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