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 #pragma once 8 9 #include <ceed.h> 10 #include <math.h> 11 12 #ifndef M_PI 13 #define M_PI 3.14159265358979323846 14 #endif 15 16 CEED_QFUNCTION_HELPER CeedScalar Max(CeedScalar a, CeedScalar b) { return a < b ? b : a; } 17 CEED_QFUNCTION_HELPER CeedScalar Min(CeedScalar a, CeedScalar b) { return a < b ? a : b; } 18 19 CEED_QFUNCTION_HELPER void SwapScalar(CeedScalar *a, CeedScalar *b) { 20 CeedScalar temp = *a; 21 *a = *b; 22 *b = temp; 23 } 24 25 CEED_QFUNCTION_HELPER CeedScalar Square(CeedScalar x) { return x * x; } 26 CEED_QFUNCTION_HELPER CeedScalar Cube(CeedScalar x) { return x * x * x; } 27 28 // @brief Scale vector of length N by scalar alpha 29 CEED_QFUNCTION_HELPER void ScaleN(CeedScalar *u, const CeedScalar alpha, const CeedInt N) { 30 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) u[i] *= alpha; 31 } 32 33 // @brief Set vector of length N to a value alpha 34 CEED_QFUNCTION_HELPER void SetValueN(CeedScalar *u, const CeedScalar alpha, const CeedInt N) { 35 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) u[i] = alpha; 36 } 37 38 // @brief Copy N elements from x to y 39 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]; } 40 41 // @brief Copy 3x3 matrix from A to B 42 CEED_QFUNCTION_HELPER void CopyMat3(const CeedScalar A[3][3], CeedScalar B[3][3]) { CopyN((const CeedScalar *)A, (CeedScalar *)B, 9); } 43 44 // @brief Dot product of vectors with N elements 45 CEED_QFUNCTION_HELPER CeedScalar DotN(const CeedScalar *u, const CeedScalar *v, const CeedInt N) { 46 CeedScalar output = 0; 47 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) output += u[i] * v[i]; 48 return output; 49 } 50 51 // @brief Dot product of 3 element vectors 52 CEED_QFUNCTION_HELPER CeedScalar Dot3(const CeedScalar *u, const CeedScalar *v) { return u[0] * v[0] + u[1] * v[1] + u[2] * v[2]; } 53 54 // @brief Cross product of vectors with 3 elements 55 CEED_QFUNCTION_HELPER void Cross3(const CeedScalar u[3], const CeedScalar v[3], CeedScalar w[3]) { 56 w[0] = (u[1] * v[2]) - (u[2] * v[1]); 57 w[1] = (u[2] * v[0]) - (u[0] * v[2]); 58 w[2] = (u[0] * v[1]) - (u[1] * v[0]); 59 } 60 61 // @brief Curl of vector given its gradient 62 CEED_QFUNCTION_HELPER void Curl3(const CeedScalar gradient[3][3], CeedScalar v[3]) { 63 v[0] = gradient[2][1] - gradient[1][2]; 64 v[1] = gradient[0][2] - gradient[2][0]; 65 v[2] = gradient[1][0] - gradient[0][1]; 66 } 67 68 // @brief Matrix vector product, b = Ax + b. A is NxM, x is M, b is N 69 CEED_QFUNCTION_HELPER void MatVecNM(const CeedScalar *A, const CeedScalar *x, const CeedInt N, const CeedInt M, const CeedTransposeMode transpose_A, 70 CeedScalar *b) { 71 switch (transpose_A) { 72 case CEED_NOTRANSPOSE: 73 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) b[i] += DotN(&A[i * M], x, M); 74 break; 75 case CEED_TRANSPOSE: 76 CeedPragmaSIMD for (CeedInt i = 0; i < M; i++) { CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) b[i] += A[j * M + i] * x[j]; } 77 break; 78 } 79 } 80 81 // @brief 3x3 Matrix vector product b = Ax + b. 82 CEED_QFUNCTION_HELPER void MatVec3(const CeedScalar A[3][3], const CeedScalar x[3], const CeedTransposeMode transpose_A, CeedScalar b[3]) { 83 MatVecNM((const CeedScalar *)A, (const CeedScalar *)x, 3, 3, transpose_A, (CeedScalar *)b); 84 } 85 86 // @brief Matrix-Matrix product, B = DA + B, where D is diagonal. 87 // @details A is NxM, D is diagonal NxN, represented by a vector of length N, and B is NxM. Optionally, A may be transposed. 88 CEED_QFUNCTION_HELPER void MatDiagNM(const CeedScalar *A, const CeedScalar *D, const CeedInt N, const CeedInt M, const CeedTransposeMode transpose_A, 89 CeedScalar *B) { 90 switch (transpose_A) { 91 case CEED_NOTRANSPOSE: 92 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]; } 93 break; 94 case CEED_TRANSPOSE: 95 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]; } 96 break; 97 } 98 } 99 100 // @brief 3x3 Matrix-Matrix product, B = DA + B, where D is diagonal. 101 // @details Optionally, A may be transposed. 102 CEED_QFUNCTION_HELPER void MatDiag3(const CeedScalar A[3][3], const CeedScalar D[3], const CeedTransposeMode transpose_A, CeedScalar B[3][3]) { 103 MatDiagNM((const CeedScalar *)A, (const CeedScalar *)D, 3, 3, transpose_A, (CeedScalar *)B); 104 } 105 // @brief NxN Matrix-Matrix product, C = AB + C 106 CEED_QFUNCTION_HELPER void MatMatN(const CeedScalar *A, const CeedScalar *B, const CeedInt N, const CeedTransposeMode transpose_A, 107 const CeedTransposeMode transpose_B, CeedScalar *C) { 108 switch (transpose_A) { 109 case CEED_NOTRANSPOSE: 110 switch (transpose_B) { 111 case CEED_NOTRANSPOSE: 112 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) { 113 CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) { 114 CeedPragmaSIMD for (CeedInt k = 0; k < N; k++) C[i * N + j] += A[i * N + k] * B[k * N + j]; 115 } 116 } 117 break; 118 case CEED_TRANSPOSE: 119 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) { 120 CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) { 121 CeedPragmaSIMD for (CeedInt k = 0; k < N; k++) C[i * N + j] += A[i * N + k] * B[j * N + k]; 122 } 123 } 124 break; 125 } 126 break; 127 case CEED_TRANSPOSE: 128 switch (transpose_B) { 129 case CEED_NOTRANSPOSE: 130 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) { 131 CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) { 132 CeedPragmaSIMD for (CeedInt k = 0; k < N; k++) C[i * N + j] += A[k * N + i] * B[k * N + j]; 133 } 134 } 135 break; 136 case CEED_TRANSPOSE: 137 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) { 138 CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) { 139 CeedPragmaSIMD for (CeedInt k = 0; k < N; k++) C[i * N + j] += A[k * N + i] * B[j * N + k]; 140 } 141 } 142 break; 143 } 144 break; 145 } 146 } 147 148 // @brief 3x3 Matrix-Matrix product, C = AB + C 149 CEED_QFUNCTION_HELPER void MatMat3(const CeedScalar A[3][3], const CeedScalar B[3][3], const CeedTransposeMode transpose_A, 150 const CeedTransposeMode transpose_B, CeedScalar C[3][3]) { 151 MatMatN((const CeedScalar *)A, (const CeedScalar *)B, 3, transpose_A, transpose_B, (CeedScalar *)C); 152 } 153 154 // @brief Unpack Kelvin-Mandel notation symmetric tensor into full tensor 155 CEED_QFUNCTION_HELPER void KMUnpack(const CeedScalar v[6], CeedScalar A[3][3]) { 156 const CeedScalar weight = 1 / sqrt(2.); 157 A[0][0] = v[0]; 158 A[1][1] = v[1]; 159 A[2][2] = v[2]; 160 A[2][1] = A[1][2] = weight * v[3]; 161 A[2][0] = A[0][2] = weight * v[4]; 162 A[1][0] = A[0][1] = weight * v[5]; 163 } 164 165 // @brief Pack full tensor into Kelvin-Mandel notation symmetric tensor 166 CEED_QFUNCTION_HELPER void KMPack(const CeedScalar A[3][3], CeedScalar v[6]) { 167 const CeedScalar weight = sqrt(2.); 168 v[0] = A[0][0]; 169 v[1] = A[1][1]; 170 v[2] = A[2][2]; 171 v[3] = A[2][1] * weight; 172 v[4] = A[2][0] * weight; 173 v[5] = A[1][0] * weight; 174 } 175 176 // @brief Calculate metric tensor from mapping, g_{ij} = xi_{k,i} xi_{k,j} = dXdx^T dXdx 177 CEED_QFUNCTION_HELPER void KMMetricTensor(const CeedScalar dXdx[3][3], CeedScalar km_g_ij[6]) { 178 CeedScalar g_ij[3][3] = {{0.}}; 179 MatMat3(dXdx, dXdx, CEED_TRANSPOSE, CEED_NOTRANSPOSE, g_ij); 180 KMPack(g_ij, km_g_ij); 181 } 182 183 // @brief Linear ramp evaluation 184 CEED_QFUNCTION_HELPER CeedScalar LinearRampCoefficient(CeedScalar amplitude, CeedScalar length, CeedScalar start, CeedScalar x) { 185 if (x < start) { 186 return amplitude; 187 } else if (x < start + length) { 188 return amplitude * ((x - start) * (-1 / length) + 1); 189 } else { 190 return 0; 191 } 192 } 193 194 /** 195 @brief Pack stored values at quadrature point 196 197 @param[in] Q Number of quadrature points 198 @param[in] i Current quadrature point 199 @param[in] start Starting index to store components 200 @param[in] num_comp Number of components to store 201 @param[in] values_at_qpnt Local values for quadrature point i 202 @param[out] stored Stored values 203 204 @return An error code: 0 - success, otherwise - failure 205 **/ 206 CEED_QFUNCTION_HELPER int StoredValuesPack(CeedInt Q, CeedInt i, CeedInt start, CeedInt num_comp, const CeedScalar *values_at_qpnt, 207 CeedScalar *stored) { 208 for (CeedInt j = 0; j < num_comp; j++) stored[(start + j) * Q + i] = values_at_qpnt[j]; 209 210 return CEED_ERROR_SUCCESS; 211 } 212 213 /** 214 @brief Unpack stored values at quadrature point 215 216 @param[in] Q Number of quadrature points 217 @param[in] i Current quadrature point 218 @param[in] start Starting index to store components 219 @param[in] num_comp Number of components to store 220 @param[in] stored Stored values 221 @param[out] values_at_qpnt Local values for quadrature point i 222 223 @return An error code: 0 - success, otherwise - failure 224 **/ 225 CEED_QFUNCTION_HELPER int StoredValuesUnpack(CeedInt Q, CeedInt i, CeedInt start, CeedInt num_comp, const CeedScalar *stored, 226 CeedScalar *values_at_qpnt) { 227 for (CeedInt j = 0; j < num_comp; j++) values_at_qpnt[j] = stored[(start + j) * Q + i]; 228 229 return CEED_ERROR_SUCCESS; 230 } 231 232 /** 233 @brief Unpack 3D element q_data at quadrature point 234 235 @param[in] Q Number of quadrature points 236 @param[in] i Current quadrature point 237 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:Setup`) 238 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian 239 @param[out] dXdx Inverse of the mapping Jacobian (shape [3][3]) 240 241 @return An error code: 0 - success, otherwise - failure 242 **/ 243 CEED_QFUNCTION_HELPER int QdataUnpack_3D(CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar dXdx[3][3]) { 244 StoredValuesUnpack(Q, i, 0, 1, q_data, wdetJ); 245 StoredValuesUnpack(Q, i, 1, 9, q_data, (CeedScalar *)dXdx); 246 return CEED_ERROR_SUCCESS; 247 } 248 249 /** 250 @brief Unpack boundary element q_data for 3D problem at quadrature point 251 252 @param[in] Q Number of quadrature points 253 @param[in] i Current quadrature point 254 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:SetupBoundary`) 255 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian, or `NULL` 256 @param[out] dXdx Inverse of the mapping Jacobian (shape [2][3]), or `NULL` 257 @param[out] normal Components of the normal vector (shape [3]), or `NULL` 258 259 @return An error code: 0 - success, otherwise - failure 260 **/ 261 CEED_QFUNCTION_HELPER int QdataBoundaryUnpack_3D(CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar dXdx[2][3], 262 CeedScalar normal[3]) { 263 if (wdetJ) StoredValuesUnpack(Q, i, 0, 1, q_data, wdetJ); 264 if (normal) StoredValuesUnpack(Q, i, 1, 3, q_data, normal); 265 if (dXdx) StoredValuesUnpack(Q, i, 4, 6, q_data, (CeedScalar *)dXdx); 266 return CEED_ERROR_SUCCESS; 267 } 268 269 /** 270 @brief Unpack 2D element q_data at quadrature point 271 272 @param[in] Q Number of quadrature points 273 @param[in] i Current quadrature point 274 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:Setup`) 275 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian 276 @param[out] dXdx Inverse of the mapping Jacobian (shape [2][2]) 277 278 @return An error code: 0 - success, otherwise - failure 279 **/ 280 CEED_QFUNCTION_HELPER int QdataUnpack_2D(CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar dXdx[2][2]) { 281 StoredValuesUnpack(Q, i, 0, 1, q_data, wdetJ); 282 StoredValuesUnpack(Q, i, 1, 4, q_data, (CeedScalar *)dXdx); 283 return CEED_ERROR_SUCCESS; 284 } 285 286 /** 287 @brief Unpack boundary element q_data for 2D problem at quadrature point 288 289 @param[in] Q Number of quadrature points 290 @param[in] i Current quadrature point 291 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:SetupBoundary2d`) 292 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian, or `NULL` 293 @param[out] normal Components of the normal vector (shape [2]), or `NULL` 294 295 @return An error code: 0 - success, otherwise - failure 296 **/ 297 CEED_QFUNCTION_HELPER int QdataBoundaryUnpack_2D(CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar normal[2]) { 298 if (wdetJ) StoredValuesUnpack(Q, i, 0, 1, q_data, wdetJ); 299 if (normal) StoredValuesUnpack(Q, i, 1, 2, q_data, normal); 300 return CEED_ERROR_SUCCESS; 301 } 302