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 /// libCEED QFunctions for diffusion operator example using PETSc 10 11 #ifndef bp3_h 12 #define bp3_h 13 14 #include <ceed.h> 15 #include <math.h> 16 17 // ----------------------------------------------------------------------------- 18 // This QFunction sets up the geometric factors required to apply the 19 // diffusion operator 20 // 21 // We require the product of the inverse of the Jacobian and its transpose to 22 // properly compute integrals of the form: int( gradv gradu) 23 // 24 // Determinant of Jacobian: 25 // detJ = J11*A11 + J21*A12 + J31*A13 26 // Jij = Jacobian entry ij 27 // Aij = Adjoint ij 28 // 29 // Inverse of Jacobian: 30 // Bij = Aij / detJ 31 // 32 // Product of Inverse and Transpose: 33 // BBij = sum( Bik Bkj ) 34 // 35 // Stored: w B^T B detJ = w A^T A / detJ 36 // Note: This matrix is symmetric, so we only store 6 distinct entries 37 // qd: 0 3 6 38 // 1 4 7 39 // 2 5 8 40 // ----------------------------------------------------------------------------- 41 CEED_QFUNCTION(SetupDiffGeo)(void *ctx, CeedInt Q, 42 const CeedScalar *const *in, 43 CeedScalar *const *out) { 44 const CeedScalar *J = in[1], *w = in[2]; // Note: *X = in[0] 45 CeedScalar *qd = out[0]; 46 47 // Quadrature Point Loop 48 CeedPragmaSIMD 49 for (CeedInt i=0; i<Q; i++) { 50 const CeedScalar J11 = J[i+Q*0]; 51 const CeedScalar J21 = J[i+Q*1]; 52 const CeedScalar J31 = J[i+Q*2]; 53 const CeedScalar J12 = J[i+Q*3]; 54 const CeedScalar J22 = J[i+Q*4]; 55 const CeedScalar J32 = J[i+Q*5]; 56 const CeedScalar J13 = J[i+Q*6]; 57 const CeedScalar J23 = J[i+Q*7]; 58 const CeedScalar J33 = J[i+Q*8]; 59 const CeedScalar A11 = J22*J33 - J23*J32; 60 const CeedScalar A12 = J13*J32 - J12*J33; 61 const CeedScalar A13 = J12*J23 - J13*J22; 62 const CeedScalar A21 = J23*J31 - J21*J33; 63 const CeedScalar A22 = J11*J33 - J13*J31; 64 const CeedScalar A23 = J13*J21 - J11*J23; 65 const CeedScalar A31 = J21*J32 - J22*J31; 66 const CeedScalar A32 = J12*J31 - J11*J32; 67 const CeedScalar A33 = J11*J22 - J12*J21; 68 const CeedScalar qw = w[i] / (J11*A11 + J21*A12 + J31*A13); 69 qd[i+Q*0] = qw * (A11*A11 + A12*A12 + A13*A13); 70 qd[i+Q*1] = qw * (A11*A21 + A12*A22 + A13*A23); 71 qd[i+Q*2] = qw * (A11*A31 + A12*A32 + A13*A33); 72 qd[i+Q*3] = qw * (A21*A21 + A22*A22 + A23*A23); 73 qd[i+Q*4] = qw * (A21*A31 + A22*A32 + A23*A33); 74 qd[i+Q*5] = qw * (A31*A31 + A32*A32 + A33*A33); 75 qd[i+Q*6] = w[i] * (J11*A11 + J21*A12 + J31*A13); 76 } // End of Quadrature Point Loop 77 78 return 0; 79 } 80 81 // ----------------------------------------------------------------------------- 82 // This QFunction sets up the rhs and true solution for the problem 83 // ----------------------------------------------------------------------------- 84 CEED_QFUNCTION(SetupDiffRhs)(void *ctx, CeedInt Q, 85 const CeedScalar *const *in, 86 CeedScalar *const *out) { 87 #ifndef M_PI 88 # define M_PI 3.14159265358979323846 89 #endif 90 const CeedScalar *x = in[0], *w = in[1]; 91 CeedScalar *true_soln = out[0], *rhs = out[1]; 92 93 // Quadrature Point Loop 94 CeedPragmaSIMD 95 for (CeedInt i=0; i<Q; i++) { 96 const CeedScalar c[3] = { 0, 1., 2. }; 97 const CeedScalar k[3] = { 1., 2., 3. }; 98 99 true_soln[i] = sin(M_PI*(c[0] + k[0]*x[i+Q*0])) * 100 sin(M_PI*(c[1] + k[1]*x[i+Q*1])) * 101 sin(M_PI*(c[2] + k[2]*x[i+Q*2])); 102 103 rhs[i] = w[i+Q*6] * M_PI*M_PI * (k[0]*k[0] + k[1]*k[1] + k[2]*k[2]) * 104 true_soln[i]; 105 } // End of Quadrature Point Loop 106 107 return 0; 108 } 109 110 // ----------------------------------------------------------------------------- 111 // This QFunction applies the diffusion operator for a scalar field. 112 // 113 // Inputs: 114 // ug - Input vector gradient at quadrature points 115 // q_data - Geometric factors 116 // 117 // Output: 118 // vg - Output vector (test functions) gradient at quadrature points 119 // 120 // ----------------------------------------------------------------------------- 121 CEED_QFUNCTION(Diff)(void *ctx, CeedInt Q, 122 const CeedScalar *const *in, CeedScalar *const *out) { 123 const CeedScalar *ug = in[0], *q_data = in[1]; 124 CeedScalar *vg = out[0]; 125 126 // Quadrature Point Loop 127 CeedPragmaSIMD 128 for (CeedInt i=0; i<Q; i++) { 129 // Read spatial derivatives of u 130 const CeedScalar du[3] = {ug[i+Q*0], 131 ug[i+Q*1], 132 ug[i+Q*2] 133 }; 134 // Read q_data (dXdxdXdx_T symmetric matrix) 135 const CeedScalar dXdxdXdx_T[3][3] = {{q_data[i+0*Q], 136 q_data[i+1*Q], 137 q_data[i+2*Q]}, 138 {q_data[i+1*Q], 139 q_data[i+3*Q], 140 q_data[i+4*Q]}, 141 {q_data[i+2*Q], 142 q_data[i+4*Q], 143 q_data[i+5*Q]} 144 }; 145 146 for (int j=0; j<3; j++) // j = direction of vg 147 vg[i+j*Q] = (du[0] * dXdxdXdx_T[0][j] + 148 du[1] * dXdxdXdx_T[1][j] + 149 du[2] * dXdxdXdx_T[2][j]); 150 151 } // End of Quadrature Point Loop 152 return 0; 153 } 154 // ----------------------------------------------------------------------------- 155 156 #endif // bp3_h 157