1 // SPDX-FileCopyrightText: Copyright (c) 2017-2024, HONEE contributors. 2 // SPDX-License-Identifier: Apache-2.0 OR BSD-2-Clause 3 #pragma once 4 5 #include <ceed/types.h> 6 #ifndef CEED_RUNNING_JIT_PASS 7 #include <math.h> 8 #endif 9 10 #ifndef M_PI 11 #define M_PI 3.14159265358979323846 12 #endif 13 14 CEED_QFUNCTION_HELPER CeedScalar Max(CeedScalar a, CeedScalar b) { return a < b ? b : a; } 15 CEED_QFUNCTION_HELPER CeedScalar Min(CeedScalar a, CeedScalar b) { return a < b ? a : b; } 16 17 CEED_QFUNCTION_HELPER void SwapScalar(CeedScalar *a, CeedScalar *b) { 18 CeedScalar temp = *a; 19 *a = *b; 20 *b = temp; 21 } 22 23 CEED_QFUNCTION_HELPER CeedScalar Square(CeedScalar x) { return x * x; } 24 CEED_QFUNCTION_HELPER CeedScalar Cube(CeedScalar x) { return x * x * x; } 25 26 // @brief Scale vector of length N by scalar alpha 27 CEED_QFUNCTION_HELPER void ScaleN(CeedScalar *u, const CeedScalar alpha, const CeedInt N) { 28 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) u[i] *= alpha; 29 } 30 31 // @brief Set vector of length N to a value alpha 32 CEED_QFUNCTION_HELPER void SetValueN(CeedScalar *u, const CeedScalar alpha, const CeedInt N) { 33 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) u[i] = alpha; 34 } 35 36 // @brief Copy N elements from x to y 37 CEED_QFUNCTION_HELPER void CopyN(const CeedScalar *x, CeedScalar *y, const CeedInt N) { CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) y[i] = x[i]; } 38 39 // @brief Copy 3x3 matrix from A to B 40 CEED_QFUNCTION_HELPER void CopyMat3(const CeedScalar A[3][3], CeedScalar B[3][3]) { CopyN((const CeedScalar *)A, (CeedScalar *)B, 9); } 41 42 // @brief Dot product of vectors with N elements 43 CEED_QFUNCTION_HELPER CeedScalar DotN(const CeedScalar *u, const CeedScalar *v, const CeedInt N) { 44 CeedScalar output = 0; 45 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) output += u[i] * v[i]; 46 return output; 47 } 48 49 // @brief y = \alpha x + y 50 CEED_QFUNCTION_HELPER void AXPY(CeedScalar alpha, const CeedScalar *x, CeedScalar *y, CeedInt N) { 51 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) y[i] += alpha * x[i]; 52 } 53 54 // @brief Dot product of 3 element vectors 55 CEED_QFUNCTION_HELPER CeedScalar Dot3(const CeedScalar *u, const CeedScalar *v) { return u[0] * v[0] + u[1] * v[1] + u[2] * v[2]; } 56 57 // @brief Dot product of 2 element vectors 58 CEED_QFUNCTION_HELPER CeedScalar Dot2(const CeedScalar *u, const CeedScalar *v) { return u[0] * v[0] + u[1] * v[1]; } 59 60 // @brief \ell^2 norm of 3 element vectors 61 CEED_QFUNCTION_HELPER CeedScalar Norm3(const CeedScalar *u) { return sqrt(u[0] * u[0] + u[1] * u[1] + u[2] * u[2]); } 62 63 // @brief \ell^2 norm of 2 element vectors 64 CEED_QFUNCTION_HELPER CeedScalar Norm2(const CeedScalar *u) { return sqrt(u[0] * u[0] + u[1] * u[1]); } 65 66 // @brief Cross product of vectors with 3 elements 67 CEED_QFUNCTION_HELPER void Cross3(const CeedScalar u[3], const CeedScalar v[3], CeedScalar w[3]) { 68 w[0] = (u[1] * v[2]) - (u[2] * v[1]); 69 w[1] = (u[2] * v[0]) - (u[0] * v[2]); 70 w[2] = (u[0] * v[1]) - (u[1] * v[0]); 71 } 72 73 // @brief Curl of vector given its gradient 74 CEED_QFUNCTION_HELPER void Curl3(const CeedScalar gradient[3][3], CeedScalar v[3]) { 75 v[0] = gradient[2][1] - gradient[1][2]; 76 v[1] = gradient[0][2] - gradient[2][0]; 77 v[2] = gradient[1][0] - gradient[0][1]; 78 } 79 80 // @brief Matrix vector product, b = Ax + b. A is NxM, x is M, b is N 81 CEED_QFUNCTION_HELPER void MatVecNM(const CeedScalar *A, const CeedScalar *x, const CeedInt N, const CeedInt M, const CeedTransposeMode transpose_A, 82 CeedScalar *b) { 83 switch (transpose_A) { 84 case CEED_NOTRANSPOSE: 85 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) b[i] += DotN(&A[i * M], x, M); 86 break; 87 case CEED_TRANSPOSE: 88 CeedPragmaSIMD for (CeedInt i = 0; i < M; i++) { CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) b[i] += A[j * M + i] * x[j]; } 89 break; 90 } 91 } 92 93 // @brief 3x3 Matrix vector product b = Ax + b. 94 CEED_QFUNCTION_HELPER void MatVec3(const CeedScalar A[3][3], const CeedScalar x[3], const CeedTransposeMode transpose_A, CeedScalar b[3]) { 95 MatVecNM((const CeedScalar *)A, (const CeedScalar *)x, 3, 3, transpose_A, (CeedScalar *)b); 96 } 97 98 // @brief 2x2 Matrix vector product b = Ax + b. 99 CEED_QFUNCTION_HELPER void MatVec2(const CeedScalar A[2][2], const CeedScalar x[2], const CeedTransposeMode transpose_A, CeedScalar b[2]) { 100 MatVecNM((const CeedScalar *)A, (const CeedScalar *)x, 2, 2, transpose_A, (CeedScalar *)b); 101 } 102 103 // @brief Matrix-Matrix product, B = DA + B, where D is diagonal. 104 // @details A is NxM, D is diagonal NxN, represented by a vector of length N, and B is NxM. Optionally, A may be transposed. 105 CEED_QFUNCTION_HELPER void MatDiagNM(const CeedScalar *A, const CeedScalar *D, const CeedInt N, const CeedInt M, const CeedTransposeMode transpose_A, 106 CeedScalar *B) { 107 switch (transpose_A) { 108 case CEED_NOTRANSPOSE: 109 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) { CeedPragmaSIMD for (CeedInt j = 0; j < M; j++) B[i * M + j] += D[i] * A[i * M + j]; } 110 break; 111 case CEED_TRANSPOSE: 112 CeedPragmaSIMD for (CeedInt i = 0; i < M; i++) { CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) B[i * N + j] += D[i] * A[j * M + i]; } 113 break; 114 } 115 } 116 117 // @brief 3x3 Matrix-Matrix product, B = DA + B, where D is diagonal. 118 // @details Optionally, A may be transposed. 119 CEED_QFUNCTION_HELPER void MatDiag3(const CeedScalar A[3][3], const CeedScalar D[3], const CeedTransposeMode transpose_A, CeedScalar B[3][3]) { 120 MatDiagNM((const CeedScalar *)A, (const CeedScalar *)D, 3, 3, transpose_A, (CeedScalar *)B); 121 } 122 // @brief NxN Matrix-Matrix product, C = AB + C 123 CEED_QFUNCTION_HELPER void MatMatN(const CeedScalar *A, const CeedScalar *B, const CeedInt N, const CeedTransposeMode transpose_A, 124 const CeedTransposeMode transpose_B, CeedScalar *C) { 125 switch (transpose_A) { 126 case CEED_NOTRANSPOSE: 127 switch (transpose_B) { 128 case CEED_NOTRANSPOSE: 129 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) { 130 CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) { 131 CeedPragmaSIMD for (CeedInt k = 0; k < N; k++) C[i * N + j] += A[i * N + k] * B[k * N + j]; 132 } 133 } 134 break; 135 case CEED_TRANSPOSE: 136 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) { 137 CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) { 138 CeedPragmaSIMD for (CeedInt k = 0; k < N; k++) C[i * N + j] += A[i * N + k] * B[j * N + k]; 139 } 140 } 141 break; 142 } 143 break; 144 case CEED_TRANSPOSE: 145 switch (transpose_B) { 146 case CEED_NOTRANSPOSE: 147 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) { 148 CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) { 149 CeedPragmaSIMD for (CeedInt k = 0; k < N; k++) C[i * N + j] += A[k * N + i] * B[k * N + j]; 150 } 151 } 152 break; 153 case CEED_TRANSPOSE: 154 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) { 155 CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) { 156 CeedPragmaSIMD for (CeedInt k = 0; k < N; k++) C[i * N + j] += A[k * N + i] * B[j * N + k]; 157 } 158 } 159 break; 160 } 161 break; 162 } 163 } 164 165 // @brief 3x3 Matrix-Matrix product, C = AB + C 166 CEED_QFUNCTION_HELPER void MatMat3(const CeedScalar A[3][3], const CeedScalar B[3][3], const CeedTransposeMode transpose_A, 167 const CeedTransposeMode transpose_B, CeedScalar C[3][3]) { 168 MatMatN((const CeedScalar *)A, (const CeedScalar *)B, 3, transpose_A, transpose_B, (CeedScalar *)C); 169 } 170 171 // @brief 2x2 Matrix-Matrix product, C = AB + C 172 CEED_QFUNCTION_HELPER void MatMat2(const CeedScalar A[2][2], const CeedScalar B[2][2], const CeedTransposeMode transpose_A, 173 const CeedTransposeMode transpose_B, CeedScalar C[2][2]) { 174 MatMatN((const CeedScalar *)A, (const CeedScalar *)B, 2, transpose_A, transpose_B, (CeedScalar *)C); 175 } 176 177 /** 178 * @brief Calculate inverse of 2x2 matrix 179 * 180 * @param[in] A Input matrix 181 * @param[out] detJ_ptr Determinate of A, may be NULL is not desired 182 * @param[out] A_inv Output matrix inverse 183 */ 184 CEED_QFUNCTION_HELPER void MatInv2(const CeedScalar A[2][2], CeedScalar A_inv[2][2], CeedScalar *detJ_ptr) { 185 const CeedScalar detJ = A[0][0] * A[1][1] - A[1][0] * A[0][1]; 186 187 A_inv[0][0] = A[1][1] / detJ; 188 A_inv[0][1] = -A[0][1] / detJ; 189 A_inv[1][0] = -A[1][0] / detJ; 190 A_inv[1][1] = A[0][0] / detJ; 191 if (detJ_ptr) *detJ_ptr = detJ; 192 } 193 194 /** 195 * @brief Calculate inverse of 3x3 matrix 196 * 197 * @param[in] A Input matrix 198 * @param[out] detJ_ptr Determinate of A, may be NULL is not desired 199 * @param[out] A_inv Output matrix inverse 200 */ 201 CEED_QFUNCTION_HELPER void MatInv3(const CeedScalar A[3][3], CeedScalar A_inv[3][3], CeedScalar *detJ_ptr) { 202 // Compute Adjugate of dxdX 203 A_inv[0][0] = A[1][1] * A[2][2] - A[1][2] * A[2][1]; 204 A_inv[0][1] = A[0][2] * A[2][1] - A[0][1] * A[2][2]; 205 A_inv[0][2] = A[0][1] * A[1][2] - A[0][2] * A[1][1]; 206 A_inv[1][0] = A[1][2] * A[2][0] - A[1][0] * A[2][2]; 207 A_inv[1][1] = A[0][0] * A[2][2] - A[0][2] * A[2][0]; 208 A_inv[1][2] = A[0][2] * A[1][0] - A[0][0] * A[1][2]; 209 A_inv[2][0] = A[1][0] * A[2][1] - A[1][1] * A[2][0]; 210 A_inv[2][1] = A[0][1] * A[2][0] - A[0][0] * A[2][1]; 211 A_inv[2][2] = A[0][0] * A[1][1] - A[0][1] * A[1][0]; 212 213 const CeedScalar detJ = A[0][0] * A_inv[0][0] + A[1][0] * A_inv[0][1] + A[2][0] * A_inv[0][2]; 214 ScaleN((CeedScalar *)A_inv, 1 / detJ, 9); 215 if (detJ_ptr) *detJ_ptr = detJ; 216 } 217 218 /** 219 @brief MxN Matrix-Matrix product, C = AB + C 220 221 C is NxM, A is NxP, B is PxM 222 223 @param[in] mat_A Row-major matrix `A` 224 @param[in] mat_B Row-major matrix `B` 225 @param[out] mat_C Row-major output matrix `C` 226 @param[in] N Number of rows of `C` 227 @param[in] M Number of columns of `C` 228 @param[in] P Number of columns of `A`/rows of `B` 229 **/ 230 CEED_QFUNCTION_HELPER void MatMatNM(const CeedScalar *mat_A, const CeedScalar *mat_B, CeedScalar *mat_C, CeedInt N, CeedInt M, CeedInt P) { 231 for (CeedInt i = 0; i < N; i++) { 232 for (CeedInt j = 0; j < M; j++) { 233 for (CeedInt k = 0; k < P; k++) mat_C[i * M + j] += mat_A[i * P + k] * mat_B[k * M + j]; 234 } 235 } 236 } 237 238 // @brief Unpack Kelvin-Mandel notation symmetric tensor into full tensor 239 CEED_QFUNCTION_HELPER void KMUnpack(const CeedScalar v[6], CeedScalar A[3][3]) { 240 const CeedScalar weight = 1 / sqrt(2.); 241 A[0][0] = v[0]; 242 A[1][1] = v[1]; 243 A[2][2] = v[2]; 244 A[2][1] = A[1][2] = weight * v[3]; 245 A[2][0] = A[0][2] = weight * v[4]; 246 A[1][0] = A[0][1] = weight * v[5]; 247 } 248 249 // @brief Pack full tensor into Kelvin-Mandel notation symmetric tensor 250 CEED_QFUNCTION_HELPER void KMPack(const CeedScalar A[3][3], CeedScalar v[6]) { 251 const CeedScalar weight = sqrt(2.); 252 v[0] = A[0][0]; 253 v[1] = A[1][1]; 254 v[2] = A[2][2]; 255 v[3] = A[2][1] * weight; 256 v[4] = A[2][0] * weight; 257 v[5] = A[1][0] * weight; 258 } 259 260 // @brief Calculate metric tensor from mapping, g_{ij} = xi_{k,i} xi_{k,j} = dXdx^T dXdx 261 CEED_QFUNCTION_HELPER void KMMetricTensor(const CeedScalar dXdx[3][3], CeedScalar km_g_ij[6]) { 262 CeedScalar g_ij[3][3] = {{0.}}; 263 MatMat3(dXdx, dXdx, CEED_TRANSPOSE, CEED_NOTRANSPOSE, g_ij); 264 KMPack(g_ij, km_g_ij); 265 } 266 267 // @brief Linear ramp evaluation 268 CEED_QFUNCTION_HELPER CeedScalar LinearRampCoefficient(CeedScalar amplitude, CeedScalar length, CeedScalar start, CeedScalar x) { 269 if (x < start) { 270 return amplitude; 271 } else if (x < start + length) { 272 return amplitude * ((x - start) * (-1 / length) + 1); 273 } else { 274 return 0; 275 } 276 } 277 278 /** 279 @brief Pack stored values at quadrature point 280 281 @param[in] Q Number of quadrature points 282 @param[in] i Current quadrature point 283 @param[in] start Starting index to store components 284 @param[in] num_comp Number of components to store 285 @param[in] values_at_qpnt Local values for quadrature point i 286 @param[out] stored Stored values 287 288 @return An error code: 0 - success, otherwise - failure 289 **/ 290 CEED_QFUNCTION_HELPER int StoredValuesPack(CeedInt Q, CeedInt i, CeedInt start, CeedInt num_comp, const CeedScalar *values_at_qpnt, 291 CeedScalar *stored) { 292 for (CeedInt j = 0; j < num_comp; j++) stored[(start + j) * Q + i] = values_at_qpnt[j]; 293 294 return CEED_ERROR_SUCCESS; 295 } 296 297 /** 298 @brief Unpack stored values at quadrature point 299 300 @param[in] Q Number of quadrature points 301 @param[in] i Current quadrature point 302 @param[in] start Starting index to store components 303 @param[in] num_comp Number of components to store 304 @param[in] stored Stored values 305 @param[out] values_at_qpnt Local values for quadrature point i 306 307 @return An error code: 0 - success, otherwise - failure 308 **/ 309 CEED_QFUNCTION_HELPER int StoredValuesUnpack(CeedInt Q, CeedInt i, CeedInt start, CeedInt num_comp, const CeedScalar *stored, 310 CeedScalar *values_at_qpnt) { 311 for (CeedInt j = 0; j < num_comp; j++) values_at_qpnt[j] = stored[(start + j) * Q + i]; 312 313 return CEED_ERROR_SUCCESS; 314 } 315 316 /** 317 @brief Unpack N-D element q_data at quadrature point 318 319 @param[in] dim Dimension of the element 320 @param[in] Q Number of quadrature points 321 @param[in] i Current quadrature point 322 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:Setup`) 323 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian, or `NULL` 324 @param[out] dXdx Inverse of the mapping Jacobian (shape [dim][dim]), or `NULL` 325 326 @return An error code: 0 - success, otherwise - failure 327 **/ 328 CEED_QFUNCTION_HELPER int QdataUnpack_ND(CeedInt dim, CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar *dXdx) { 329 switch (dim) { 330 case 2: 331 if (wdetJ) StoredValuesUnpack(Q, i, 0, 1, q_data, wdetJ); 332 if (dXdx) StoredValuesUnpack(Q, i, 1, 4, q_data, dXdx); 333 break; 334 case 3: 335 if (wdetJ) StoredValuesUnpack(Q, i, 0, 1, q_data, wdetJ); 336 if (dXdx) StoredValuesUnpack(Q, i, 1, 9, q_data, dXdx); 337 break; 338 } 339 return CEED_ERROR_SUCCESS; 340 } 341 342 /** 343 @brief Unpack boundary element q_data for N-D problem at quadrature point 344 345 @param[in] dim Dimension of the element 346 @param[in] Q Number of quadrature points 347 @param[in] i Current quadrature point 348 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:SetupBoundary`) 349 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian, or `NULL` 350 @param[out] dXdx Inverse of the mapping Jacobian (shape [dim - 1][dim]), or `NULL` 351 @param[out] normal Components of the normal vector (shape [dim]), or `NULL` 352 353 @return An error code: 0 - success, otherwise - failure 354 **/ 355 CEED_QFUNCTION_HELPER int QdataBoundaryUnpack_ND(CeedInt dim, CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar *dXdx, 356 CeedScalar *normal) { 357 switch (dim) { 358 case 2: 359 if (wdetJ) StoredValuesUnpack(Q, i, 0, 1, q_data, wdetJ); 360 if (normal) StoredValuesUnpack(Q, i, 1, 2, q_data, normal); 361 break; 362 case 3: 363 if (wdetJ) StoredValuesUnpack(Q, i, 0, 1, q_data, wdetJ); 364 if (normal) StoredValuesUnpack(Q, i, 1, 3, q_data, normal); 365 if (dXdx) StoredValuesUnpack(Q, i, 4, 6, q_data, (CeedScalar *)dXdx); 366 break; 367 } 368 return CEED_ERROR_SUCCESS; 369 } 370 371 /** 372 @brief Unpack boundary element q_data for N-D problem at quadrature point 373 374 @param[in] dim Dimension of the element 375 @param[in] Q Number of quadrature points 376 @param[in] i Current quadrature point 377 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:SetupBoundaryGradient`) 378 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian, or `NULL` 379 @param[out] dXdx Inverse of the mapping Jacobian (shape [dim][dim]), or `NULL` 380 @param[out] normal Components of the normal vector (shape [dim]), or `NULL` 381 382 @return An error code: 0 - success, otherwise - failure 383 **/ 384 CEED_QFUNCTION_HELPER int QdataBoundaryGradientUnpack_ND(CeedInt dim, CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, 385 CeedScalar *dXdx, CeedScalar *normal) { 386 switch (dim) { 387 case 2: 388 if (wdetJ) StoredValuesUnpack(Q, i, 0, 1, q_data, wdetJ); 389 if (dXdx) StoredValuesUnpack(Q, i, 1, 4, q_data, dXdx); 390 if (normal) StoredValuesUnpack(Q, i, 5, 2, q_data, normal); 391 break; 392 case 3: 393 if (wdetJ) StoredValuesUnpack(Q, i, 0, 1, q_data, wdetJ); 394 if (dXdx) StoredValuesUnpack(Q, i, 1, 9, q_data, dXdx); 395 if (normal) StoredValuesUnpack(Q, i, 10, 3, q_data, normal); 396 break; 397 } 398 return CEED_ERROR_SUCCESS; 399 } 400 401 /** 402 @brief Unpack 3D element q_data at quadrature point 403 404 @param[in] Q Number of quadrature points 405 @param[in] i Current quadrature point 406 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:Setup`) 407 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian 408 @param[out] dXdx Inverse of the mapping Jacobian (shape [3][3]) 409 410 @return An error code: 0 - success, otherwise - failure 411 **/ 412 CEED_QFUNCTION_HELPER int QdataUnpack_3D(CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar dXdx[3][3]) { 413 return QdataUnpack_ND(3, Q, i, q_data, wdetJ, (CeedScalar *)dXdx); 414 } 415 416 /** 417 @brief Unpack boundary element q_data for 3D problem at quadrature point 418 419 @param[in] Q Number of quadrature points 420 @param[in] i Current quadrature point 421 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:SetupBoundary`) 422 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian, or `NULL` 423 @param[out] dXdx Inverse of the mapping Jacobian (shape [2][3]), or `NULL` 424 @param[out] normal Components of the normal vector (shape [3]), or `NULL` 425 426 @return An error code: 0 - success, otherwise - failure 427 **/ 428 CEED_QFUNCTION_HELPER int QdataBoundaryUnpack_3D(CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar dXdx[2][3], 429 CeedScalar normal[3]) { 430 return QdataBoundaryUnpack_ND(3, Q, i, q_data, wdetJ, (CeedScalar *)dXdx, normal); 431 } 432 433 /** 434 @brief Unpack boundary element q_data for 3D problem at quadrature point 435 436 @param[in] Q Number of quadrature points 437 @param[in] i Current quadrature point 438 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:SetupBoundary`) 439 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian, or `NULL` 440 @param[out] dXdx Inverse of the mapping Jacobian (shape [3][3]), or `NULL` 441 @param[out] normal Components of the normal vector (shape [3]), or `NULL` 442 443 @return An error code: 0 - success, otherwise - failure 444 **/ 445 CEED_QFUNCTION_HELPER int QdataBoundaryGradientUnpack_3D(CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar dXdx[3][3], 446 CeedScalar normal[3]) { 447 return QdataBoundaryGradientUnpack_ND(3, Q, i, q_data, wdetJ, (CeedScalar *)dXdx, normal); 448 } 449 450 /** 451 @brief Unpack 2D element q_data at quadrature point 452 453 @param[in] Q Number of quadrature points 454 @param[in] i Current quadrature point 455 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:Setup`) 456 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian 457 @param[out] dXdx Inverse of the mapping Jacobian (shape [2][2]) 458 459 @return An error code: 0 - success, otherwise - failure 460 **/ 461 CEED_QFUNCTION_HELPER int QdataUnpack_2D(CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar dXdx[2][2]) { 462 QdataUnpack_ND(2, Q, i, q_data, wdetJ, (CeedScalar *)dXdx); 463 return CEED_ERROR_SUCCESS; 464 } 465 466 /** 467 @brief Unpack boundary element q_data for 2D problem at quadrature point 468 469 @param[in] Q Number of quadrature points 470 @param[in] i Current quadrature point 471 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:SetupBoundary2d`) 472 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian, or `NULL` 473 @param[out] normal Components of the normal vector (shape [2]), or `NULL` 474 475 @return An error code: 0 - success, otherwise - failure 476 **/ 477 CEED_QFUNCTION_HELPER int QdataBoundaryUnpack_2D(CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar normal[2]) { 478 QdataBoundaryUnpack_ND(3, Q, i, q_data, wdetJ, NULL, normal); 479 return CEED_ERROR_SUCCESS; 480 } 481 482 /** 483 @brief Unpack boundary element q_data for 2D problem at quadrature point 484 485 @param[in] Q Number of quadrature points 486 @param[in] i Current quadrature point 487 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:SetupBoundary`) 488 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian, or `NULL` 489 @param[out] dXdx Inverse of the mapping Jacobian (shape [2][2]), or `NULL` 490 @param[out] normal Components of the normal vector (shape [2]), or `NULL` 491 492 @return An error code: 0 - success, otherwise - failure 493 **/ 494 CEED_QFUNCTION_HELPER int QdataBoundaryGradientUnpack_2D(CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar dXdx[2][2], 495 CeedScalar normal[2]) { 496 return QdataBoundaryGradientUnpack_ND(2, Q, i, q_data, wdetJ, (CeedScalar *)dXdx, normal); 497 } 498 499 /** 500 @brief Unpack `CEED_EVAL_GRAD` QF input into quadrature-point local array 501 502 @param[in] Q Number of quadrature points 503 @param[in] i Current quadrature point 504 @param[in] num_comp Number of components of the input 505 @param[in] dim Topological dimension of the element (ie. number of derivative terms per component) 506 @param[in] grad QF gradient input, shape `[dim][num_comp][Q]` 507 @param[out] grad_local Gradient array at quadrature point Q, shape `[num_comp][dim]` 508 **/ 509 CEED_QFUNCTION_HELPER void GradUnpackN(CeedInt Q, CeedInt i, CeedInt num_comp, CeedInt dim, const CeedScalar *grad, CeedScalar *grad_local) { 510 for (CeedInt d = 0; d < dim; d++) { 511 for (CeedInt c = 0; c < num_comp; c++) { 512 grad_local[dim * c + d] = grad[(Q * num_comp) * d + Q * c + i]; 513 } 514 } 515 } 516 517 /** 518 @brief Unpack `CEED_EVAL_GRAD` QF input into quadrature-point local array for 3D elements 519 520 @param[in] Q Number of quadrature points 521 @param[in] i Current quadrature point 522 @param[in] num_comp Number of components of the input 523 @param[in] grad QF gradient input, shape `[3][num_comp][Q]` 524 @param[out] grad_local Gradient array at quadrature point Q, shape `[num_comp][3]` 525 **/ 526 CEED_QFUNCTION_HELPER void GradUnpack3(CeedInt Q, CeedInt i, CeedInt num_comp, const CeedScalar *grad, CeedScalar (*grad_local)[3]) { 527 GradUnpackN(Q, i, num_comp, 3, grad, (CeedScalar *)grad_local); 528 } 529 530 /** 531 @brief Unpack `CEED_EVAL_GRAD` QF input into quadrature-point local array for 2D elements 532 533 @param[in] Q Number of quadrature points 534 @param[in] i Current quadrature point 535 @param[in] num_comp Number of components of the input 536 @param[in] grad QF gradient input, shape `[2][num_comp][Q]` 537 @param[out] grad_local Gradient array at quadrature point Q, shape `[num_comp][2]` 538 **/ 539 CEED_QFUNCTION_HELPER void GradUnpack2(CeedInt Q, CeedInt i, CeedInt num_comp, const CeedScalar *grad, CeedScalar (*grad_local)[2]) { 540 GradUnpackN(Q, i, num_comp, 2, grad, (CeedScalar *)grad_local); 541 } 542 543 /** 544 @brief Calculate divergence from reference gradient 545 546 Given gradient array G_{ij} and inverse element mapping X_{ij}, then the divergence is 547 548 G_{ij} X{ji} 549 550 @param[in] grad_qn Gradient array, orientation [vector component][gradient direction] 551 @param[in] dXdx Inverse of the mapping Jacobian (shape [dim][dim]) 552 @param[in] dim Dimension of the problem 553 @param[out] divergence The divergence 554 **/ 555 CEED_QFUNCTION_HELPER void DivergenceND(const CeedScalar *grad_qn, const CeedScalar *dXdx, const CeedInt dim, CeedScalar *divergence) { 556 for (CeedInt i = 0; i < dim; i++) { 557 for (CeedInt j = 0; j < dim; j++) { 558 *divergence += grad_qn[i * dim + j] * dXdx[j * dim + i]; 559 } 560 } 561 } 562 563 /** 564 @brief Calculate divergence from reference gradient for 3D problem 565 566 Given gradient array G_{ij} and inverse element mapping X_{ij}, then the divergence is 567 568 G_{ij} X{ji} 569 570 @param[in] grad_qn Gradient array, orientation [vector component][gradient direction] 571 @param[in] dXdx Inverse of the mapping Jacobian (shape [3][3]) 572 @param[out] divergence The divergence 573 **/ 574 CEED_QFUNCTION_HELPER void Divergence3D(const CeedScalar grad_qn[3][3], const CeedScalar dXdx[3][3], CeedScalar *divergence) { 575 DivergenceND((const CeedScalar *)grad_qn, (const CeedScalar *)dXdx, 3, divergence); 576 } 577