1 // Copyright (c) 2017-2022, 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 #ifndef utils_h 9 #define utils_h 10 11 #include <ceed.h> 12 #include <math.h> 13 14 #ifndef M_PI 15 #define M_PI 3.14159265358979323846 16 #endif 17 18 CEED_QFUNCTION_HELPER CeedScalar Max(CeedScalar a, CeedScalar b) { return a < b ? b : a; } 19 CEED_QFUNCTION_HELPER CeedScalar Min(CeedScalar a, CeedScalar b) { return a < b ? a : b; } 20 21 CEED_QFUNCTION_HELPER void SwapScalar(CeedScalar *a, CeedScalar *b) { 22 CeedScalar temp = *a; 23 *a = *b; 24 *b = temp; 25 } 26 27 CEED_QFUNCTION_HELPER CeedScalar Square(CeedScalar x) { return x * x; } 28 CEED_QFUNCTION_HELPER CeedScalar Cube(CeedScalar x) { return x * x * x; } 29 30 // @brief Scale vector of length N by scalar alpha 31 CEED_QFUNCTION_HELPER void ScaleN(CeedScalar *u, const CeedScalar alpha, const CeedInt N) { 32 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) u[i] *= alpha; 33 } 34 35 // @brief Set vector of length N to a value alpha 36 CEED_QFUNCTION_HELPER void SetValueN(CeedScalar *u, const CeedScalar alpha, const CeedInt N) { 37 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) u[i] = alpha; 38 } 39 40 // @brief Copy N elements from x to y 41 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]; } 42 43 // @brief Copy 3x3 matrix from A to B 44 CEED_QFUNCTION_HELPER void CopyMat3(const CeedScalar A[3][3], CeedScalar B[3][3]) { CopyN((const CeedScalar *)A, (CeedScalar *)B, 9); } 45 46 // @brief Dot product of vectors with N elements 47 CEED_QFUNCTION_HELPER CeedScalar DotN(const CeedScalar *u, const CeedScalar *v, const CeedInt N) { 48 CeedScalar output = 0; 49 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) output += u[i] * v[i]; 50 return output; 51 } 52 53 // @brief Dot product of 3 element vectors 54 CEED_QFUNCTION_HELPER CeedScalar Dot3(const CeedScalar *u, const CeedScalar *v) { return u[0] * v[0] + u[1] * v[1] + u[2] * v[2]; } 55 56 // @brief Cross product of vectors with 3 elements 57 CEED_QFUNCTION_HELPER void Cross3(const CeedScalar u[3], const CeedScalar v[3], CeedScalar w[3]) { 58 w[0] = (u[1] * v[2]) - (u[2] * v[1]); 59 w[1] = (u[2] * v[0]) - (u[0] * v[2]); 60 w[2] = (u[0] * v[1]) - (u[1] * v[0]); 61 } 62 63 // @brief Curl of vector given its gradient 64 CEED_QFUNCTION_HELPER void Curl3(const CeedScalar gradient[3][3], CeedScalar v[3]) { 65 v[0] = gradient[2][1] - gradient[1][2]; 66 v[1] = gradient[0][2] - gradient[2][0]; 67 v[2] = gradient[1][0] - gradient[0][1]; 68 } 69 70 // @brief Matrix vector product, b = Ax + b. A is NxM, x is M, b is N 71 CEED_QFUNCTION_HELPER void MatVecNM(const CeedScalar *A, const CeedScalar *x, const CeedInt N, const CeedInt M, const CeedTransposeMode transpose_A, 72 CeedScalar *b) { 73 switch (transpose_A) { 74 case CEED_NOTRANSPOSE: 75 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) b[i] += DotN(&A[i * M], x, M); 76 break; 77 case CEED_TRANSPOSE: 78 CeedPragmaSIMD for (CeedInt i = 0; i < M; i++) { CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) b[i] += A[j * M + i] * x[j]; } 79 break; 80 } 81 } 82 83 // @brief 3x3 Matrix vector product b = Ax + b. 84 CEED_QFUNCTION_HELPER void MatVec3(const CeedScalar A[3][3], const CeedScalar x[3], const CeedTransposeMode transpose_A, CeedScalar b[3]) { 85 MatVecNM((const CeedScalar *)A, (const CeedScalar *)x, 3, 3, transpose_A, (CeedScalar *)b); 86 } 87 88 // @brief Matrix-Matrix product, B = DA + B, where D is diagonal. 89 // @details A is NxM, D is diagonal NxN, represented by a vector of length N, and B is NxM. Optionally, A may be transposed. 90 CEED_QFUNCTION_HELPER void MatDiagNM(const CeedScalar *A, const CeedScalar *D, const CeedInt N, const CeedInt M, const CeedTransposeMode transpose_A, 91 CeedScalar *B) { 92 switch (transpose_A) { 93 case CEED_NOTRANSPOSE: 94 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]; } 95 break; 96 case CEED_TRANSPOSE: 97 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]; } 98 break; 99 } 100 } 101 102 // @brief 3x3 Matrix-Matrix product, B = DA + B, where D is diagonal. 103 // @details Optionally, A may be transposed. 104 CEED_QFUNCTION_HELPER void MatDiag3(const CeedScalar A[3][3], const CeedScalar D[3], const CeedTransposeMode transpose_A, CeedScalar B[3][3]) { 105 MatDiagNM((const CeedScalar *)A, (const CeedScalar *)D, 3, 3, transpose_A, (CeedScalar *)B); 106 } 107 // @brief NxN Matrix-Matrix product, C = AB + C 108 CEED_QFUNCTION_HELPER void MatMatN(const CeedScalar *A, const CeedScalar *B, const CeedInt N, const CeedTransposeMode transpose_A, 109 const CeedTransposeMode transpose_B, CeedScalar *C) { 110 switch (transpose_A) { 111 case CEED_NOTRANSPOSE: 112 switch (transpose_B) { 113 case CEED_NOTRANSPOSE: 114 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) { 115 CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) { 116 CeedPragmaSIMD for (CeedInt k = 0; k < N; k++) C[i * N + j] += A[i * N + k] * B[k * N + j]; 117 } 118 } 119 break; 120 case CEED_TRANSPOSE: 121 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) { 122 CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) { 123 CeedPragmaSIMD for (CeedInt k = 0; k < N; k++) C[i * N + j] += A[i * N + k] * B[j * N + k]; 124 } 125 } 126 break; 127 } 128 break; 129 case CEED_TRANSPOSE: 130 switch (transpose_B) { 131 case CEED_NOTRANSPOSE: 132 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) { 133 CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) { 134 CeedPragmaSIMD for (CeedInt k = 0; k < N; k++) C[i * N + j] += A[k * N + i] * B[k * N + j]; 135 } 136 } 137 break; 138 case CEED_TRANSPOSE: 139 CeedPragmaSIMD for (CeedInt i = 0; i < N; i++) { 140 CeedPragmaSIMD for (CeedInt j = 0; j < N; j++) { 141 CeedPragmaSIMD for (CeedInt k = 0; k < N; k++) C[i * N + j] += A[k * N + i] * B[j * N + k]; 142 } 143 } 144 break; 145 } 146 break; 147 } 148 } 149 150 // @brief 3x3 Matrix-Matrix product, C = AB + C 151 CEED_QFUNCTION_HELPER void MatMat3(const CeedScalar A[3][3], const CeedScalar B[3][3], const CeedTransposeMode transpose_A, 152 const CeedTransposeMode transpose_B, CeedScalar C[3][3]) { 153 MatMatN((const CeedScalar *)A, (const CeedScalar *)B, 3, transpose_A, transpose_B, (CeedScalar *)C); 154 } 155 156 // @brief Unpack Kelvin-Mandel notation symmetric tensor into full tensor 157 CEED_QFUNCTION_HELPER void KMUnpack(const CeedScalar v[6], CeedScalar A[3][3]) { 158 const CeedScalar weight = 1 / sqrt(2.); 159 A[0][0] = v[0]; 160 A[1][1] = v[1]; 161 A[2][2] = v[2]; 162 A[2][1] = A[1][2] = weight * v[3]; 163 A[2][0] = A[0][2] = weight * v[4]; 164 A[1][0] = A[0][1] = weight * v[5]; 165 } 166 167 // @brief Pack full tensor into Kelvin-Mandel notation symmetric tensor 168 CEED_QFUNCTION_HELPER void KMPack(const CeedScalar A[3][3], CeedScalar v[6]) { 169 const CeedScalar weight = sqrt(2.); 170 v[0] = A[0][0]; 171 v[1] = A[1][1]; 172 v[2] = A[2][2]; 173 v[3] = A[2][1] * weight; 174 v[4] = A[2][0] * weight; 175 v[5] = A[1][0] * weight; 176 } 177 178 // @brief Calculate metric tensor from mapping, g_{ij} = xi_{k,i} xi_{k,j} = dXdx^T dXdx 179 CEED_QFUNCTION_HELPER void KMMetricTensor(const CeedScalar dXdx[3][3], CeedScalar km_g_ij[6]) { 180 CeedScalar g_ij[3][3] = {{0.}}; 181 MatMat3(dXdx, dXdx, CEED_TRANSPOSE, CEED_NOTRANSPOSE, g_ij); 182 KMPack(g_ij, km_g_ij); 183 } 184 185 // @brief Linear ramp evaluation 186 CEED_QFUNCTION_HELPER CeedScalar LinearRampCoefficient(CeedScalar amplitude, CeedScalar length, CeedScalar start, CeedScalar x) { 187 if (x < start) { 188 return amplitude; 189 } else if (x < start + length) { 190 return amplitude * ((x - start) * (-1 / length) + 1); 191 } else { 192 return 0; 193 } 194 } 195 196 /** 197 @brief Pack stored values at quadrature point 198 199 @param[in] Q Number of quadrature points 200 @param[in] i Current quadrature point 201 @param[in] start Starting index to store components 202 @param[in] num_comp Number of components to store 203 @param[in] values_at_qpnt Local values for quadrature point i 204 @param[out] stored Stored values 205 206 @return An error code: 0 - success, otherwise - failure 207 **/ 208 CEED_QFUNCTION_HELPER int StoredValuesPack(CeedInt Q, CeedInt i, CeedInt start, CeedInt num_comp, const CeedScalar *values_at_qpnt, 209 CeedScalar *stored) { 210 for (CeedInt j = 0; j < num_comp; j++) stored[(start + j) * Q + i] = values_at_qpnt[j]; 211 212 return CEED_ERROR_SUCCESS; 213 } 214 215 /** 216 @brief Unpack stored values at quadrature point 217 218 @param[in] Q Number of quadrature points 219 @param[in] i Current quadrature point 220 @param[in] start Starting index to store components 221 @param[in] num_comp Number of components to store 222 @param[in] stored Stored values 223 @param[out] values_at_qpnt Local values for quadrature point i 224 225 @return An error code: 0 - success, otherwise - failure 226 **/ 227 CEED_QFUNCTION_HELPER int StoredValuesUnpack(CeedInt Q, CeedInt i, CeedInt start, CeedInt num_comp, const CeedScalar *stored, 228 CeedScalar *values_at_qpnt) { 229 for (CeedInt j = 0; j < num_comp; j++) values_at_qpnt[j] = stored[(start + j) * Q + i]; 230 231 return CEED_ERROR_SUCCESS; 232 } 233 234 /** 235 @brief Unpack 3D element q_data at quadrature point 236 237 @param[in] Q Number of quadrature points 238 @param[in] i Current quadrature point 239 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:Setup`) 240 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian 241 @param[out] dXdx Inverse of the mapping Jacobian (shape [3][3]) 242 243 @return An error code: 0 - success, otherwise - failure 244 **/ 245 CEED_QFUNCTION_HELPER int QdataUnpack_3D(CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar dXdx[3][3]) { 246 StoredValuesUnpack(Q, i, 0, 1, q_data, wdetJ); 247 StoredValuesUnpack(Q, i, 1, 9, q_data, (CeedScalar *)dXdx); 248 return CEED_ERROR_SUCCESS; 249 } 250 251 /** 252 @brief Unpack boundary element q_data for 3D problem at quadrature point 253 254 @param[in] Q Number of quadrature points 255 @param[in] i Current quadrature point 256 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:SetupBoundary`) 257 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian, or `NULL` 258 @param[out] dXdx Inverse of the mapping Jacobian (shape [2][3]), or `NULL` 259 @param[out] normal Components of the normal vector (shape [3]), or `NULL` 260 261 @return An error code: 0 - success, otherwise - failure 262 **/ 263 CEED_QFUNCTION_HELPER int QdataBoundaryUnpack_3D(CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar dXdx[2][3], 264 CeedScalar normal[3]) { 265 if (wdetJ) StoredValuesUnpack(Q, i, 0, 1, q_data, wdetJ); 266 if (normal) StoredValuesUnpack(Q, i, 1, 3, q_data, normal); 267 if (dXdx) StoredValuesUnpack(Q, i, 4, 6, q_data, (CeedScalar *)dXdx); 268 return CEED_ERROR_SUCCESS; 269 } 270 271 /** 272 @brief Unpack 2D element q_data at quadrature point 273 274 @param[in] Q Number of quadrature points 275 @param[in] i Current quadrature point 276 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:Setup`) 277 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian 278 @param[out] dXdx Inverse of the mapping Jacobian (shape [2][2]) 279 280 @return An error code: 0 - success, otherwise - failure 281 **/ 282 CEED_QFUNCTION_HELPER int QdataUnpack_2D(CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar dXdx[2][2]) { 283 StoredValuesUnpack(Q, i, 0, 1, q_data, wdetJ); 284 StoredValuesUnpack(Q, i, 1, 4, q_data, (CeedScalar *)dXdx); 285 return CEED_ERROR_SUCCESS; 286 } 287 288 /** 289 @brief Unpack boundary element q_data for 2D problem at quadrature point 290 291 @param[in] Q Number of quadrature points 292 @param[in] i Current quadrature point 293 @param[in] q_data Pointer to q_data (generated by `setupgeo.h:SetupBoundary2d`) 294 @param[out] wdetJ Quadrature weight times determinant of the mapping Jacobian, or `NULL` 295 @param[out] normal Components of the normal vector (shape [2]), or `NULL` 296 297 @return An error code: 0 - success, otherwise - failure 298 **/ 299 CEED_QFUNCTION_HELPER int QdataBoundaryUnpack_2D(CeedInt Q, CeedInt i, const CeedScalar *q_data, CeedScalar *wdetJ, CeedScalar normal[2]) { 300 if (wdetJ) StoredValuesUnpack(Q, i, 0, 1, q_data, wdetJ); 301 if (normal) StoredValuesUnpack(Q, i, 1, 2, q_data, normal); 302 return CEED_ERROR_SUCCESS; 303 } 304 305 #endif // utils_h 306