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 /// @file 9 /// Geometric factors (3D) for Navier-Stokes example using PETSc 10 11 #ifndef setup_geo_h 12 #define setup_geo_h 13 14 #include <ceed.h> 15 #include <math.h> 16 17 // ***************************************************************************** 18 // This QFunction sets up the geometric factors required for integration and 19 // coordinate transformations 20 // 21 // Reference (parent) coordinates: X 22 // Physical (current) coordinates: x 23 // Change of coordinate matrix: dxdX_{i,j} = x_{i,j} (indicial notation) 24 // Inverse of change of coordinate matrix: dXdx_{i,j} = (detJ^-1) * X_{i,j} 25 // 26 // All quadrature data is stored in 10 field vector of quadrature data. 27 // 28 // We require the determinant of the Jacobian to properly compute integrals of 29 // the form: int( v u ) 30 // 31 // Determinant of Jacobian: 32 // detJ = J11*A11 + J21*A12 + J31*A13 33 // Jij = Jacobian entry ij 34 // Aij = Adjoint ij 35 // 36 // Stored: w detJ 37 // in q_data[0] 38 // 39 // We require the transpose of the inverse of the Jacobian to properly compute 40 // integrals of the form: int( gradv u ) 41 // 42 // Inverse of Jacobian: 43 // dXdx_i,j = Aij / detJ 44 // 45 // Stored: Aij / detJ 46 // in q_data[1:9] as 47 // (detJ^-1) * [A11 A12 A13] 48 // [A21 A22 A23] 49 // [A31 A32 A33] 50 // 51 // ***************************************************************************** 52 CEED_QFUNCTION(Setup)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 53 // Inputs 54 const CeedScalar(*J)[3][CEED_Q_VLA] = (const CeedScalar(*)[3][CEED_Q_VLA])in[0], (*w) = in[1]; 55 56 // Outputs 57 CeedScalar(*q_data)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 58 59 CeedPragmaSIMD 60 // Quadrature Point Loop 61 for (CeedInt i = 0; i < Q; i++) { 62 // Setup 63 const CeedScalar J11 = J[0][0][i]; 64 const CeedScalar J21 = J[0][1][i]; 65 const CeedScalar J31 = J[0][2][i]; 66 const CeedScalar J12 = J[1][0][i]; 67 const CeedScalar J22 = J[1][1][i]; 68 const CeedScalar J32 = J[1][2][i]; 69 const CeedScalar J13 = J[2][0][i]; 70 const CeedScalar J23 = J[2][1][i]; 71 const CeedScalar J33 = J[2][2][i]; 72 const CeedScalar A11 = J22 * J33 - J23 * J32; 73 const CeedScalar A12 = J13 * J32 - J12 * J33; 74 const CeedScalar A13 = J12 * J23 - J13 * J22; 75 const CeedScalar A21 = J23 * J31 - J21 * J33; 76 const CeedScalar A22 = J11 * J33 - J13 * J31; 77 const CeedScalar A23 = J13 * J21 - J11 * J23; 78 const CeedScalar A31 = J21 * J32 - J22 * J31; 79 const CeedScalar A32 = J12 * J31 - J11 * J32; 80 const CeedScalar A33 = J11 * J22 - J12 * J21; 81 const CeedScalar detJ = J11 * A11 + J21 * A12 + J31 * A13; 82 83 // Qdata 84 // -- Interp-to-Interp q_data 85 q_data[0][i] = w[i] * detJ; 86 // -- Interp-to-Grad q_data 87 // Inverse of change of coordinate matrix: X_i,j 88 q_data[1][i] = A11 / detJ; 89 q_data[2][i] = A12 / detJ; 90 q_data[3][i] = A13 / detJ; 91 q_data[4][i] = A21 / detJ; 92 q_data[5][i] = A22 / detJ; 93 q_data[6][i] = A23 / detJ; 94 q_data[7][i] = A31 / detJ; 95 q_data[8][i] = A32 / detJ; 96 q_data[9][i] = A33 / detJ; 97 98 } // End of Quadrature Point Loop 99 100 // Return 101 return 0; 102 } 103 104 // ***************************************************************************** 105 // This QFunction sets up the geometric factor required for integration when 106 // reference coordinates are in 2D and the physical coordinates are in 3D 107 // 108 // Reference (parent) 2D coordinates: X 109 // Physical (current) 3D coordinates: x 110 // Change of coordinate matrix: 111 // dxdX_{i,j} = dx_i/dX_j (indicial notation) [3 * 2] 112 // Inverse change of coordinate matrix: 113 // dXdx_{i,j} = dX_i/dx_j (indicial notation) [2 * 3] 114 // 115 // (J1,J2,J3) is given by the cross product of the columns of dxdX_{i,j} 116 // 117 // detJb is the magnitude of (J1,J2,J3) 118 // 119 // dXdx is calculated via Moore–Penrose inverse: 120 // 121 // dX_i/dx_j = (dxdX^T dxdX)^(-1) dxdX 122 // = (dx_l/dX_i * dx_l/dX_k)^(-1) dx_j/dX_k 123 // 124 // All quadrature data is stored in 10 field vector of quadrature data. 125 // 126 // We require the determinant of the Jacobian to properly compute integrals of 127 // the form: int( u v ) 128 // 129 // Stored: w detJb 130 // in q_data_sur[0] 131 // 132 // Normal vector = (J1,J2,J3) / detJb 133 // 134 // - TODO Could possibly remove normal vector, as it could be calculated in the Qfunction from dXdx 135 // Stored: (J1,J2,J3) / detJb 136 // in q_data_sur[1:3] as 137 // (detJb^-1) * [ J1 ] 138 // [ J2 ] 139 // [ J3 ] 140 // 141 // Stored: dXdx_{i,j} 142 // in q_data_sur[4:9] as 143 // [dXdx_11 dXdx_12 dXdx_13] 144 // [dXdx_21 dXdx_22 dXdx_23] 145 // 146 // ***************************************************************************** 147 CEED_QFUNCTION(SetupBoundary)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 148 // Inputs 149 const CeedScalar(*J)[3][CEED_Q_VLA] = (const CeedScalar(*)[3][CEED_Q_VLA])in[0], (*w) = in[1]; 150 // Outputs 151 CeedScalar(*q_data_sur)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 152 153 CeedPragmaSIMD 154 // Quadrature Point Loop 155 for (CeedInt i = 0; i < Q; i++) { 156 // Setup 157 const CeedScalar dxdX[3][2] = { 158 {J[0][0][i], J[1][0][i]}, 159 {J[0][1][i], J[1][1][i]}, 160 {J[0][2][i], J[1][2][i]} 161 }; 162 // J1, J2, and J3 are given by the cross product of the columns of dxdX 163 const CeedScalar J1 = dxdX[1][0] * dxdX[2][1] - dxdX[2][0] * dxdX[1][1]; 164 const CeedScalar J2 = dxdX[2][0] * dxdX[0][1] - dxdX[0][0] * dxdX[2][1]; 165 const CeedScalar J3 = dxdX[0][0] * dxdX[1][1] - dxdX[1][0] * dxdX[0][1]; 166 167 const CeedScalar detJb = sqrt(J1 * J1 + J2 * J2 + J3 * J3); 168 169 // q_data_sur 170 // -- Interp-to-Interp q_data_sur 171 q_data_sur[0][i] = w[i] * detJb; 172 q_data_sur[1][i] = J1 / detJb; 173 q_data_sur[2][i] = J2 / detJb; 174 q_data_sur[3][i] = J3 / detJb; 175 176 // dxdX_k,j * dxdX_j,k 177 CeedScalar dxdXTdxdX[2][2] = {{0.}}; 178 for (CeedInt j = 0; j < 2; j++) { 179 for (CeedInt k = 0; k < 2; k++) { 180 for (CeedInt l = 0; l < 3; l++) dxdXTdxdX[j][k] += dxdX[l][j] * dxdX[l][k]; 181 } 182 } 183 184 const CeedScalar detdxdXTdxdX = dxdXTdxdX[0][0] * dxdXTdxdX[1][1] - dxdXTdxdX[1][0] * dxdXTdxdX[0][1]; 185 186 // Compute inverse of dxdXTdxdX 187 CeedScalar dxdXTdxdX_inv[2][2]; 188 dxdXTdxdX_inv[0][0] = dxdXTdxdX[1][1] / detdxdXTdxdX; 189 dxdXTdxdX_inv[0][1] = -dxdXTdxdX[0][1] / detdxdXTdxdX; 190 dxdXTdxdX_inv[1][0] = -dxdXTdxdX[1][0] / detdxdXTdxdX; 191 dxdXTdxdX_inv[1][1] = dxdXTdxdX[0][0] / detdxdXTdxdX; 192 193 // Compute dXdx from dxdXTdxdX^-1 and dxdX 194 CeedScalar dXdx[2][3] = {{0.}}; 195 for (CeedInt j = 0; j < 2; j++) { 196 for (CeedInt k = 0; k < 3; k++) { 197 for (CeedInt l = 0; l < 2; l++) dXdx[j][k] += dxdXTdxdX_inv[l][j] * dxdX[k][l]; 198 } 199 } 200 201 q_data_sur[4][i] = dXdx[0][0]; 202 q_data_sur[5][i] = dXdx[0][1]; 203 q_data_sur[6][i] = dXdx[0][2]; 204 q_data_sur[7][i] = dXdx[1][0]; 205 q_data_sur[8][i] = dXdx[1][1]; 206 q_data_sur[9][i] = dXdx[1][2]; 207 208 } // End of Quadrature Point Loop 209 210 // Return 211 return 0; 212 } 213 214 // ***************************************************************************** 215 216 #endif // setup_geo_h 217