1 // Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at 2 // the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights 3 // reserved. See files LICENSE and NOTICE for details. 4 // 5 // This file is part of CEED, a collection of benchmarks, miniapps, software 6 // libraries and APIs for efficient high-order finite element and spectral 7 // element discretizations for exascale applications. For more information and 8 // source code availability see http://github.com/ceed. 9 // 10 // The CEED research is supported by the Exascale Computing Project 17-SC-20-SC, 11 // a collaborative effort of two U.S. Department of Energy organizations (Office 12 // of Science and the National Nuclear Security Administration) responsible for 13 // the planning and preparation of a capable exascale ecosystem, including 14 // software, applications, hardware, advanced system engineering and early 15 // testbed platforms, in support of the nation's exascale computing imperative. 16 17 /// @file 18 /// MFEM diffusion operator based on libCEED 19 20 #include <ceed.h> 21 #include <mfem.hpp> 22 23 /// A structure used to pass additional data to f_build_diff and f_apply_diff 24 struct DiffContext { CeedInt dim, space_dim; }; 25 26 /// libCEED Q-function for building quadrature data for a diffusion operator 27 static int f_build_diff(void *ctx, void *qdata, CeedInt Q, 28 const CeedScalar *const *u, CeedScalar *const *v) { 29 // u[1] is Jacobians, size (Q x nc x dim) with column-major layout 30 // u[4] is quadrature weights, size (Q) 31 // 32 // At every quadrature point, compute qw/det(J).adj(J).adj(J)^T and store 33 // the symmetric part of the result. 34 DiffContext *dc = (DiffContext*)ctx; 35 CeedScalar *qd = (CeedScalar*)qdata; 36 const CeedScalar *J = u[1], *qw = u[4]; 37 switch (dc->dim + 10*dc->space_dim) { 38 case 11: 39 for (CeedInt i=0; i<Q; i++) { 40 qd[i] = qw[i] / J[i]; 41 } 42 break; 43 case 22: 44 for (CeedInt i=0; i<Q; i++) { 45 // J: 0 2 qd: 0 1 adj(J): J22 -J12 46 // 1 3 1 2 -J21 J11 47 const CeedScalar J11 = J[i+Q*0]; 48 const CeedScalar J21 = J[i+Q*1]; 49 const CeedScalar J12 = J[i+Q*2]; 50 const CeedScalar J22 = J[i+Q*3]; 51 const CeedScalar w = qw[i] / (J11*J22 - J21*J12); 52 qd[i+Q*0] = w * (J12*J12 + J22*J22); 53 qd[i+Q*1] = - w * (J11*J12 + J21*J22); 54 qd[i+Q*2] = w * (J11*J11 + J21*J21); 55 } 56 break; 57 case 33: 58 for (CeedInt i=0; i<Q; i++) { 59 // J: 0 3 6 qd: 0 1 2 60 // 1 4 7 1 3 4 61 // 2 5 8 2 4 5 62 const CeedScalar J11 = J[i+Q*0]; 63 const CeedScalar J21 = J[i+Q*1]; 64 const CeedScalar J31 = J[i+Q*2]; 65 const CeedScalar J12 = J[i+Q*3]; 66 const CeedScalar J22 = J[i+Q*4]; 67 const CeedScalar J32 = J[i+Q*5]; 68 const CeedScalar J13 = J[i+Q*6]; 69 const CeedScalar J23 = J[i+Q*7]; 70 const CeedScalar J33 = J[i+Q*8]; 71 const CeedScalar A11 = J22*J33 - J23*J32; 72 const CeedScalar A12 = J13*J32 - J12*J33; 73 const CeedScalar A13 = J12*J23 - J13*J22; 74 const CeedScalar A21 = J23*J31 - J21*J33; 75 const CeedScalar A22 = J11*J33 - J13*J31; 76 const CeedScalar A23 = J13*J21 - J11*J23; 77 const CeedScalar A31 = J21*J32 - J22*J31; 78 const CeedScalar A32 = J12*J31 - J11*J32; 79 const CeedScalar A33 = J11*J22 - J12*J21; 80 const CeedScalar w = qw[i] / (J11*A11 + J21*A12 + J31*A13); 81 qd[i+Q*0] = w * (A11*A11 + A12*A12 + A13*A13); 82 qd[i+Q*1] = w * (A11*A21 + A12*A22 + A13*A23); 83 qd[i+Q*2] = w * (A11*A31 + A12*A32 + A13*A33); 84 qd[i+Q*3] = w * (A21*A21 + A22*A22 + A23*A23); 85 qd[i+Q*4] = w * (A21*A31 + A22*A32 + A23*A33); 86 qd[i+Q*5] = w * (A31*A31 + A32*A32 + A33*A33); 87 } 88 break; 89 default: 90 return CeedError(NULL, 1, "dim=%d, space_dim=%d is not supported", 91 dc->dim, dc->space_dim); 92 } 93 return 0; 94 } 95 96 /// libCEED Q-function for applying a diff operator 97 static int f_apply_diff(void *ctx, void *qdata, CeedInt Q, 98 const CeedScalar *const *u, CeedScalar *const *v) { 99 DiffContext *dc = (DiffContext*)ctx; 100 const CeedScalar *qd = (const CeedScalar*)qdata; 101 // u[1], v[1]: size: (Q x nc x dim) with column-major layout (nc == 1) 102 const CeedScalar *ug = u[1]; 103 CeedScalar *vg = v[1]; 104 switch (dc->dim) { 105 case 1: 106 for (CeedInt i=0; i<Q; i++) { 107 vg[i] = ug[i] * qd[i]; 108 } 109 break; 110 case 2: 111 for (CeedInt i=0; i<Q; i++) { 112 const CeedScalar ug0 = ug[i+Q*0]; 113 const CeedScalar ug1 = ug[i+Q*1]; 114 vg[i+Q*0] = qd[i+Q*0]*ug0 + qd[i+Q*1]*ug1; 115 vg[i+Q*1] = qd[i+Q*1]*ug0 + qd[i+Q*2]*ug1; 116 } 117 break; 118 case 3: 119 for (CeedInt i=0; i<Q; i++) { 120 const CeedScalar ug0 = ug[i+Q*0]; 121 const CeedScalar ug1 = ug[i+Q*1]; 122 const CeedScalar ug2 = ug[i+Q*2]; 123 vg[i+Q*0] = qd[i+Q*0]*ug0 + qd[i+Q*1]*ug1 + qd[i+Q*2]*ug2; 124 vg[i+Q*1] = qd[i+Q*1]*ug0 + qd[i+Q*3]*ug1 + qd[i+Q*4]*ug2; 125 vg[i+Q*2] = qd[i+Q*2]*ug0 + qd[i+Q*4]*ug1 + qd[i+Q*5]*ug2; 126 } 127 break; 128 default: 129 return CeedError(NULL, 1, "topo_dim=%d is not supported", dc->dim); 130 } 131 return 0; 132 } 133 134 /// Wrapper for a diffusion CeedOperator as an mfem::Operator 135 class CeedDiffusionOperator : public mfem::Operator { 136 protected: 137 const mfem::FiniteElementSpace *fes; 138 CeedOperator build_oper, oper; 139 CeedBasis basis, mesh_basis; 140 CeedElemRestriction restr, mesh_restr; 141 CeedQFunction apply_qfunc, build_qfunc; 142 CeedVector node_coords, qdata; 143 144 DiffContext diff_ctx; 145 146 CeedVector u, v; 147 148 static void FESpace2Ceed(const mfem::FiniteElementSpace *fes, 149 const mfem::IntegrationRule &ir, 150 Ceed ceed, CeedBasis *basis, 151 CeedElemRestriction *restr) { 152 mfem::Mesh *mesh = fes->GetMesh(); 153 const mfem::FiniteElement *fe = fes->GetFE(0); 154 const int order = fes->GetOrder(0); 155 mfem::Array<int> dof_map; 156 switch (mesh->Dimension()) { 157 case 1: { 158 const mfem::H1_SegmentElement *h1_fe = 159 dynamic_cast<const mfem::H1_SegmentElement*>(fe); 160 MFEM_VERIFY(h1_fe, "invalid FE"); 161 h1_fe->GetDofMap().Copy(dof_map); 162 break; 163 } 164 case 2: { 165 const mfem::H1_QuadrilateralElement *h1_fe = 166 dynamic_cast<const mfem::H1_QuadrilateralElement*>(fe); 167 MFEM_VERIFY(h1_fe, "invalid FE"); 168 h1_fe->GetDofMap().Copy(dof_map); 169 break; 170 } 171 case 3: { 172 const mfem::H1_HexahedronElement *h1_fe = 173 dynamic_cast<const mfem::H1_HexahedronElement*>(fe); 174 MFEM_VERIFY(h1_fe, "invalid FE"); 175 h1_fe->GetDofMap().Copy(dof_map); 176 break; 177 } 178 } 179 const mfem::FiniteElement *fe1d = 180 fes->FEColl()->FiniteElementForGeometry(mfem::Geometry::SEGMENT); 181 mfem::DenseMatrix shape1d(fe1d->GetDof(), ir.GetNPoints()); 182 mfem::DenseMatrix grad1d(fe1d->GetDof(), ir.GetNPoints()); 183 mfem::Vector qref1d(ir.GetNPoints()), qweight1d(ir.GetNPoints()); 184 mfem::Vector shape_i(shape1d.Height()); 185 mfem::DenseMatrix grad_i(grad1d.Height(), 1); 186 const mfem::H1_SegmentElement *h1_fe1d = 187 dynamic_cast<const mfem::H1_SegmentElement*>(fe1d); 188 MFEM_VERIFY(h1_fe1d, "invalid FE"); 189 const mfem::Array<int> &dof_map_1d = h1_fe1d->GetDofMap(); 190 for (int i = 0; i < ir.GetNPoints(); i++) { 191 const mfem::IntegrationPoint &ip = ir.IntPoint(i); 192 qref1d(i) = ip.x; 193 qweight1d(i) = ip.weight; 194 fe1d->CalcShape(ip, shape_i); 195 fe1d->CalcDShape(ip, grad_i); 196 for (int j = 0; j < shape1d.Height(); j++) { 197 shape1d(j,i) = shape_i(dof_map_1d[j]); 198 grad1d(j,i) = grad_i(dof_map_1d[j],0); 199 } 200 } 201 CeedBasisCreateTensorH1(ceed, mesh->Dimension(), fes->GetVDim(), order+1, 202 ir.GetNPoints(), shape1d.GetData(), 203 grad1d.GetData(), qref1d.GetData(), 204 qweight1d.GetData(), basis); 205 206 const mfem::Table &el_dof = fes->GetElementToDofTable(); 207 mfem::Array<int> tp_el_dof(el_dof.Size_of_connections()); 208 for (int i = 0; i < mesh->GetNE(); i++) { 209 const int el_offset = fe->GetDof()*i; 210 for (int j = 0; j < fe->GetDof(); j++) { 211 tp_el_dof[j + el_offset] = el_dof.GetJ()[dof_map[j] + el_offset]; 212 } 213 } 214 CeedElemRestrictionCreate(ceed, mesh->GetNE(), fe->GetDof(), 215 fes->GetNDofs(), CEED_MEM_HOST, CEED_COPY_VALUES, 216 tp_el_dof.GetData(), restr); 217 } 218 219 public: 220 /// Constructor. Assumes @a fes is a scalar FE space. 221 CeedDiffusionOperator(Ceed ceed, const mfem::FiniteElementSpace *fes) 222 : Operator(fes->GetNDofs()), 223 fes(fes) { 224 mfem::Mesh *mesh = fes->GetMesh(); 225 const int order = fes->GetOrder(0); 226 const int ir_order = 2*(order + 2) - 1; // <----- 227 const mfem::IntegrationRule &ir = 228 mfem::IntRules.Get(mfem::Geometry::SEGMENT, ir_order); 229 230 FESpace2Ceed(fes, ir, ceed, &basis, &restr); 231 232 const mfem::FiniteElementSpace *mesh_fes = mesh->GetNodalFESpace(); 233 MFEM_VERIFY(mesh_fes, "the Mesh has no nodal FE space"); 234 FESpace2Ceed(mesh_fes, ir, ceed, &mesh_basis, &mesh_restr); 235 236 CeedVectorCreate(ceed, mesh->GetNodes()->Size(), &node_coords); 237 CeedVectorSetArray(node_coords, CEED_MEM_HOST, CEED_USE_POINTER, 238 mesh->GetNodes()->GetData()); 239 240 const int dim = mesh->Dimension(); 241 diff_ctx.dim = dim; 242 diff_ctx.space_dim = mesh->SpaceDimension(); 243 244 const int qsize = dim*(dim+1)/2; 245 CeedQFunctionCreateInterior(ceed, 1, 1, qsize*sizeof(CeedScalar), 246 (CeedEvalMode)(CEED_EVAL_GRAD|CEED_EVAL_WEIGHT), 247 CEED_EVAL_NONE, f_build_diff, 248 __FILE__":f_build_diff", &build_qfunc); 249 CeedQFunctionSetContext(build_qfunc, &diff_ctx, sizeof(diff_ctx)); 250 CeedOperatorCreate(ceed, mesh_restr, mesh_basis, build_qfunc, NULL, NULL, 251 &build_oper); 252 CeedOperatorGetQData(build_oper, &qdata); 253 CeedOperatorApply(build_oper, qdata, node_coords, NULL, 254 CEED_REQUEST_IMMEDIATE); 255 256 CeedQFunctionCreateInterior(ceed, 1, 1, qsize*sizeof(CeedScalar), 257 CEED_EVAL_GRAD, CEED_EVAL_GRAD, f_apply_diff, 258 __FILE__":f_apply_diff", &apply_qfunc); 259 CeedQFunctionSetContext(apply_qfunc, &diff_ctx, sizeof(diff_ctx)); 260 CeedOperatorCreate(ceed, restr, basis, apply_qfunc, NULL, NULL, &oper); 261 262 CeedVectorCreate(ceed, fes->GetNDofs(), &u); 263 CeedVectorCreate(ceed, fes->GetNDofs(), &v); 264 } 265 266 /// Destructor 267 ~CeedDiffusionOperator() { 268 CeedVectorDestroy(&v); 269 CeedVectorDestroy(&u); 270 CeedOperatorDestroy(&oper); 271 CeedQFunctionDestroy(&apply_qfunc); 272 // qdata is owned by build_oper 273 CeedOperatorDestroy(&build_oper); 274 CeedQFunctionDestroy(&build_qfunc); 275 CeedVectorDestroy(&node_coords); 276 CeedElemRestrictionDestroy(&mesh_restr); 277 CeedBasisDestroy(&mesh_basis); 278 CeedElemRestrictionDestroy(&restr); 279 CeedBasisDestroy(&basis); 280 } 281 282 /// Operator action 283 virtual void Mult(const mfem::Vector &x, mfem::Vector &y) const { 284 CeedVectorSetArray(u, CEED_MEM_HOST, CEED_USE_POINTER, x.GetData()); 285 CeedVectorSetArray(v, CEED_MEM_HOST, CEED_USE_POINTER, y.GetData()); 286 287 CeedOperatorApply(oper, qdata, u, v, CEED_REQUEST_IMMEDIATE); 288 } 289 }; 290