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 /// libCEED QFunctions for diffusion operator example using PETSc 19 20 #ifndef bp3_h 21 #define bp3_h 22 23 #ifndef __CUDACC__ 24 # include <math.h> 25 #endif 26 27 // ----------------------------------------------------------------------------- 28 // This QFunction sets up the geometric factors required to apply the 29 // diffusion operator 30 // 31 // We require the product of the inverse of the Jacobian and its transpose to 32 // properly compute integrals of the form: int( gradv gradu) 33 // 34 // Determinant of Jacobian: 35 // detJ = J11*A11 + J21*A12 + J31*A13 36 // Jij = Jacobian entry ij 37 // Aij = Adjoint ij 38 // 39 // Inverse of Jacobian: 40 // Bij = Aij / detJ 41 // 42 // Product of Inverse and Transpose: 43 // BBij = sum( Bik Bkj ) 44 // 45 // Stored: w B^T B detJ = w A^T A / detJ 46 // Note: This matrix is symmetric, so we only store 6 distinct entries 47 // qd: 0 3 6 48 // 1 4 7 49 // 2 5 8 50 // ----------------------------------------------------------------------------- 51 CEED_QFUNCTION(SetupDiffGeo)(void *ctx, CeedInt Q, 52 const CeedScalar *const *in, 53 CeedScalar *const *out) { 54 const CeedScalar *J = in[1], *w = in[2]; // Note: *X = in[0] 55 CeedScalar *qd = out[0]; 56 57 // Quadrature Point Loop 58 CeedPragmaSIMD 59 for (CeedInt i=0; i<Q; i++) { 60 const CeedScalar J11 = J[i+Q*0]; 61 const CeedScalar J21 = J[i+Q*1]; 62 const CeedScalar J31 = J[i+Q*2]; 63 const CeedScalar J12 = J[i+Q*3]; 64 const CeedScalar J22 = J[i+Q*4]; 65 const CeedScalar J32 = J[i+Q*5]; 66 const CeedScalar J13 = J[i+Q*6]; 67 const CeedScalar J23 = J[i+Q*7]; 68 const CeedScalar J33 = J[i+Q*8]; 69 const CeedScalar A11 = J22*J33 - J23*J32; 70 const CeedScalar A12 = J13*J32 - J12*J33; 71 const CeedScalar A13 = J12*J23 - J13*J22; 72 const CeedScalar A21 = J23*J31 - J21*J33; 73 const CeedScalar A22 = J11*J33 - J13*J31; 74 const CeedScalar A23 = J13*J21 - J11*J23; 75 const CeedScalar A31 = J21*J32 - J22*J31; 76 const CeedScalar A32 = J12*J31 - J11*J32; 77 const CeedScalar A33 = J11*J22 - J12*J21; 78 const CeedScalar qw = w[i] / (J11*A11 + J21*A12 + J31*A13); 79 qd[i+Q*0] = qw * (A11*A11 + A12*A12 + A13*A13); 80 qd[i+Q*1] = qw * (A11*A21 + A12*A22 + A13*A23); 81 qd[i+Q*2] = qw * (A11*A31 + A12*A32 + A13*A33); 82 qd[i+Q*3] = qw * (A21*A21 + A22*A22 + A23*A23); 83 qd[i+Q*4] = qw * (A21*A31 + A22*A32 + A23*A33); 84 qd[i+Q*5] = qw * (A31*A31 + A32*A32 + A33*A33); 85 qd[i+Q*6] = w[i] * (J11*A11 + J21*A12 + J31*A13); 86 } // End of Quadrature Point Loop 87 88 return 0; 89 } 90 91 // ----------------------------------------------------------------------------- 92 // This QFunction sets up the rhs and true solution for the problem 93 // ----------------------------------------------------------------------------- 94 CEED_QFUNCTION(SetupDiffRhs)(void *ctx, CeedInt Q, 95 const CeedScalar *const *in, 96 CeedScalar *const *out) { 97 #ifndef M_PI 98 # define M_PI 3.14159265358979323846 99 #endif 100 const CeedScalar *x = in[0], *w = in[1]; 101 CeedScalar *true_soln = out[0], *rhs = out[1]; 102 103 // Quadrature Point Loop 104 CeedPragmaSIMD 105 for (CeedInt i=0; i<Q; i++) { 106 const CeedScalar c[3] = { 0, 1., 2. }; 107 const CeedScalar k[3] = { 1., 2., 3. }; 108 109 true_soln[i] = sin(M_PI*(c[0] + k[0]*x[i+Q*0])) * 110 sin(M_PI*(c[1] + k[1]*x[i+Q*1])) * 111 sin(M_PI*(c[2] + k[2]*x[i+Q*2])); 112 113 rhs[i] = w[i+Q*6] * M_PI*M_PI * (k[0]*k[0] + k[1]*k[1] + k[2]*k[2]) * 114 true_soln[i]; 115 } // End of Quadrature Point Loop 116 117 return 0; 118 } 119 120 // ----------------------------------------------------------------------------- 121 // This QFunction applies the diffusion operator for a scalar field. 122 // 123 // Inputs: 124 // ug - Input vector gradient at quadrature points 125 // q_data - Geometric factors 126 // 127 // Output: 128 // vg - Output vector (test functions) gradient at quadrature points 129 // 130 // ----------------------------------------------------------------------------- 131 CEED_QFUNCTION(Diff)(void *ctx, CeedInt Q, 132 const CeedScalar *const *in, CeedScalar *const *out) { 133 const CeedScalar *ug = in[0], *q_data = in[1]; 134 CeedScalar *vg = out[0]; 135 136 // Quadrature Point Loop 137 CeedPragmaSIMD 138 for (CeedInt i=0; i<Q; i++) { 139 // Read spatial derivatives of u 140 const CeedScalar du[3] = {ug[i+Q*0], 141 ug[i+Q*1], 142 ug[i+Q*2] 143 }; 144 // Read q_data (dXdxdXdx_T symmetric matrix) 145 const CeedScalar dXdxdXdx_T[3][3] = {{q_data[i+0*Q], 146 q_data[i+1*Q], 147 q_data[i+2*Q]}, 148 {q_data[i+1*Q], 149 q_data[i+3*Q], 150 q_data[i+4*Q]}, 151 {q_data[i+2*Q], 152 q_data[i+4*Q], 153 q_data[i+5*Q]} 154 }; 155 156 for (int j=0; j<3; j++) // j = direction of vg 157 vg[i+j*Q] = (du[0] * dXdxdXdx_T[0][j] + 158 du[1] * dXdxdXdx_T[1][j] + 159 du[2] * dXdxdXdx_T[2][j]); 160 161 } // End of Quadrature Point Loop 162 return 0; 163 } 164 // ----------------------------------------------------------------------------- 165 166 #endif // bp3_h 167