1 // Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at 2 // the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights 3 // reserved. See files LICENSE and NOTICE for details. 4 // 5 // This file is part of CEED, a collection of benchmarks, miniapps, software 6 // libraries and APIs for efficient high-order finite element and spectral 7 // element discretizations for exascale applications. For more information and 8 // source code availability see http://github.com/ceed. 9 // 10 // The CEED research is supported by the Exascale Computing Project 17-SC-20-SC, 11 // a collaborative effort of two U.S. Department of Energy organizations (Office 12 // of Science and the National Nuclear Security Administration) responsible for 13 // the planning and preparation of a capable exascale ecosystem, including 14 // software, applications, hardware, advanced system engineering and early 15 // testbed platforms, in support of the nation's exascale computing imperative. 16 17 /// @file 18 /// Geometric factors (3D) for Navier-Stokes example using PETSc 19 20 #ifndef setup_geo_h 21 #define setup_geo_h 22 23 #include <math.h> 24 25 // ***************************************************************************** 26 // This QFunction sets up the geometric factors required for integration and 27 // coordinate transformations 28 // 29 // Reference (parent) coordinates: X 30 // Physical (current) coordinates: x 31 // Change of coordinate matrix: dxdX_{i,j} = x_{i,j} (indicial notation) 32 // Inverse of change of coordinate matrix: dXdx_{i,j} = (detJ^-1) * X_{i,j} 33 // 34 // All quadrature data is stored in 10 field vector of quadrature data. 35 // 36 // We require the determinant of the Jacobian to properly compute integrals of 37 // the form: int( v u ) 38 // 39 // Determinant of Jacobian: 40 // detJ = J11*A11 + J21*A12 + J31*A13 41 // Jij = Jacobian entry ij 42 // Aij = Adjoint ij 43 // 44 // Stored: w detJ 45 // in q_data[0] 46 // 47 // We require the transpose of the inverse of the Jacobian to properly compute 48 // integrals of the form: int( gradv u ) 49 // 50 // Inverse of Jacobian: 51 // dXdx_i,j = Aij / detJ 52 // 53 // Stored: Aij / detJ 54 // in q_data[1:9] as 55 // (detJ^-1) * [A11 A12 A13] 56 // [A21 A22 A23] 57 // [A31 A32 A33] 58 // 59 // ***************************************************************************** 60 CEED_QFUNCTION(Setup)(void *ctx, CeedInt Q, 61 const CeedScalar *const *in, CeedScalar *const *out) { 62 // *INDENT-OFF* 63 // Inputs 64 const CeedScalar (*J)[3][CEED_Q_VLA] = (const CeedScalar(*)[3][CEED_Q_VLA])in[0], 65 (*w) = in[1]; 66 67 // Outputs 68 CeedScalar (*q_data)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 69 // *INDENT-ON* 70 71 CeedPragmaSIMD 72 // Quadrature Point Loop 73 for (CeedInt i=0; i<Q; i++) { 74 // Setup 75 const CeedScalar J11 = J[0][0][i]; 76 const CeedScalar J21 = J[0][1][i]; 77 const CeedScalar J31 = J[0][2][i]; 78 const CeedScalar J12 = J[1][0][i]; 79 const CeedScalar J22 = J[1][1][i]; 80 const CeedScalar J32 = J[1][2][i]; 81 const CeedScalar J13 = J[2][0][i]; 82 const CeedScalar J23 = J[2][1][i]; 83 const CeedScalar J33 = J[2][2][i]; 84 const CeedScalar A11 = J22*J33 - J23*J32; 85 const CeedScalar A12 = J13*J32 - J12*J33; 86 const CeedScalar A13 = J12*J23 - J13*J22; 87 const CeedScalar A21 = J23*J31 - J21*J33; 88 const CeedScalar A22 = J11*J33 - J13*J31; 89 const CeedScalar A23 = J13*J21 - J11*J23; 90 const CeedScalar A31 = J21*J32 - J22*J31; 91 const CeedScalar A32 = J12*J31 - J11*J32; 92 const CeedScalar A33 = J11*J22 - J12*J21; 93 const CeedScalar detJ = J11*A11 + J21*A12 + J31*A13; 94 95 // Qdata 96 // -- Interp-to-Interp q_data 97 q_data[0][i] = w[i] * detJ; 98 // -- Interp-to-Grad q_data 99 // Inverse of change of coordinate matrix: X_i,j 100 q_data[1][i] = A11 / detJ; 101 q_data[2][i] = A12 / detJ; 102 q_data[3][i] = A13 / detJ; 103 q_data[4][i] = A21 / detJ; 104 q_data[5][i] = A22 / detJ; 105 q_data[6][i] = A23 / detJ; 106 q_data[7][i] = A31 / detJ; 107 q_data[8][i] = A32 / detJ; 108 q_data[9][i] = A33 / detJ; 109 110 } // End of Quadrature Point Loop 111 112 // Return 113 return 0; 114 } 115 116 // ***************************************************************************** 117 // This QFunction sets up the geometric factor required for integration when 118 // reference coordinates are in 2D and the physical coordinates are in 3D 119 // 120 // Reference (parent) 2D coordinates: X 121 // Physical (current) 3D coordinates: x 122 // Change of coordinate matrix: 123 // dxdX_{i,j} = dx_i/dX_j (indicial notation) [3 * 2] 124 // 125 // (J1,J2,J3) is given by the cross product of the columns of dxdX_{i,j} 126 // 127 // detJb is the magnitude of (J1,J2,J3) 128 // 129 // All quadrature data is stored in 4 field vector of quadrature data. 130 // 131 // We require the determinant of the Jacobian to properly compute integrals of 132 // the form: int( u v ) 133 // 134 // Stored: w detJb 135 // in q_data_sur[0] 136 // 137 // Normal vector = (J1,J2,J3) / detJb 138 // 139 // Stored: (J1,J2,J3) / detJb 140 // in q_data_sur[1:3] as 141 // (detJb^-1) * [ J1 ] 142 // [ J2 ] 143 // [ J3 ] 144 // 145 // ***************************************************************************** 146 CEED_QFUNCTION(SetupBoundary)(void *ctx, CeedInt Q, 147 const CeedScalar *const *in, CeedScalar *const *out) { 148 // *INDENT-OFF* 149 // Inputs 150 const CeedScalar (*J)[3][CEED_Q_VLA] = (const CeedScalar(*)[3][CEED_Q_VLA])in[0], 151 (*w) = in[1]; 152 // Outputs 153 CeedScalar (*q_data_sur)[CEED_Q_VLA] = (CeedScalar(*)[CEED_Q_VLA])out[0]; 154 155 CeedPragmaSIMD 156 // Quadrature Point Loop 157 for (CeedInt i=0; i<Q; i++) { 158 // Setup 159 const CeedScalar dxdX[3][2] = {{J[0][0][i], 160 J[1][0][i]}, 161 {J[0][1][i], 162 J[1][1][i]}, 163 {J[0][2][i], 164 J[1][2][i]} 165 }; 166 // *INDENT-ON* 167 // J1, J2, and J3 are given by the cross product of the columns of dxdX 168 const CeedScalar J1 = dxdX[1][0]*dxdX[2][1] - dxdX[2][0]*dxdX[1][1]; 169 const CeedScalar J2 = dxdX[2][0]*dxdX[0][1] - dxdX[0][0]*dxdX[2][1]; 170 const CeedScalar J3 = dxdX[0][0]*dxdX[1][1] - dxdX[1][0]*dxdX[0][1]; 171 172 const CeedScalar detJb = sqrt(J1*J1 + J2*J2 + J3*J3); 173 174 // q_data_sur 175 // -- Interp-to-Interp q_data_sur 176 q_data_sur[0][i] = w[i] * detJb; 177 q_data_sur[1][i] = J1 / detJb; 178 q_data_sur[2][i] = J2 / detJb; 179 q_data_sur[3][i] = J3 / detJb; 180 181 } // End of Quadrature Point Loop 182 183 // Return 184 return 0; 185 } 186 187 // ***************************************************************************** 188 189 #endif // setup_geo_h 190