comp, &eval_mode_offsets_out[index]));
1524         for (CeedInt d = 0; d < q_comp; d++) {
1525           eval_modes_out[index][num_eval_modes_out[index] + d]        = eval_mode;
1526           eval_mode_offsets_out[index][num_eval_modes_out[index] + d] = offset;
1527           offset += num_comp;
1528         }
1529         num_eval_modes_out[index] += q_comp;
1530       }
1531       CeedCall(CeedBasisDestroy(&basis_out));
1532     }
1533     CeedCall(CeedVectorDestroy(&vec));
1534   }
1535   (*data)->num_active_bases_in   = num_active_bases_in;
1536   (*data)->num_eval_modes_in     = num_eval_modes_in;
1537   (*data)->eval_modes_in         = eval_modes_in;
1538   (*data)->eval_mode_offsets_in  = eval_mode_offsets_in;
1539   (*data)->num_active_bases_out  = num_active_bases_out;
1540   (*data)->num_eval_modes_out    = num_eval_modes_out;
1541   (*data)->eval_modes_out        = eval_modes_out;
1542   (*data)->eval_mode_offsets_out = eval_mode_offsets_out;
1543   (*data)->num_output_components = offset;
1544   return CEED_ERROR_SUCCESS;
1545 }
1546 
1547 /**
1548   @brief Get `CeedOperator` @ref CeedEvalMode for assembly.
1549 
1550   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1551 
1552   @param[in]  data                  `CeedOperatorAssemblyData`
1553   @param[out] num_active_bases_in   Total number of active bases for input
1554   @param[out] num_eval_modes_in     Pointer to hold array of numbers of input @ref CeedEvalMode, or `NULL`.
1555                                       `eval_modes_in[0]` holds an array of eval modes for the first active `CeedBasis`.
1556   @param[out] eval_modes_in         Pointer to hold arrays of input @ref CeedEvalMode, or `NULL`
1557   @param[out] eval_mode_offsets_in  Pointer to hold arrays of input offsets at each quadrature point
1558   @param[out] num_active_bases_out  Total number of active bases for output
1559   @param[out] num_eval_modes_out    Pointer to hold array of numbers of output @ref CeedEvalMode, or `NULL`
1560   @param[out] eval_modes_out        Pointer to hold arrays of output @ref CeedEvalMode, or `NULL`
1561   @param[out] eval_mode_offsets_out Pointer to hold arrays of output offsets at each quadrature point
1562   @param[out] num_output_components The number of columns in the assembled `CeedQFunction` matrix for each quadrature point, including contributions of all active bases
1563 
1564   @return An error code: 0 - success, otherwise - failure
1565 
1566   @ref Backend
1567 **/
1568 int CeedOperatorAssemblyDataGetEvalModes(CeedOperatorAssemblyData data, CeedInt *num_active_bases_in, CeedInt **num_eval_modes_in,
1569                                          const CeedEvalMode ***eval_modes_in, CeedSize ***eval_mode_offsets_in, CeedInt *num_active_bases_out,
1570                                          CeedInt **num_eval_modes_out, const CeedEvalMode ***eval_modes_out, CeedSize ***eval_mode_offsets_out,
1571                                          CeedSize *num_output_components) {
1572   if (num_active_bases_in) *num_active_bases_in = data->num_active_bases_in;
1573   if (num_eval_modes_in) *num_eval_modes_in = data->num_eval_modes_in;
1574   if (eval_modes_in) *eval_modes_in = (const CeedEvalMode **)data->eval_modes_in;
1575   if (eval_mode_offsets_in) *eval_mode_offsets_in = data->eval_mode_offsets_in;
1576   if (num_active_bases_out) *num_active_bases_out = data->num_active_bases_out;
1577   if (num_eval_modes_out) *num_eval_modes_out = data->num_eval_modes_out;
1578   if (eval_modes_out) *eval_modes_out = (const CeedEvalMode **)data->eval_modes_out;
1579   if (eval_mode_offsets_out) *eval_mode_offsets_out = data->eval_mode_offsets_out;
1580   if (num_output_components) *num_output_components = data->num_output_components;
1581   return CEED_ERROR_SUCCESS;
1582 }
1583 
1584 /**
1585   @brief Get `CeedOperator` `CeedBasis` data for assembly.
1586 
1587   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1588 
1589   @param[in]  data                 `CeedOperatorAssemblyData`
1590   @param[out] num_active_bases_in  Number of active input bases, or `NULL`
1591   @param[out] active_bases_in      Pointer to hold active input `CeedBasis`, or `NULL`
1592   @param[out] assembled_bases_in   Pointer to hold assembled active input `B` , or `NULL`
1593   @param[out] num_active_bases_out Number of active output bases, or `NULL`
1594   @param[out] active_bases_out     Pointer to hold active output `CeedBasis`, or `NULL`
1595   @param[out] assembled_bases_out  Pointer to hold assembled active output `B` , or `NULL`
1596 
1597   @return An error code: 0 - success, otherwise - failure
1598 
1599   @ref Backend
1600 **/
1601 int CeedOperatorAssemblyDataGetBases(CeedOperatorAssemblyData data, CeedInt *num_active_bases_in, CeedBasis **active_bases_in,
1602                                      const CeedScalar ***assembled_bases_in, CeedInt *num_active_bases_out, CeedBasis **active_bases_out,
1603                                      const CeedScalar ***assembled_bases_out) {
1604   // Assemble B_in, B_out if needed
1605   if (assembled_bases_in && !data->assembled_bases_in[0]) {
1606     CeedInt num_qpts;
1607 
1608     if (data->active_bases_in[0] == CEED_BASIS_NONE) CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_in[0], &num_qpts));
1609     else CeedCall(CeedBasisGetNumQuadraturePoints(data->active_bases_in[0], &num_qpts));
1610     for (CeedInt b = 0; b < data->num_active_bases_in; b++) {
1611       bool        has_eval_none = false;
1612       CeedInt     num_nodes;
1613       CeedScalar *B_in = NULL, *identity = NULL;
1614 
1615       CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_in[b], &num_nodes));
1616       CeedCall(CeedCalloc(num_qpts * num_nodes * data->num_eval_modes_in[b], &B_in));
1617 
1618       for (CeedInt i = 0; i < data->num_eval_modes_in[b]; i++) {
1619         has_eval_none = has_eval_none || (data->eval_modes_in[b][i] == CEED_EVAL_NONE);
1620       }
1621       if (has_eval_none) {
1622         CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
1623         for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) {
1624           identity[i * num_nodes + i] = 1.0;
1625         }
1626       }
1627 
1628       for (CeedInt q = 0; q < num_qpts; q++) {
1629         for (CeedInt n = 0; n < num_nodes; n++) {
1630           CeedInt      d_in              = 0, q_comp_in;
1631           CeedEvalMode eval_mode_in_prev = CEED_EVAL_NONE;
1632 
1633           for (CeedInt e_in = 0; e_in < data->num_eval_modes_in[b]; e_in++) {
1634             const CeedInt     qq = data->num_eval_modes_in[b] * q;
1635             const CeedScalar *B  = NULL;
1636 
1637             CeedCall(CeedOperatorGetBasisPointer(data->active_bases_in[b], data->eval_modes_in[b][e_in], identity, &B));
1638             CeedCall(CeedBasisGetNumQuadratureComponents(data->active_bases_in[b], data->eval_modes_in[b][e_in], &q_comp_in));
1639             if (q_comp_in > 1) {
1640               if (e_in == 0 || data->eval_modes_in[b][e_in] != eval_mode_in_prev) d_in = 0;
1641               else B = &B[(++d_in) * num_qpts * num_nodes];
1642             }
1643             eval_mode_in_prev                 = data->eval_modes_in[b][e_in];
1644             B_in[(qq + e_in) * num_nodes + n] = B[q * num_nodes + n];
1645           }
1646         }
1647       }
1648       if (identity) CeedCall(CeedFree(&identity));
1649       data->assembled_bases_in[b] = B_in;
1650     }
1651   }
1652 
1653   if (assembled_bases_out && !data->assembled_bases_out[0]) {
1654     CeedInt num_qpts;
1655 
1656     if (data->active_bases_out[0] == CEED_BASIS_NONE) CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_out[0], &num_qpts));
1657     else CeedCall(CeedBasisGetNumQuadraturePoints(data->active_bases_out[0], &num_qpts));
1658     for (CeedInt b = 0; b < data->num_active_bases_out; b++) {
1659       bool        has_eval_none = false;
1660       CeedInt     num_nodes;
1661       CeedScalar *B_out = NULL, *identity = NULL;
1662 
1663       CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_out[b], &num_nodes));
1664       CeedCall(CeedCalloc(num_qpts * num_nodes * data->num_eval_modes_out[b], &B_out));
1665 
1666       for (CeedInt i = 0; i < data->num_eval_modes_out[b]; i++) {
1667         has_eval_none = has_eval_none || (data->eval_modes_out[b][i] == CEED_EVAL_NONE);
1668       }
1669       if (has_eval_none) {
1670         CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
1671         for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) {
1672           identity[i * num_nodes + i] = 1.0;
1673         }
1674       }
1675 
1676       for (CeedInt q = 0; q < num_qpts; q++) {
1677         for (CeedInt n = 0; n < num_nodes; n++) {
1678           CeedInt      d_out              = 0, q_comp_out;
1679           CeedEvalMode eval_mode_out_prev = CEED_EVAL_NONE;
1680 
1681           for (CeedInt e_out = 0; e_out < data->num_eval_modes_out[b]; e_out++) {
1682             const CeedInt     qq = data->num_eval_modes_out[b] * q;
1683             const CeedScalar *B  = NULL;
1684 
1685             CeedCall(CeedOperatorGetBasisPointer(data->active_bases_out[b], data->eval_modes_out[b][e_out], identity, &B));
1686             CeedCall(CeedBasisGetNumQuadratureComponents(data->active_bases_out[b], data->eval_modes_out[b][e_out], &q_comp_out));
1687             if (q_comp_out > 1) {
1688               if (e_out == 0 || data->eval_modes_out[b][e_out] != eval_mode_out_prev) d_out = 0;
1689               else B = &B[(++d_out) * num_qpts * num_nodes];
1690             }
1691             eval_mode_out_prev                  = data->eval_modes_out[b][e_out];
1692             B_out[(qq + e_out) * num_nodes + n] = B[q * num_nodes + n];
1693           }
1694         }
1695       }
1696       if (identity) CeedCall(CeedFree(&identity));
1697       data->assembled_bases_out[b] = B_out;
1698     }
1699   }
1700 
1701   // Pass out assembled data
1702   if (num_active_bases_in) *num_active_bases_in = data->num_active_bases_in;
1703   if (active_bases_in) *active_bases_in = data->active_bases_in;
1704   if (assembled_bases_in) *assembled_bases_in = (const CeedScalar **)data->assembled_bases_in;
1705   if (num_active_bases_out) *num_active_bases_out = data->num_active_bases_out;
1706   if (active_bases_out) *active_bases_out = data->active_bases_out;
1707   if (assembled_bases_out) *assembled_bases_out = (const CeedScalar **)data->assembled_bases_out;
1708   return CEED_ERROR_SUCCESS;
1709 }
1710 
1711 /**
1712   @brief Get `CeedOperator` `CeedBasis` data for assembly.
1713 
1714   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1715 
1716   @param[in]  data                      `CeedOperatorAssemblyData`
1717   @param[out] num_active_elem_rstrs_in  Number of active input element restrictions, or `NULL`
1718   @param[out] active_elem_rstrs_in      Pointer to hold active input `CeedElemRestriction`, or `NULL`
1719   @param[out] num_active_elem_rstrs_out Number of active output element restrictions, or `NULL`
1720   @param[out] active_elem_rstrs_out     Pointer to hold active output `CeedElemRestriction`, or `NULL`
1721 
1722   @return An error code: 0 - success, otherwise - failure
1723 
1724   @ref Backend
1725 **/
1726 int CeedOperatorAssemblyDataGetElemRestrictions(CeedOperatorAssemblyData data, CeedInt *num_active_elem_rstrs_in,
1727                                                 CeedElemRestriction **active_elem_rstrs_in, CeedInt *num_active_elem_rstrs_out,
1728                                                 CeedElemRestriction **active_elem_rstrs_out) {
1729   if (num_active_elem_rstrs_in) *num_active_elem_rstrs_in = data->num_active_bases_in;
1730   if (active_elem_rstrs_in) *active_elem_rstrs_in = data->active_elem_rstrs_in;
1731   if (num_active_elem_rstrs_out) *num_active_elem_rstrs_out = data->num_active_bases_out;
1732   if (active_elem_rstrs_out) *active_elem_rstrs_out = data->active_elem_rstrs_out;
1733   return CEED_ERROR_SUCCESS;
1734 }
1735 
1736 /**
1737   @brief Destroy `CeedOperatorAssemblyData`
1738 
1739   @param[in,out] data `CeedOperatorAssemblyData` to destroy
1740 
1741   @return An error code: 0 - success, otherwise - failure
1742 
1743   @ref Backend
1744 **/
1745 int CeedOperatorAssemblyDataDestroy(CeedOperatorAssemblyData *data) {
1746   if (!*data) {
1747     *data = NULL;
1748     return CEED_ERROR_SUCCESS;
1749   }
1750   CeedCall(CeedDestroy(&(*data)->ceed));
1751   for (CeedInt b = 0; b < (*data)->num_active_bases_in; b++) {
1752     CeedCall(CeedBasisDestroy(&(*data)->active_bases_in[b]));
1753     CeedCall(CeedElemRestrictionDestroy(&(*data)->active_elem_rstrs_in[b]));
1754     CeedCall(CeedFree(&(*data)->eval_modes_in[b]));
1755     CeedCall(CeedFree(&(*data)->eval_mode_offsets_in[b]));
1756     CeedCall(CeedFree(&(*data)->assembled_bases_in[b]));
1757   }
1758   for (CeedInt b = 0; b < (*data)->num_active_bases_out; b++) {
1759     CeedCall(CeedBasisDestroy(&(*data)->active_bases_out[b]));
1760     CeedCall(CeedElemRestrictionDestroy(&(*data)->active_elem_rstrs_out[b]));
1761     CeedCall(CeedFree(&(*data)->eval_modes_out[b]));
1762     CeedCall(CeedFree(&(*data)->eval_mode_offsets_out[b]));
1763     CeedCall(CeedFree(&(*data)->assembled_bases_out[b]));
1764   }
1765   CeedCall(CeedFree(&(*data)->active_bases_in));
1766   CeedCall(CeedFree(&(*data)->active_bases_out));
1767   CeedCall(CeedFree(&(*data)->active_elem_rstrs_in));
1768   CeedCall(CeedFree(&(*data)->active_elem_rstrs_out));
1769   CeedCall(CeedFree(&(*data)->num_eval_modes_in));
1770   CeedCall(CeedFree(&(*data)->num_eval_modes_out));
1771   CeedCall(CeedFree(&(*data)->eval_modes_in));
1772   CeedCall(CeedFree(&(*data)->eval_modes_out));
1773   CeedCall(CeedFree(&(*data)->eval_mode_offsets_in));
1774   CeedCall(CeedFree(&(*data)->eval_mode_offsets_out));
1775   CeedCall(CeedFree(&(*data)->assembled_bases_in));
1776   CeedCall(CeedFree(&(*data)->assembled_bases_out));
1777 
1778   CeedCall(CeedFree(data));
1779   return CEED_ERROR_SUCCESS;
1780 }
1781 
1782 /**
1783   @brief Retrieve fallback `CeedOperator` with a reference `Ceed` for advanced `CeedOperator` functionality
1784 
1785   @param[in]  op          `CeedOperator` to retrieve fallback for
1786   @param[out] op_fallback Fallback `CeedOperator`
1787 
1788   @return An error code: 0 - success, otherwise - failure
1789 
1790   @ref Backend
1791 **/
1792 int CeedOperatorGetFallback(CeedOperator op, CeedOperator *op_fallback) {
1793   // Create if needed
1794   if (!op->op_fallback) CeedCall(CeedOperatorCreateFallback(op));
1795   if (op->op_fallback) {
1796     bool is_debug;
1797     Ceed ceed;
1798 
1799     CeedCall(CeedOperatorGetCeed(op, &ceed));
1800     CeedCall(CeedIsDebug(ceed, &is_debug));
1801     if (is_debug) {
1802       Ceed        ceed_fallback;
1803       const char *resource, *resource_fallback;
1804 
1805       CeedCall(CeedGetOperatorFallbackCeed(ceed, &ceed_fallback));
1806       CeedCall(CeedGetResource(ceed, &resource));
1807       CeedCall(CeedGetResource(ceed_fallback, &resource_fallback));
1808 
1809       CeedDebug256(ceed, CEED_DEBUG_COLOR_SUCCESS, "---------- CeedOperator Fallback ----------\n");
1810       CeedDebug(ceed, "Falling back from %s operator at address %p to %s operator at address %p\n", resource, op, resource_fallback, op->op_fallback);
1811     }
1812   }
1813   *op_fallback = op->op_fallback;
1814   return CEED_ERROR_SUCCESS;
1815 }
1816 
1817 /**
1818   @brief Get the parent `CeedOperator` for a fallback `CeedOperator`
1819 
1820   @param[in]  op     `CeedOperator` context
1821   @param[out] parent Variable to store parent `CeedOperator` context
1822 
1823   @return An error code: 0 - success, otherwise - failure
1824 
1825   @ref Backend
1826 **/
1827 int CeedOperatorGetFallbackParent(CeedOperator op, CeedOperator *parent) {
1828   *parent = op->op_fallback_parent ? op->op_fallback_parent : NULL;
1829   return CEED_ERROR_SUCCESS;
1830 }
1831 
1832 /**
1833   @brief Get the `Ceed` context of the parent `CeedOperator` for a fallback `CeedOperator`
1834 
1835   @param[in]  op     `CeedOperator` context
1836   @param[out] parent Variable to store parent `Ceed` context
1837 
1838   @return An error code: 0 - success, otherwise - failure
1839 
1840   @ref Backend
1841 **/
1842 int CeedOperatorGetFallbackParentCeed(CeedOperator op, Ceed *parent) {
1843   *parent = op->op_fallback_parent ? op->op_fallback_parent->ceed : op->ceed;
1844   return CEED_ERROR_SUCCESS;
1845 }
1846 
1847 /// @}
1848 
1849 /// ----------------------------------------------------------------------------
1850 /// CeedOperator Public API
1851 /// ----------------------------------------------------------------------------
1852 /// @addtogroup CeedOperatorUser
1853 /// @{
1854 
1855 /**
1856   @brief Assemble a linear `CeedQFunction` associated with a `CeedOperator`.
1857 
1858   This returns a `CeedVector` containing a matrix at each quadrature point providing the action of the `CeedQFunction` associated with the `CeedOperator`.
1859   The vector `assembled` is of shape `[num_elements, num_input_fields, num_output_fields, num_quad_points]` and contains column-major matrices representing the action of the `CeedQFunction` for a corresponding quadrature point on an element.
1860 
1861   Inputs and outputs are in the order provided by the user when adding `CeedOperator` fields.
1862   For example, a `CeedQFunction` with inputs `u` and `gradu` and outputs `gradv` and `v` , provided in that order, would result in an assembled `CeedQFunction` that consists of `(1 + dim) x (dim + 1)` matrices at each quadrature point acting on the input ` [u, du_0, du_1]` and producing the output `[dv_0, dv_1, v]`.
1863 
1864   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
1865 
1866   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1867   @param[out] assembled `CeedVector` to store assembled `CeedQFunction` at quadrature points
1868   @param[out] rstr      `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1869   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1870 
1871   @return An error code: 0 - success, otherwise - failure
1872 
1873   @ref User
1874 **/
1875 int CeedOperatorLinearAssembleQFunction(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1876   CeedCall(CeedOperatorCheckReady(op));
1877 
1878   if (op->LinearAssembleQFunction) {
1879     // Backend version
1880     CeedCall(op->LinearAssembleQFunction(op, assembled, rstr, request));
1881   } else {
1882     // Operator fallback
1883     Ceed         ceed;
1884     CeedOperator op_fallback;
1885 
1886     CeedCall(CeedOperatorGetCeed(op, &ceed));
1887     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1888     if (op_fallback) CeedCall(CeedOperatorLinearAssembleQFunction(op_fallback, assembled, rstr, request));
1889     else return CeedError(ceed, CEED_ERROR_UNSUPPORTED, "Backend does not support CeedOperatorLinearAssembleQFunction");
1890   }
1891   return CEED_ERROR_SUCCESS;
1892 }
1893 
1894 /**
1895   @brief Assemble `CeedQFunction` and store result internally.
1896 
1897   Return copied references of stored data to the caller.
1898   Caller is responsible for ownership and destruction of the copied references.
1899   See also @ref CeedOperatorLinearAssembleQFunction().
1900 
1901   Note: If the value of `assembled` or `rstr` passed to this function are non-`NULL` , then it is assumed that they hold valid pointers.
1902         These objects will be destroyed if `*assembled` or `*rstr` is the only reference to the object.
1903 
1904   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1905   @param[out] assembled `CeedVector` to store assembled `CeedQFunction` at quadrature points
1906   @param[out] rstr      `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1907   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1908 
1909   @return An error code: 0 - success, otherwise - failure
1910 
1911   @ref User
1912 **/
1913 int CeedOperatorLinearAssembleQFunctionBuildOrUpdate(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1914   int (*LinearAssembleQFunctionUpdate)(CeedOperator, CeedVector, CeedElemRestriction, CeedRequest *) = NULL;
1915   CeedOperator op_assemble                                                                           = NULL;
1916   CeedOperator op_fallback_parent                                                                    = NULL;
1917 
1918   CeedCall(CeedOperatorCheckReady(op));
1919 
1920   // Determine if fallback parent or operator has implementation
1921   CeedCall(CeedOperatorGetFallbackParent(op, &op_fallback_parent));
1922   if (op_fallback_parent && op_fallback_parent->LinearAssembleQFunctionUpdate) {
1923     // -- Backend version for op fallback parent is faster, if it exists
1924     LinearAssembleQFunctionUpdate = op_fallback_parent->LinearAssembleQFunctionUpdate;
1925     op_assemble                   = op_fallback_parent;
1926   } else if (op->LinearAssembleQFunctionUpdate) {
1927     // -- Backend version for op
1928     LinearAssembleQFunctionUpdate = op->LinearAssembleQFunctionUpdate;
1929     op_assemble                   = op;
1930   }
1931 
1932   // Assemble QFunction
1933   if (LinearAssembleQFunctionUpdate) {
1934     // Backend or fallback parent version
1935     CeedQFunctionAssemblyData data;
1936     bool                      data_is_setup;
1937     CeedVector                assembled_vec  = NULL;
1938     CeedElemRestriction       assembled_rstr = NULL;
1939 
1940     CeedCall(CeedOperatorGetQFunctionAssemblyData(op, &data));
1941     CeedCall(CeedQFunctionAssemblyDataIsSetup(data, &data_is_setup));
1942     if (data_is_setup) {
1943       bool update_needed;
1944 
1945       CeedCall(CeedQFunctionAssemblyDataGetObjects(data, &assembled_vec, &assembled_rstr));
1946       CeedCall(CeedQFunctionAssemblyDataIsUpdateNeeded(data, &update_needed));
1947       if (update_needed) CeedCall(LinearAssembleQFunctionUpdate(op_assemble, assembled_vec, assembled_rstr, request));
1948     } else {
1949       CeedCall(CeedOperatorLinearAssembleQFunction(op_assemble, &assembled_vec, &assembled_rstr, request));
1950       CeedCall(CeedQFunctionAssemblyDataSetObjects(data, assembled_vec, assembled_rstr));
1951     }
1952     CeedCall(CeedQFunctionAssemblyDataSetUpdateNeeded(data, false));
1953 
1954     // Copy reference from internally held copy
1955     CeedCall(CeedVectorReferenceCopy(assembled_vec, assembled));
1956     CeedCall(CeedElemRestrictionReferenceCopy(assembled_rstr, rstr));
1957     CeedCall(CeedVectorDestroy(&assembled_vec));
1958     CeedCall(CeedElemRestrictionDestroy(&assembled_rstr));
1959   } else {
1960     // Operator fallback
1961     Ceed         ceed;
1962     CeedOperator op_fallback;
1963 
1964     CeedCall(CeedOperatorGetCeed(op, &ceed));
1965     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1966     if (op_fallback) CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op_fallback, assembled, rstr, request));
1967     else return CeedError(ceed, CEED_ERROR_UNSUPPORTED, "Backend does not support CeedOperatorLinearAssembleQFunctionUpdate");
1968   }
1969   return CEED_ERROR_SUCCESS;
1970 }
1971 
1972 /**
1973   @brief Assemble the diagonal of a square linear `CeedOperator`
1974 
1975   This overwrites a `CeedVector` with the diagonal of a linear `CeedOperator`.
1976 
1977   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
1978 
1979   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
1980 
1981   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1982   @param[out] assembled `CeedVector` to store assembled `CeedOperator` diagonal
1983   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1984 
1985   @return An error code: 0 - success, otherwise - failure
1986 
1987   @ref User
1988 **/
1989 int CeedOperatorLinearAssembleDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
1990   bool     is_composite;
1991   CeedSize input_size = 0, output_size = 0;
1992   Ceed     ceed;
1993 
1994   CeedCall(CeedOperatorGetCeed(op, &ceed));
1995   CeedCall(CeedOperatorCheckReady(op));
1996   CeedCall(CeedOperatorIsComposite(op, &is_composite));
1997 
1998   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
1999   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
2000 
2001   // Early exit for empty operator
2002   if (!is_composite) {
2003     CeedInt num_elem = 0;
2004 
2005     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2006     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2007   }
2008 
2009   if (op->LinearAssembleDiagonal) {
2010     // Backend version
2011     CeedCall(op->LinearAssembleDiagonal(op, assembled, request));
2012     return CEED_ERROR_SUCCESS;
2013   } else if (op->LinearAssembleAddDiagonal) {
2014     // Backend version with zeroing first
2015     CeedCall(CeedVectorSetValue(assembled, 0.0));
2016     CeedCall(op->LinearAssembleAddDiagonal(op, assembled, request));
2017     return CEED_ERROR_SUCCESS;
2018   } else {
2019     // Operator fallback
2020     CeedOperator op_fallback;
2021 
2022     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2023     if (op_fallback) {
2024       CeedCall(CeedOperatorLinearAssembleDiagonal(op_fallback, assembled, request));
2025       return CEED_ERROR_SUCCESS;
2026     }
2027   }
2028   // Default interface implementation
2029   CeedCall(CeedVectorSetValue(assembled, 0.0));
2030   CeedCall(CeedOperatorLinearAssembleAddDiagonal(op, assembled, request));
2031   return CEED_ERROR_SUCCESS;
2032 }
2033 
2034 /**
2035   @brief Assemble the diagonal of a square linear `CeedOperator`.
2036 
2037   This sums into a `CeedVector` the diagonal of a linear `CeedOperator`.
2038 
2039   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
2040 
2041   Note: Calling this function asserts that setup is complete and sets the CeedOperator as immutable.
2042 
2043   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
2044   @param[out] assembled `CeedVector` to store assembled `CeedOperator` diagonal
2045   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2046 
2047   @return An error code: 0 - success, otherwise - failure
2048 
2049   @ref User
2050 **/
2051 int CeedOperatorLinearAssembleAddDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
2052   bool     is_composite;
2053   CeedSize input_size = 0, output_size = 0;
2054   Ceed     ceed;
2055 
2056   CeedCall(CeedOperatorGetCeed(op, &ceed));
2057   CeedCall(CeedOperatorCheckReady(op));
2058   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2059 
2060   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2061   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
2062 
2063   // Early exit for empty operator
2064   if (!is_composite) {
2065     CeedInt num_elem = 0;
2066 
2067     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2068     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2069   }
2070 
2071   if (op->LinearAssembleAddDiagonal) {
2072     // Backend version
2073     CeedCall(op->LinearAssembleAddDiagonal(op, assembled, request));
2074     return CEED_ERROR_SUCCESS;
2075   } else {
2076     // Operator fallback
2077     CeedOperator op_fallback;
2078 
2079     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2080     if (op_fallback) {
2081       CeedCall(CeedOperatorLinearAssembleAddDiagonal(op_fallback, assembled, request));
2082       return CEED_ERROR_SUCCESS;
2083     }
2084   }
2085   // Default interface implementation
2086   if (is_composite) {
2087     CeedCall(CeedCompositeOperatorLinearAssembleAddDiagonal(op, request, false, assembled));
2088   } else {
2089     CeedCall(CeedSingleOperatorLinearAssembleAddDiagonal(op, request, false, assembled));
2090   }
2091   return CEED_ERROR_SUCCESS;
2092 }
2093 
2094 /**
2095    @brief Fully assemble the point-block diagonal pattern of a linear `CeedOperator`.
2096 
2097    Expected to be used in conjunction with @ref CeedOperatorLinearAssemblePointBlockDiagonal().
2098 
2099    The assembly routines use coordinate format, with `num_entries` tuples of the form `(i, j, value)` which indicate that value should be added to the matrix in entry `(i, j)`.
2100    Note that the `(i, j)` pairs are unique.
2101    This function returns the number of entries and their `(i, j)` locations, while @ref CeedOperatorLinearAssemblePointBlockDiagonal() provides the values in the same ordering.
2102 
2103    This will generally be slow unless your operator is low-order.
2104 
2105    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2106 
2107    @param[in]  op          `CeedOperator` to assemble
2108    @param[out] num_entries Number of entries in coordinate nonzero pattern
2109    @param[out] rows        Row number for each entry
2110    @param[out] cols        Column number for each entry
2111 
2112    @ref User
2113 **/
2114 int CeedOperatorLinearAssemblePointBlockDiagonalSymbolic(CeedOperator op, CeedSize *num_entries, CeedInt **rows, CeedInt **cols) {
2115   Ceed          ceed;
2116   bool          is_composite;
2117   CeedInt       num_active_components, num_sub_operators;
2118   CeedOperator *sub_operators;
2119 
2120   CeedCall(CeedOperatorGetCeed(op, &ceed));
2121   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2122 
2123   CeedSize input_size = 0, output_size = 0;
2124   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2125   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
2126 
2127   if (is_composite) {
2128     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_sub_operators));
2129     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2130   } else {
2131     sub_operators     = &op;
2132     num_sub_operators = 1;
2133   }
2134 
2135   // Verify operator can be assembled correctly
2136   {
2137     CeedOperatorAssemblyData data;
2138     CeedInt                  num_active_elem_rstrs, comp_stride;
2139     CeedElemRestriction     *active_elem_rstrs;
2140 
2141     // Get initial values to check against
2142     CeedCall(CeedOperatorGetOperatorAssemblyData(sub_operators[0], &data));
2143     CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, &num_active_elem_rstrs, &active_elem_rstrs, NULL, NULL));
2144     CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstrs[0], &comp_stride));
2145     CeedCall(CeedElemRestrictionGetNumComponents(active_elem_rstrs[0], &num_active_components));
2146 
2147     // Verify that all active element restrictions have same component stride and number of components
2148     for (CeedInt k = 0; k < num_sub_operators; k++) {
2149       CeedCall(CeedOperatorGetOperatorAssemblyData(sub_operators[k], &data));
2150       CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, &num_active_elem_rstrs, &active_elem_rstrs, NULL, NULL));
2151       for (CeedInt i = 0; i < num_active_elem_rstrs; i++) {
2152         CeedInt comp_stride_sub, num_active_components_sub;
2153 
2154         CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstrs[i], &comp_stride_sub));
2155         CeedCheck(comp_stride == comp_stride_sub, ceed, CEED_ERROR_DIMENSION,
2156                   "Active element restrictions must have the same component stride: %d vs %d", comp_stride, comp_stride_sub);
2157         CeedCall(CeedElemRestrictionGetNumComponents(active_elem_rstrs[i], &num_active_components_sub));
2158         CeedCheck(num_active_components == num_active_components_sub, ceed, CEED_ERROR_INCOMPATIBLE,
2159                   "All suboperators must have the same number of output components."
2160                   " Previous: %" CeedInt_FMT " Current: %" CeedInt_FMT,
2161                   num_active_components, num_active_components_sub);
2162       }
2163     }
2164   }
2165   *num_entries = input_size * num_active_components;
2166   CeedCall(CeedCalloc(*num_entries, rows));
2167   CeedCall(CeedCalloc(*num_entries, cols));
2168 
2169   for (CeedInt o = 0; o < num_sub_operators; o++) {
2170     CeedElemRestriction active_elem_rstr, point_block_active_elem_rstr;
2171     CeedInt             comp_stride, num_elem, elem_size;
2172     const CeedInt      *offsets, *point_block_offsets;
2173 
2174     CeedCall(CeedOperatorGetActiveElemRestriction(sub_operators[o], &active_elem_rstr));
2175     CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstr, &comp_stride));
2176     CeedCall(CeedElemRestrictionGetNumElements(active_elem_rstr, &num_elem));
2177     CeedCall(CeedElemRestrictionGetElementSize(active_elem_rstr, &elem_size));
2178     CeedCall(CeedElemRestrictionGetOffsets(active_elem_rstr, CEED_MEM_HOST, &offsets));
2179 
2180     CeedCall(CeedOperatorCreateActivePointBlockRestriction(active_elem_rstr, &point_block_active_elem_rstr));
2181     CeedCall(CeedElemRestrictionGetOffsets(point_block_active_elem_rstr, CEED_MEM_HOST, &point_block_offsets));
2182 
2183     for (CeedSize i = 0; i < num_elem * elem_size; i++) {
2184       for (CeedInt c_out = 0; c_out < num_active_components; c_out++) {
2185         for (CeedInt c_in = 0; c_in < num_active_components; c_in++) {
2186           (*rows)[point_block_offsets[i] + c_out * num_active_components + c_in] = offsets[i] + c_out * comp_stride;
2187           (*cols)[point_block_offsets[i] + c_out * num_active_components + c_in] = offsets[i] + c_in * comp_stride;
2188         }
2189       }
2190     }
2191 
2192     CeedCall(CeedElemRestrictionRestoreOffsets(active_elem_rstr, &offsets));
2193     CeedCall(CeedElemRestrictionRestoreOffsets(point_block_active_elem_rstr, &point_block_offsets));
2194     CeedCall(CeedElemRestrictionDestroy(&active_elem_rstr));
2195     CeedCall(CeedElemRestrictionDestroy(&point_block_active_elem_rstr));
2196   }
2197   return CEED_ERROR_SUCCESS;
2198 }
2199 
2200 /**
2201   @brief Assemble the point block diagonal of a square linear `CeedOperator`.
2202 
2203   This overwrites a `CeedVector` with the point block diagonal of a linear `CeedOperator`.
2204 
2205   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
2206 
2207   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2208 
2209   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
2210   @param[out] assembled `CeedVector` to store assembled `CeedOperator` point block diagonal, provided in row-major form with an `num_comp * num_comp` block at each node.
2211                           The dimensions of this vector are derived from the active vector for the `CeedOperator`.
2212                           The array has shape `[nodes, component out, component in]`.
2213   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2214 
2215   @return An error code: 0 - success, otherwise - failure
2216 
2217   @ref User
2218 **/
2219 int CeedOperatorLinearAssemblePointBlockDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
2220   bool     is_composite;
2221   CeedSize input_size = 0, output_size = 0;
2222   Ceed     ceed;
2223 
2224   CeedCall(CeedOperatorGetCeed(op, &ceed));
2225   CeedCall(CeedOperatorCheckReady(op));
2226   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2227 
2228   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2229   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
2230 
2231   // Early exit for empty operator
2232   if (!is_composite) {
2233     CeedInt num_elem = 0;
2234 
2235     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2236     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2237   }
2238 
2239   if (op->LinearAssemblePointBlockDiagonal) {
2240     // Backend version
2241     CeedCall(op->LinearAssemblePointBlockDiagonal(op, assembled, request));
2242     return CEED_ERROR_SUCCESS;
2243   } else if (op->LinearAssembleAddPointBlockDiagonal) {
2244     // Backend version with zeroing first
2245     CeedCall(CeedVectorSetValue(assembled, 0.0));
2246     CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op, assembled, request));
2247     return CEED_ERROR_SUCCESS;
2248   } else {
2249     // Operator fallback
2250     CeedOperator op_fallback;
2251 
2252     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2253     if (op_fallback) {
2254       CeedCall(CeedOperatorLinearAssemblePointBlockDiagonal(op_fallback, assembled, request));
2255       return CEED_ERROR_SUCCESS;
2256     }
2257   }
2258   // Default interface implementation
2259   CeedCall(CeedVectorSetValue(assembled, 0.0));
2260   CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op, assembled, request));
2261   return CEED_ERROR_SUCCESS;
2262 }
2263 
2264 /**
2265   @brief Assemble the point block diagonal of a square linear `CeedOperator`.
2266 
2267   This sums into a `CeedVector` with the point block diagonal of a linear `CeedOperator`.
2268 
2269   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
2270 
2271   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2272 
2273   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
2274   @param[out] assembled `CeedVector` to store assembled CeedOperator point block diagonal, provided in row-major form with an `num_comp * num_comp` block at each node.
2275                           The dimensions of this vector are derived from the active vector for the `CeedOperator`.
2276                           The array has shape `[nodes, component out, component in]`.
2277   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2278 
2279   @return An error code: 0 - success, otherwise - failure
2280 
2281   @ref User
2282 **/
2283 int CeedOperatorLinearAssembleAddPointBlockDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
2284   bool     is_composite;
2285   CeedSize input_size = 0, output_size = 0;
2286   Ceed     ceed;
2287 
2288   CeedCall(CeedOperatorGetCeed(op, &ceed));
2289   CeedCall(CeedOperatorCheckReady(op));
2290   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2291 
2292   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2293   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
2294 
2295   // Early exit for empty operator
2296   if (!is_composite) {
2297     CeedInt num_elem = 0;
2298 
2299     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2300     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2301   }
2302 
2303   if (op->LinearAssembleAddPointBlockDiagonal) {
2304     // Backend version
2305     CeedCall(op->LinearAssembleAddPointBlockDiagonal(op, assembled, request));
2306     return CEED_ERROR_SUCCESS;
2307   } else {
2308     // Operator fallback
2309     CeedOperator op_fallback;
2310 
2311     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2312     if (op_fallback) {
2313       CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op_fallback, assembled, request));
2314       return CEED_ERROR_SUCCESS;
2315     }
2316   }
2317   // Default interface implementation
2318   if (is_composite) {
2319     CeedCall(CeedCompositeOperatorLinearAssembleAddDiagonal(op, request, true, assembled));
2320   } else {
2321     CeedCall(CeedSingleOperatorLinearAssembleAddDiagonal(op, request, true, assembled));
2322   }
2323   return CEED_ERROR_SUCCESS;
2324 }
2325 
2326 /**
2327    @brief Fully assemble the nonzero pattern of a linear `CeedOperator`.
2328 
2329    Expected to be used in conjunction with @ref CeedOperatorLinearAssemble().
2330 
2331    The assembly routines use coordinate format, with `num_entries` tuples of the form `(i, j, value)` which indicate that value should be added to the matrix in entry `(i, j)`.
2332    Note that the `(i, j)` pairs are not unique and may repeat.
2333    This function returns the number of entries and their `(i, j)` locations, while @ref CeedOperatorLinearAssemble() provides the values in the same ordering.
2334 
2335    This will generally be slow unless your operator is low-order.
2336 
2337    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2338 
2339    @param[in]  op          `CeedOperator` to assemble
2340    @param[out] num_entries Number of entries in coordinate nonzero pattern
2341    @param[out] rows        Row number for each entry
2342    @param[out] cols        Column number for each entry
2343 
2344    @ref User
2345 **/
2346 int CeedOperatorLinearAssembleSymbolic(CeedOperator op, CeedSize *num_entries, CeedInt **rows, CeedInt **cols) {
2347   bool          is_composite;
2348   CeedInt       num_suboperators, offset = 0;
2349   CeedSize      single_entries;
2350   CeedOperator *sub_operators;
2351 
2352   CeedCall(CeedOperatorCheckReady(op));
2353   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2354 
2355   if (op->LinearAssembleSymbolic) {
2356     // Backend version
2357     CeedCall(op->LinearAssembleSymbolic(op, num_entries, rows, cols));
2358     return CEED_ERROR_SUCCESS;
2359   } else {
2360     // Operator fallback
2361     CeedOperator op_fallback;
2362 
2363     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2364     if (op_fallback) {
2365       CeedCall(CeedOperatorLinearAssembleSymbolic(op_fallback, num_entries, rows, cols));
2366       return CEED_ERROR_SUCCESS;
2367     }
2368   }
2369 
2370   // Default interface implementation
2371 
2372   // Count entries and allocate rows, cols arrays
2373   *num_entries = 0;
2374   if (is_composite) {
2375     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2376     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2377     for (CeedInt k = 0; k < num_suboperators; ++k) {
2378       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2379       *num_entries += single_entries;
2380     }
2381   } else {
2382     CeedCall(CeedSingleOperatorAssemblyCountEntries(op, &single_entries));
2383     *num_entries += single_entries;
2384   }
2385   CeedCall(CeedCalloc(*num_entries, rows));
2386   CeedCall(CeedCalloc(*num_entries, cols));
2387 
2388   // Assemble nonzero locations
2389   if (is_composite) {
2390     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2391     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2392     for (CeedInt k = 0; k < num_suboperators; ++k) {
2393       CeedCall(CeedSingleOperatorAssembleSymbolic(sub_operators[k], offset, *rows, *cols));
2394       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2395       offset += single_entries;
2396     }
2397   } else {
2398     CeedCall(CeedSingleOperatorAssembleSymbolic(op, offset, *rows, *cols));
2399   }
2400   return CEED_ERROR_SUCCESS;
2401 }
2402 
2403 /**
2404    @brief Fully assemble the nonzero entries of a linear operator.
2405 
2406    Expected to be used in conjunction with @ref CeedOperatorLinearAssembleSymbolic().
2407 
2408    The assembly routines use coordinate format, with `num_entries` tuples of the form `(i, j, value)` which indicate that value should be added to the matrix in entry `(i, j)`.
2409    Note that the `(i, j)` pairs are not unique and may repeat.
2410    This function returns the values of the nonzero entries to be added, their `(i, j)` locations are provided by @ref CeedOperatorLinearAssembleSymbolic().
2411 
2412    This will generally be slow unless your operator is low-order.
2413 
2414    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2415 
2416    @param[in]  op     `CeedOperator` to assemble
2417    @param[out] values Values to assemble into matrix
2418 
2419    @ref User
2420 **/
2421 int CeedOperatorLinearAssemble(CeedOperator op, CeedVector values) {
2422   bool          is_composite;
2423   CeedInt       num_suboperators, offset = 0;
2424   CeedSize      single_entries = 0;
2425   CeedOperator *sub_operators;
2426 
2427   CeedCall(CeedOperatorCheckReady(op));
2428   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2429 
2430   // Early exit for empty operator
2431   if (!is_composite) {
2432     CeedInt num_elem = 0;
2433 
2434     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2435     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2436   }
2437 
2438   if (op->LinearAssemble) {
2439     // Backend version
2440     CeedCall(op->LinearAssemble(op, values));
2441     return CEED_ERROR_SUCCESS;
2442   } else {
2443     // Operator fallback
2444     CeedOperator op_fallback;
2445 
2446     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2447     if (op_fallback) {
2448       CeedCall(CeedOperatorLinearAssemble(op_fallback, values));
2449       return CEED_ERROR_SUCCESS;
2450     }
2451   }
2452 
2453   // Default interface implementation
2454   CeedCall(CeedVectorSetValue(values, 0.0));
2455   if (is_composite) {
2456     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2457     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2458     for (CeedInt k = 0; k < num_suboperators; k++) {
2459       CeedCall(CeedSingleOperatorAssemble(sub_operators[k], offset, values));
2460       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2461       offset += single_entries;
2462     }
2463   } else {
2464     CeedCall(CeedSingleOperatorAssemble(op, offset, values));
2465   }
2466   return CEED_ERROR_SUCCESS;
2467 }
2468 
2469 /**
2470   @brief Get the multiplicity of nodes across sub-operators in a composite `CeedOperator`.
2471 
2472   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2473 
2474   @param[in]  op               Composite `CeedOperator`
2475   @param[in]  num_skip_indices Number of sub-operators to skip
2476   @param[in]  skip_indices     Array of indices of sub-operators to skip
2477   @param[out] mult             Vector to store multiplicity (of size `l_size` )
2478 
2479   @return An error code: 0 - success, otherwise - failure
2480 
2481   @ref User
2482 **/
2483 int CeedCompositeOperatorGetMultiplicity(CeedOperator op, CeedInt num_skip_indices, CeedInt *skip_indices, CeedVector mult) {
2484   Ceed                ceed;
2485   CeedInt             num_suboperators;
2486   CeedSize            l_vec_len;
2487   CeedScalar         *mult_array;
2488   CeedVector          ones_l_vec;
2489   CeedElemRestriction elem_rstr, mult_elem_rstr;
2490   CeedOperator       *sub_operators;
2491 
2492   CeedCall(CeedOperatorCheckReady(op));
2493 
2494   CeedCall(CeedOperatorGetCeed(op, &ceed));
2495 
2496   // Zero mult vector
2497   CeedCall(CeedVectorSetValue(mult, 0.0));
2498 
2499   // Get suboperators
2500   CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2501   CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2502   if (num_suboperators == 0) return CEED_ERROR_SUCCESS;
2503 
2504   // Work vector
2505   CeedCall(CeedVectorGetLength(mult, &l_vec_len));
2506   CeedCall(CeedVectorCreate(ceed, l_vec_len, &ones_l_vec));
2507   CeedCall(CeedVectorSetValue(ones_l_vec, 1.0));
2508   CeedCall(CeedVectorGetArray(mult, CEED_MEM_HOST, &mult_array));
2509 
2510   // Compute multiplicity across suboperators
2511   for (CeedInt i = 0; i < num_suboperators; i++) {
2512     const CeedScalar *sub_mult_array;
2513     CeedVector        sub_mult_l_vec, ones_e_vec;
2514 
2515     // -- Check for suboperator to skip
2516     for (CeedInt j = 0; j < num_skip_indices; j++) {
2517       if (skip_indices[j] == i) continue;
2518     }
2519 
2520     // -- Sub operator multiplicity
2521     CeedCall(CeedOperatorGetActiveElemRestriction(sub_operators[i], &elem_rstr));
2522     CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr, &mult_elem_rstr));
2523     CeedCall(CeedElemRestrictionDestroy(&elem_rstr));
2524     CeedCall(CeedElemRestrictionCreateVector(mult_elem_rstr, &sub_mult_l_vec, &ones_e_vec));
2525     CeedCall(CeedVectorSetValue(sub_mult_l_vec, 0.0));
2526     CeedCall(CeedElemRestrictionApply(mult_elem_rstr, CEED_NOTRANSPOSE, ones_l_vec, ones_e_vec, CEED_REQUEST_IMMEDIATE));
2527     CeedCall(CeedElemRestrictionApply(mult_elem_rstr, CEED_TRANSPOSE, ones_e_vec, sub_mult_l_vec, CEED_REQUEST_IMMEDIATE));
2528     CeedCall(CeedVectorGetArrayRead(sub_mult_l_vec, CEED_MEM_HOST, &sub_mult_array));
2529     // ---- Flag every node present in the current suboperator
2530     for (CeedSize j = 0; j < l_vec_len; j++) {
2531       if (sub_mult_array[j] > 0.0) mult_array[j] += 1.0;
2532     }
2533     CeedCall(CeedVectorRestoreArrayRead(sub_mult_l_vec, &sub_mult_array));
2534     CeedCall(CeedVectorDestroy(&sub_mult_l_vec));
2535     CeedCall(CeedVectorDestroy(&ones_e_vec));
2536     CeedCall(CeedElemRestrictionDestroy(&mult_elem_rstr));
2537   }
2538   CeedCall(CeedVectorRestoreArray(mult, &mult_array));
2539   CeedCall(CeedVectorDestroy(&ones_l_vec));
2540   return CEED_ERROR_SUCCESS;
2541 }
2542 
2543 /**
2544   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator`, creating the prolongation basis from the fine and coarse grid interpolation.
2545 
2546   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2547 
2548   @param[in]  op_fine      Fine grid `CeedOperator`
2549   @param[in]  p_mult_fine  L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2550   @param[in]  rstr_coarse  Coarse grid `CeedElemRestriction`
2551   @param[in]  basis_coarse Coarse grid active vector `CeedBasis`
2552   @param[out] op_coarse    Coarse grid `CeedOperator`
2553   @param[out] op_prolong   Coarse to fine `CeedOperator`, or `NULL`
2554   @param[out] op_restrict  Fine to coarse `CeedOperator`, or `NULL`
2555 
2556   @return An error code: 0 - success, otherwise - failure
2557 
2558   @ref User
2559 **/
2560 int CeedOperatorMultigridLevelCreate(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2561                                      CeedOperator *op_coarse, CeedOperator *op_prolong, CeedOperator *op_restrict) {
2562   CeedBasis basis_c_to_f = NULL;
2563 
2564   CeedCall(CeedOperatorCheckReady(op_fine));
2565 
2566   // Build prolongation matrix, if required
2567   if (op_prolong || op_restrict) {
2568     CeedBasis basis_fine;
2569 
2570     CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2571     CeedCall(CeedBasisCreateProjection(basis_coarse, basis_fine, &basis_c_to_f));
2572     CeedCall(CeedBasisDestroy(&basis_fine));
2573   }
2574 
2575   // Core code
2576   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2577   return CEED_ERROR_SUCCESS;
2578 }
2579 
2580 /**
2581   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator` with a tensor basis for the active basis.
2582 
2583   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2584 
2585   @param[in]  op_fine       Fine grid `CeedOperator`
2586   @param[in]  p_mult_fine   L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2587   @param[in]  rstr_coarse   Coarse grid `CeedElemRestriction`
2588   @param[in]  basis_coarse  Coarse grid active vector `CeedBasis`
2589   @param[in]  interp_c_to_f Matrix for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction `CeedOperator`
2590   @param[out] op_coarse     Coarse grid `CeedOperator`
2591   @param[out] op_prolong    Coarse to fine `CeedOperator`, or `NULL`
2592   @param[out] op_restrict   Fine to coarse `CeedOperator`, or `NULL`
2593 
2594   @return An error code: 0 - success, otherwise - failure
2595 
2596   @ref User
2597 **/
2598 int CeedOperatorMultigridLevelCreateTensorH1(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2599                                              const CeedScalar *interp_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong,
2600                                              CeedOperator *op_restrict) {
2601   Ceed      ceed;
2602   CeedInt   Q_f, Q_c;
2603   CeedBasis basis_fine, basis_c_to_f = NULL;
2604 
2605   CeedCall(CeedOperatorCheckReady(op_fine));
2606   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
2607 
2608   // Check for compatible quadrature spaces
2609   CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2610   CeedCall(CeedBasisGetNumQuadraturePoints(basis_fine, &Q_f));
2611   CeedCall(CeedBasisGetNumQuadraturePoints(basis_coarse, &Q_c));
2612   CeedCheck(Q_f == Q_c, ceed, CEED_ERROR_DIMENSION,
2613             "Bases must have compatible quadrature spaces."
2614             " Fine grid: %" CeedInt_FMT " points, Coarse grid: %" CeedInt_FMT " points",
2615             Q_f, Q_c);
2616 
2617   // Create coarse to fine basis, if required
2618   if (op_prolong || op_restrict) {
2619     CeedInt     dim, num_comp, num_nodes_c, P_1d_f, P_1d_c;
2620     CeedScalar *q_ref, *q_weight, *grad;
2621 
2622     // Check if interpolation matrix is provided
2623     CeedCheck(interp_c_to_f, ceed, CEED_ERROR_INCOMPATIBLE,
2624               "Prolongation or restriction operator creation requires coarse-to-fine interpolation matrix");
2625     CeedCall(CeedBasisGetDimension(basis_fine, &dim));
2626     CeedCall(CeedBasisGetNumComponents(basis_fine, &num_comp));
2627     CeedCall(CeedBasisGetNumNodes1D(basis_fine, &P_1d_f));
2628     CeedCall(CeedBasisDestroy(&basis_fine));
2629     CeedCall(CeedElemRestrictionGetElementSize(rstr_coarse, &num_nodes_c));
2630     P_1d_c = dim == 1 ? num_nodes_c : dim == 2 ? sqrt(num_nodes_c) : cbrt(num_nodes_c);
2631     CeedCall(CeedCalloc(P_1d_f, &q_ref));
2632     CeedCall(CeedCalloc(P_1d_f, &q_weight));
2633     CeedCall(CeedCalloc(P_1d_f * P_1d_c * dim, &grad));
2634     CeedCall(CeedBasisCreateTensorH1(ceed, dim, num_comp, P_1d_c, P_1d_f, interp_c_to_f, grad, q_ref, q_weight, &basis_c_to_f));
2635     CeedCall(CeedFree(&q_ref));
2636     CeedCall(CeedFree(&q_weight));
2637     CeedCall(CeedFree(&grad));
2638   }
2639 
2640   // Core code
2641   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2642   return CEED_ERROR_SUCCESS;
2643 }
2644 
2645 /**
2646   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator` with a non-tensor basis for the active vector
2647 
2648   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2649 
2650   @param[in]  op_fine       Fine grid `CeedOperator`
2651   @param[in]  p_mult_fine   L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2652   @param[in]  rstr_coarse   Coarse grid `CeedElemRestriction`
2653   @param[in]  basis_coarse  Coarse grid active vector `CeedBasis`
2654   @param[in]  interp_c_to_f Matrix for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction `CeedOperator`
2655   @param[out] op_coarse     Coarse grid `CeedOperator`
2656   @param[out] op_prolong    Coarse to fine `CeedOperator`, or `NULL`
2657   @param[out] op_restrict   Fine to coarse `CeedOperator`, or `NULL`
2658 
2659   @return An error code: 0 - success, otherwise - failure
2660 
2661   @ref User
2662 **/
2663 int CeedOperatorMultigridLevelCreateH1(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2664                                        const CeedScalar *interp_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong,
2665                                        CeedOperator *op_restrict) {
2666   Ceed      ceed;
2667   CeedInt   Q_f, Q_c;
2668   CeedBasis basis_fine, basis_c_to_f = NULL;
2669 
2670   CeedCall(CeedOperatorCheckReady(op_fine));
2671   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
2672 
2673   // Check for compatible quadrature spaces
2674   CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2675   CeedCall(CeedBasisGetNumQuadraturePoints(basis_fine, &Q_f));
2676   CeedCall(CeedBasisGetNumQuadraturePoints(basis_coarse, &Q_c));
2677   CeedCheck(Q_f == Q_c, ceed, CEED_ERROR_DIMENSION, "Bases must have compatible quadrature spaces");
2678 
2679   // Coarse to fine basis
2680   if (op_prolong || op_restrict) {
2681     CeedInt          dim, num_comp, num_nodes_c, num_nodes_f;
2682     CeedScalar      *q_ref, *q_weight, *grad;
2683     CeedElemTopology topo;
2684 
2685     // Check if interpolation matrix is provided
2686     CeedCheck(interp_c_to_f, ceed, CEED_ERROR_INCOMPATIBLE,
2687               "Prolongation or restriction operator creation requires coarse-to-fine interpolation matrix");
2688     CeedCall(CeedBasisGetTopology(basis_fine, &topo));
2689     CeedCall(CeedBasisGetDimension(basis_fine, &dim));
2690     CeedCall(CeedBasisGetNumComponents(basis_fine, &num_comp));
2691     CeedCall(CeedBasisGetNumNodes(basis_fine, &num_nodes_f));
2692     CeedCall(CeedBasisDestroy(&basis_fine));
2693     CeedCall(CeedElemRestrictionGetElementSize(rstr_coarse, &num_nodes_c));
2694     CeedCall(CeedCalloc(num_nodes_f * dim, &q_ref));
2695     CeedCall(CeedCalloc(num_nodes_f, &q_weight));
2696     CeedCall(CeedCalloc(num_nodes_f * num_nodes_c * dim, &grad));
2697     CeedCall(CeedBasisCreateH1(ceed, topo, num_comp, num_nodes_c, num_nodes_f, interp_c_to_f, grad, q_ref, q_weight, &basis_c_to_f));
2698     CeedCall(CeedFree(&q_ref));
2699     CeedCall(CeedFree(&q_weight));
2700     CeedCall(CeedFree(&grad));
2701   }
2702 
2703   // Core code
2704   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2705   return CEED_ERROR_SUCCESS;
2706 }
2707 
2708 /**
2709   @brief Build a FDM based approximate inverse for each element for a `CeedOperator`.
2710 
2711   This returns a `CeedOperator` and `CeedVector` to apply a Fast Diagonalization Method based approximate inverse.
2712   This function obtains the simultaneous diagonalization for the 1D mass and Laplacian operators, \f$M = V^T V, K = V^T S V\f$.
2713   The assembled `CeedQFunction` is used to modify the eigenvalues from simultaneous diagonalization and obtain an approximate inverse of the form \f$V^T \hat S V\f$.
2714   The `CeedOperator` must be linear and non-composite.
2715   The associated `CeedQFunction` must therefore also be linear.
2716 
2717   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2718 
2719   @param[in]  op      `CeedOperator` to create element inverses
2720   @param[out] fdm_inv `CeedOperator` to apply the action of a FDM based inverse for each element
2721   @param[in]  request Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2722 
2723   @return An error code: 0 - success, otherwise - failure
2724 
2725   @ref User
2726 **/
2727 int CeedOperatorCreateFDMElementInverse(CeedOperator op, CeedOperator *fdm_inv, CeedRequest *request) {
2728   Ceed                 ceed, ceed_parent;
2729   bool                 interp = false, grad = false, is_tensor_basis = true;
2730   CeedInt              num_input_fields, P_1d, Q_1d, num_nodes, num_qpts, dim, num_comp = 1, num_elem = 1;
2731   CeedScalar          *mass, *laplace, *x, *fdm_interp, *lambda, *elem_avg;
2732   const CeedScalar    *interp_1d, *grad_1d, *q_weight_1d;
2733   CeedVector           q_data;
2734   CeedElemRestriction  rstr  = NULL, rstr_qd_i;
2735   CeedBasis            basis = NULL, fdm_basis;
2736   CeedQFunctionContext ctx_fdm;
2737   CeedQFunctionField  *qf_fields;
2738   CeedQFunction        qf, qf_fdm;
2739   CeedOperatorField   *op_fields;
2740 
2741   CeedCall(CeedOperatorCheckReady(op));
2742 
2743   if (op->CreateFDMElementInverse) {
2744     // Backend version
2745     CeedCall(op->CreateFDMElementInverse(op, fdm_inv, request));
2746     return CEED_ERROR_SUCCESS;
2747   } else {
2748     // Operator fallback
2749     CeedOperator op_fallback;
2750 
2751     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2752     if (op_fallback) {
2753       CeedCall(CeedOperatorCreateFDMElementInverse(op_fallback, fdm_inv, request));
2754       return CEED_ERROR_SUCCESS;
2755     }
2756   }
2757 
2758   // Default interface implementation
2759   CeedCall(CeedOperatorGetCeed(op, &ceed));
2760   CeedCall(CeedOperatorGetFallbackParentCeed(op, &ceed_parent));
2761   CeedCall(CeedOperatorGetQFunction(op, &qf));
2762 
2763   // Determine active input basis
2764   CeedCall(CeedOperatorGetFields(op, &num_input_fields, &op_fields, NULL, NULL));
2765   CeedCall(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
2766   for (CeedInt i = 0; i < num_input_fields; i++) {
2767     CeedVector vec;
2768 
2769     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
2770     if (vec == CEED_VECTOR_ACTIVE) {
2771       CeedEvalMode eval_mode;
2772 
2773       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
2774       interp = interp || eval_mode == CEED_EVAL_INTERP;
2775       grad   = grad || eval_mode == CEED_EVAL_GRAD;
2776       if (!basis) CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis));
2777       if (!rstr) CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr));
2778     }
2779     CeedCall(CeedVectorDestroy(&vec));
2780   }
2781   CeedCheck(basis, ceed, CEED_ERROR_BACKEND, "No active field set");
2782   CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d));
2783   CeedCall(CeedBasisGetNumNodes(basis, &num_nodes));
2784   CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d));
2785   CeedCall(CeedBasisGetNumQuadraturePoints(basis, &num_qpts));
2786   CeedCall(CeedBasisGetDimension(basis, &dim));
2787   CeedCall(CeedBasisGetNumComponents(basis, &num_comp));
2788   CeedCall(CeedElemRestrictionGetNumElements(rstr, &num_elem));
2789 
2790   // Build and diagonalize 1D Mass and Laplacian
2791   CeedCall(CeedBasisIsTensor(basis, &is_tensor_basis));
2792   CeedCheck(is_tensor_basis, ceed, CEED_ERROR_BACKEND, "FDMElementInverse only supported for tensor bases");
2793   CeedCall(CeedCalloc(P_1d * P_1d, &mass));
2794   CeedCall(CeedCalloc(P_1d * P_1d, &laplace));
2795   CeedCall(CeedCalloc(P_1d * P_1d, &x));
2796   CeedCall(CeedCalloc(P_1d * P_1d, &fdm_interp));
2797   CeedCall(CeedCalloc(P_1d, &lambda));
2798   // -- Build matrices
2799   CeedCall(CeedBasisGetInterp1D(basis, &interp_1d));
2800   CeedCall(CeedBasisGetGrad1D(basis, &grad_1d));
2801   CeedCall(CeedBasisGetQWeights(basis, &q_weight_1d));
2802   CeedCall(CeedBuildMassLaplace(interp_1d, grad_1d, q_weight_1d, P_1d, Q_1d, dim, mass, laplace));
2803 
2804   // -- Diagonalize
2805   CeedCall(CeedSimultaneousDiagonalization(ceed, laplace, mass, x, lambda, P_1d));
2806   CeedCall(CeedFree(&mass));
2807   CeedCall(CeedFree(&laplace));
2808   for (CeedInt i = 0; i < P_1d; i++) {
2809     for (CeedInt j = 0; j < P_1d; j++) fdm_interp[i + j * P_1d] = x[j + i * P_1d];
2810   }
2811   CeedCall(CeedFree(&x));
2812 
2813   {
2814     CeedInt             layout[3], num_modes = (interp ? 1 : 0) + (grad ? dim : 0);
2815     CeedScalar          max_norm = 0;
2816     const CeedScalar   *assembled_array, *q_weight_array;
2817     CeedVector          assembled = NULL, q_weight;
2818     CeedElemRestriction rstr_qf   = NULL;
2819 
2820     // Assemble QFunction
2821     CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled, &rstr_qf, request));
2822     CeedCall(CeedElemRestrictionGetELayout(rstr_qf, layout));
2823     CeedCall(CeedElemRestrictionDestroy(&rstr_qf));
2824     CeedCall(CeedVectorNorm(assembled, CEED_NORM_MAX, &max_norm));
2825 
2826     // Calculate element averages
2827     CeedCall(CeedVectorCreate(ceed_parent, num_qpts, &q_weight));
2828     CeedCall(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, q_weight));
2829     CeedCall(CeedVectorGetArrayRead(assembled, CEED_MEM_HOST, &assembled_array));
2830     CeedCall(CeedVectorGetArrayRead(q_weight, CEED_MEM_HOST, &q_weight_array));
2831     CeedCall(CeedCalloc(num_elem, &elem_avg));
2832     const CeedScalar qf_value_bound = max_norm * 100 * CEED_EPSILON;
2833 
2834     for (CeedInt e = 0; e < num_elem; e++) {
2835       CeedInt count = 0;
2836 
2837       for (CeedInt q = 0; q < num_qpts; q++) {
2838         for (CeedInt i = 0; i < num_comp * num_comp * num_modes * num_modes; i++) {
2839           if (fabs(assembled_array[q * layout[0] + i * layout[1] + e * layout[2]]) > qf_value_bound) {
2840             elem_avg[e] += assembled_array[q * layout[0] + i * layout[1] + e * layout[2]] / q_weight_array[q];
2841             count++;
2842           }
2843         }
2844       }
2845       if (count) {
2846         elem_avg[e] /= count;
2847       } else {
2848         elem_avg[e] = 1.0;
2849       }
2850     }
2851     CeedCall(CeedVectorRestoreArrayRead(assembled, &assembled_array));
2852     CeedCall(CeedVectorDestroy(&assembled));
2853     CeedCall(CeedVectorRestoreArrayRead(q_weight, &q_weight_array));
2854     CeedCall(CeedVectorDestroy(&q_weight));
2855   }
2856 
2857   // Build FDM diagonal
2858   {
2859     CeedScalar *q_data_array, *fdm_diagonal;
2860 
2861     CeedCall(CeedCalloc(num_comp * num_nodes, &fdm_diagonal));
2862     const CeedScalar fdm_diagonal_bound = num_nodes * CEED_EPSILON;
2863     for (CeedInt c = 0; c < num_comp; c++) {
2864       for (CeedInt n = 0; n < num_nodes; n++) {
2865         if (interp) fdm_diagonal[c * num_nodes + n] = 1.0;
2866         if (grad) {
2867           for (CeedInt d = 0; d < dim; d++) {
2868             CeedInt i = (n / CeedIntPow(P_1d, d)) % P_1d;
2869             fdm_diagonal[c * num_nodes + n] += lambda[i];
2870           }
2871         }
2872         if (fabs(fdm_diagonal[c * num_nodes + n]) < fdm_diagonal_bound) fdm_diagonal[c * num_nodes + n] = fdm_diagonal_bound;
2873       }
2874     }
2875     CeedCall(CeedVectorCreate(ceed_parent, num_elem * num_comp * num_nodes, &q_data));
2876     CeedCall(CeedVectorSetValue(q_data, 0.0));
2877     CeedCall(CeedVectorGetArrayWrite(q_data, CEED_MEM_HOST, &q_data_array));
2878     for (CeedInt e = 0; e < num_elem; e++) {
2879       for (CeedInt c = 0; c < num_comp; c++) {
2880         for (CeedInt n = 0; n < num_nodes; n++) {
2881           q_data_array[(e * num_comp + c) * num_nodes + n] = 1. / (elem_avg[e] * fdm_diagonal[c * num_nodes + n]);
2882         }
2883       }
2884     }
2885     CeedCall(CeedFree(&elem_avg));
2886     CeedCall(CeedFree(&fdm_diagonal));
2887     CeedCall(CeedVectorRestoreArray(q_data, &q_data_array));
2888   }
2889 
2890   // Setup FDM operator
2891   // -- Basis
2892   {
2893     CeedScalar *grad_dummy, *q_ref_dummy, *q_weight_dummy;
2894 
2895     CeedCall(CeedCalloc(P_1d * P_1d, &grad_dummy));
2896     CeedCall(CeedCalloc(P_1d, &q_ref_dummy));
2897     CeedCall(CeedCalloc(P_1d, &q_weight_dummy));
2898     CeedCall(CeedBasisCreateTensorH1(ceed_parent, dim, num_comp, P_1d, P_1d, fdm_interp, grad_dummy, q_ref_dummy, q_weight_dummy, &fdm_basis));
2899     CeedCall(CeedFree(&fdm_interp));
2900     CeedCall(CeedFree(&grad_dummy));
2901     CeedCall(CeedFree(&q_ref_dummy));
2902     CeedCall(CeedFree(&q_weight_dummy));
2903     CeedCall(CeedFree(&lambda));
2904   }
2905 
2906   // -- Restriction
2907   {
2908     CeedInt strides[3] = {1, num_nodes, num_nodes * num_comp};
2909     CeedCall(CeedElemRestrictionCreateStrided(ceed_parent, num_elem, num_nodes, num_comp,
2910                                               (CeedSize)num_elem * (CeedSize)num_comp * (CeedSize)num_nodes, strides, &rstr_qd_i));
2911   }
2912 
2913   // -- QFunction
2914   CeedCall(CeedQFunctionCreateInteriorByName(ceed_parent, "Scale", &qf_fdm));
2915   CeedCall(CeedQFunctionAddInput(qf_fdm, "input", num_comp, CEED_EVAL_INTERP));
2916   CeedCall(CeedQFunctionAddInput(qf_fdm, "scale", num_comp, CEED_EVAL_NONE));
2917   CeedCall(CeedQFunctionAddOutput(qf_fdm, "output", num_comp, CEED_EVAL_INTERP));
2918   CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_fdm, num_comp));
2919 
2920   // -- QFunction context
2921   {
2922     CeedInt *num_comp_data;
2923 
2924     CeedCall(CeedCalloc(1, &num_comp_data));
2925     num_comp_data[0] = num_comp;
2926     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_fdm));
2927     CeedCall(CeedQFunctionContextSetData(ctx_fdm, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_data), num_comp_data));
2928   }
2929   CeedCall(CeedQFunctionSetContext(qf_fdm, ctx_fdm));
2930   CeedCall(CeedQFunctionContextDestroy(&ctx_fdm));
2931 
2932   // -- Operator
2933   CeedCall(CeedOperatorCreate(ceed_parent, qf_fdm, NULL, NULL, fdm_inv));
2934   CeedCall(CeedOperatorSetField(*fdm_inv, "input", rstr, fdm_basis, CEED_VECTOR_ACTIVE));
2935   CeedCall(CeedOperatorSetField(*fdm_inv, "scale", rstr_qd_i, CEED_BASIS_NONE, q_data));
2936   CeedCall(CeedOperatorSetField(*fdm_inv, "output", rstr, fdm_basis, CEED_VECTOR_ACTIVE));
2937 
2938   // Cleanup
2939   CeedCall(CeedVectorDestroy(&q_data));
2940   CeedCall(CeedElemRestrictionDestroy(&rstr));
2941   CeedCall(CeedElemRestrictionDestroy(&rstr_qd_i));
2942   CeedCall(CeedBasisDestroy(&basis));
2943   CeedCall(CeedBasisDestroy(&fdm_basis));
2944   CeedCall(CeedQFunctionDestroy(&qf_fdm));
2945   return CEED_ERROR_SUCCESS;
2946 }
2947 
2948 /// @}
2949