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]; 55 const CeedScalar(*w) = in[1]; 56 57 // Outputs 58 CeedScalar(*q_data)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 59 60 CeedPragmaSIMD 61 // Quadrature Point Loop 62 for (CeedInt i = 0; i < Q; i++) { 63 // Setup 64 const CeedScalar J11 = J[0][0][i]; 65 const CeedScalar J21 = J[0][1][i]; 66 const CeedScalar J31 = J[0][2][i]; 67 const CeedScalar J12 = J[1][0][i]; 68 const CeedScalar J22 = J[1][1][i]; 69 const CeedScalar J32 = J[1][2][i]; 70 const CeedScalar J13 = J[2][0][i]; 71 const CeedScalar J23 = J[2][1][i]; 72 const CeedScalar J33 = J[2][2][i]; 73 const CeedScalar A11 = J22 * J33 - J23 * J32; 74 const CeedScalar A12 = J13 * J32 - J12 * J33; 75 const CeedScalar A13 = J12 * J23 - J13 * J22; 76 const CeedScalar A21 = J23 * J31 - J21 * J33; 77 const CeedScalar A22 = J11 * J33 - J13 * J31; 78 const CeedScalar A23 = J13 * J21 - J11 * J23; 79 const CeedScalar A31 = J21 * J32 - J22 * J31; 80 const CeedScalar A32 = J12 * J31 - J11 * J32; 81 const CeedScalar A33 = J11 * J22 - J12 * J21; 82 const CeedScalar detJ = J11 * A11 + J21 * A12 + J31 * A13; 83 84 // Qdata 85 // -- Interp-to-Interp q_data 86 q_data[0][i] = w[i] * detJ; 87 // -- Interp-to-Grad q_data 88 // Inverse of change of coordinate matrix: X_i,j 89 q_data[1][i] = A11 / detJ; 90 q_data[2][i] = A12 / detJ; 91 q_data[3][i] = A13 / detJ; 92 q_data[4][i] = A21 / detJ; 93 q_data[5][i] = A22 / detJ; 94 q_data[6][i] = A23 / detJ; 95 q_data[7][i] = A31 / detJ; 96 q_data[8][i] = A32 / detJ; 97 q_data[9][i] = A33 / detJ; 98 99 } // End of Quadrature Point Loop 100 101 // Return 102 return 0; 103 } 104 105 // ***************************************************************************** 106 // This QFunction sets up the geometric factor required for integration when 107 // reference coordinates are in 2D and the physical coordinates are in 3D 108 // 109 // Reference (parent) 2D coordinates: X 110 // Physical (current) 3D coordinates: x 111 // Change of coordinate matrix: 112 // dxdX_{i,j} = dx_i/dX_j (indicial notation) [3 * 2] 113 // Inverse change of coordinate matrix: 114 // dXdx_{i,j} = dX_i/dx_j (indicial notation) [2 * 3] 115 // 116 // (J1,J2,J3) is given by the cross product of the columns of dxdX_{i,j} 117 // 118 // detJb is the magnitude of (J1,J2,J3) 119 // 120 // dXdx is calculated via Moore–Penrose inverse: 121 // 122 // dX_i/dx_j = (dxdX^T dxdX)^(-1) dxdX 123 // = (dx_l/dX_i * dx_l/dX_k)^(-1) dx_j/dX_k 124 // 125 // All quadrature data is stored in 10 field vector of quadrature data. 126 // 127 // We require the determinant of the Jacobian to properly compute integrals of 128 // the form: int( u v ) 129 // 130 // Stored: w detJb 131 // in q_data_sur[0] 132 // 133 // Normal vector = (J1,J2,J3) / detJb 134 // 135 // - TODO Could possibly remove normal vector, as it could be calculated in the Qfunction from dXdx 136 // Stored: (J1,J2,J3) / detJb 137 // in q_data_sur[1:3] as 138 // (detJb^-1) * [ J1 ] 139 // [ J2 ] 140 // [ J3 ] 141 // 142 // Stored: dXdx_{i,j} 143 // in q_data_sur[4:9] as 144 // [dXdx_11 dXdx_12 dXdx_13] 145 // [dXdx_21 dXdx_22 dXdx_23] 146 // 147 // ***************************************************************************** 148 CEED_QFUNCTION(SetupBoundary)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 149 // Inputs 150 const CeedScalar(*J)[3][CEED_Q_VLA] = (const CeedScalar(*)[3][CEED_Q_VLA])in[0]; 151 const CeedScalar(*w) = in[1]; 152 153 // Outputs 154 CeedScalar(*q_data_sur)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 155 156 CeedPragmaSIMD 157 // Quadrature Point Loop 158 for (CeedInt i = 0; i < Q; i++) { 159 // Setup 160 const CeedScalar dxdX[3][2] = { 161 {J[0][0][i], J[1][0][i]}, 162 {J[0][1][i], J[1][1][i]}, 163 {J[0][2][i], J[1][2][i]} 164 }; 165 // J1, J2, and J3 are given by the cross product of the columns of dxdX 166 const CeedScalar J1 = dxdX[1][0] * dxdX[2][1] - dxdX[2][0] * dxdX[1][1]; 167 const CeedScalar J2 = dxdX[2][0] * dxdX[0][1] - dxdX[0][0] * dxdX[2][1]; 168 const CeedScalar J3 = dxdX[0][0] * dxdX[1][1] - dxdX[1][0] * dxdX[0][1]; 169 170 const CeedScalar detJb = sqrt(J1 * J1 + J2 * J2 + J3 * J3); 171 172 // q_data_sur 173 // -- Interp-to-Interp q_data_sur 174 q_data_sur[0][i] = w[i] * detJb; 175 q_data_sur[1][i] = J1 / detJb; 176 q_data_sur[2][i] = J2 / detJb; 177 q_data_sur[3][i] = J3 / detJb; 178 179 // dxdX_k,j * dxdX_j,k 180 CeedScalar dxdXTdxdX[2][2] = {{0.}}; 181 for (CeedInt j = 0; j < 2; j++) { 182 for (CeedInt k = 0; k < 2; k++) { 183 for (CeedInt l = 0; l < 3; l++) dxdXTdxdX[j][k] += dxdX[l][j] * dxdX[l][k]; 184 } 185 } 186 187 const CeedScalar detdxdXTdxdX = dxdXTdxdX[0][0] * dxdXTdxdX[1][1] - dxdXTdxdX[1][0] * dxdXTdxdX[0][1]; 188 189 // Compute inverse of dxdXTdxdX 190 CeedScalar dxdXTdxdX_inv[2][2]; 191 dxdXTdxdX_inv[0][0] = dxdXTdxdX[1][1] / detdxdXTdxdX; 192 dxdXTdxdX_inv[0][1] = -dxdXTdxdX[0][1] / detdxdXTdxdX; 193 dxdXTdxdX_inv[1][0] = -dxdXTdxdX[1][0] / detdxdXTdxdX; 194 dxdXTdxdX_inv[1][1] = dxdXTdxdX[0][0] / detdxdXTdxdX; 195 196 // Compute dXdx from dxdXTdxdX^-1 and dxdX 197 CeedScalar dXdx[2][3] = {{0.}}; 198 for (CeedInt j = 0; j < 2; j++) { 199 for (CeedInt k = 0; k < 3; k++) { 200 for (CeedInt l = 0; l < 2; l++) dXdx[j][k] += dxdXTdxdX_inv[l][j] * dxdX[k][l]; 201 } 202 } 203 204 q_data_sur[4][i] = dXdx[0][0]; 205 q_data_sur[5][i] = dXdx[0][1]; 206 q_data_sur[6][i] = dXdx[0][2]; 207 q_data_sur[7][i] = dXdx[1][0]; 208 q_data_sur[8][i] = dXdx[1][1]; 209 q_data_sur[9][i] = dXdx[1][2]; 210 211 } // End of Quadrature Point Loop 212 213 // Return 214 return 0; 215 } 216 217 // ***************************************************************************** 218 219 #endif // setup_geo_h 220