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 // ***************************************************************************** 21 // This QFunction sets up the geometric factors required to apply the 22 // diffusion operator 23 // 24 // We require the product of the inverse of the Jacobian and its transpose to 25 // properly compute integrals of the form: int( gradv gradu) 26 // 27 // Determinant of Jacobian: 28 // detJ = J11*A11 + J21*A12 + J31*A13 29 // Jij = Jacobian entry ij 30 // Aij = Adjoint ij 31 // 32 // Inverse of Jacobian: 33 // Bij = Aij / detJ 34 // 35 // Product of Inverse and Transpose: 36 // BBij = sum( Bik Bkj ) 37 // 38 // Stored: w B^T B detJ = w A^T A / detJ 39 // Note: This matrix is symmetric, so we only store 6 distinct entries 40 // qd: 0 3 6 41 // 1 4 7 42 // 2 5 8 43 // ***************************************************************************** 44 45 // ----------------------------------------------------------------------------- 46 CEED_QFUNCTION(SetupDiffGeo)(void *ctx, CeedInt Q, 47 const CeedScalar *const *in, 48 CeedScalar *const *out) { 49 const CeedScalar *J = in[0], *w = in[1]; 50 CeedScalar *qd = out[0]; 51 52 // Quadrature Point Loop 53 CeedPragmaSIMD 54 for (CeedInt i=0; i<Q; i++) { 55 const CeedScalar J11 = J[i+Q*0]; 56 const CeedScalar J21 = J[i+Q*1]; 57 const CeedScalar J31 = J[i+Q*2]; 58 const CeedScalar J12 = J[i+Q*3]; 59 const CeedScalar J22 = J[i+Q*4]; 60 const CeedScalar J32 = J[i+Q*5]; 61 const CeedScalar J13 = J[i+Q*6]; 62 const CeedScalar J23 = J[i+Q*7]; 63 const CeedScalar J33 = J[i+Q*8]; 64 const CeedScalar A11 = J22*J33 - J23*J32; 65 const CeedScalar A12 = J13*J32 - J12*J33; 66 const CeedScalar A13 = J12*J23 - J13*J22; 67 const CeedScalar A21 = J23*J31 - J21*J33; 68 const CeedScalar A22 = J11*J33 - J13*J31; 69 const CeedScalar A23 = J13*J21 - J11*J23; 70 const CeedScalar A31 = J21*J32 - J22*J31; 71 const CeedScalar A32 = J12*J31 - J11*J32; 72 const CeedScalar A33 = J11*J22 - J12*J21; 73 const CeedScalar qw = w[i] / (J11*A11 + J21*A12 + J31*A13); 74 qd[i+Q*0] = qw * (A11*A11 + A12*A12 + A13*A13); 75 qd[i+Q*1] = qw * (A11*A21 + A12*A22 + A13*A23); 76 qd[i+Q*2] = qw * (A11*A31 + A12*A32 + A13*A33); 77 qd[i+Q*3] = qw * (A21*A21 + A22*A22 + A23*A23); 78 qd[i+Q*4] = qw * (A21*A31 + A22*A32 + A23*A33); 79 qd[i+Q*5] = qw * (A31*A31 + A32*A32 + A33*A33); 80 } // End of Quadrature Point Loop 81 82 return 0; 83 } 84 85 // ***************************************************************************** 86 // This QFunction sets up the rhs and true solution for the problem 87 // ***************************************************************************** 88 89 // ----------------------------------------------------------------------------- 90 CEED_QFUNCTION(SetupDiffRhs)(void *ctx, CeedInt Q, 91 const CeedScalar *const *in, 92 CeedScalar *const *out) { 93 #ifndef M_PI 94 # define M_PI 3.14159265358979323846 95 #endif 96 const CeedScalar *x = in[0], *J = in[1], *w = in[2]; 97 CeedScalar *true_soln = out[0], *rhs = out[1]; 98 99 // Quadrature Point Loop 100 CeedPragmaSIMD 101 for (CeedInt i=0; i<Q; i++) { 102 const CeedScalar J11 = J[i+Q*0]; 103 const CeedScalar J21 = J[i+Q*1]; 104 const CeedScalar J31 = J[i+Q*2]; 105 const CeedScalar J12 = J[i+Q*3]; 106 const CeedScalar J22 = J[i+Q*4]; 107 const CeedScalar J32 = J[i+Q*5]; 108 const CeedScalar J13 = J[i+Q*6]; 109 const CeedScalar J23 = J[i+Q*7]; 110 const CeedScalar J33 = J[i+Q*8]; 111 const CeedScalar A11 = J22*J33 - J23*J32; 112 const CeedScalar A12 = J13*J32 - J12*J33; 113 const CeedScalar A13 = J12*J23 - J13*J22; 114 115 const CeedScalar c[3] = { 0, 1., 2. }; 116 const CeedScalar k[3] = { 1., 2., 3. }; 117 118 true_soln[i] = sin(M_PI*(c[0] + k[0]*x[i+Q*0])) * 119 sin(M_PI*(c[1] + k[1]*x[i+Q*1])) * 120 sin(M_PI*(c[2] + k[2]*x[i+Q*2])); 121 122 const CeedScalar rho = w[i] * (J11*A11 + J21*A12 + J31*A13); 123 rhs[i] = rho * M_PI*M_PI * (k[0]*k[0] + k[1]*k[1] + k[2]*k[2]) * 124 true_soln[i]; 125 } // End of Quadrature Point Loop 126 127 return 0; 128 } 129 130 // ***************************************************************************** 131 // This QFunction applies the diffusion operator for a scalar field. 132 // 133 // Inputs: 134 // ug - Input vector gradient at quadrature points 135 // qdata - Geometric factors 136 // 137 // Output: 138 // vg - Output vector (test functions) gradient at quadrature points 139 // 140 // ***************************************************************************** 141 142 // ----------------------------------------------------------------------------- 143 CEED_QFUNCTION(Diff)(void *ctx, CeedInt Q, 144 const CeedScalar *const *in, CeedScalar *const *out) { 145 const CeedScalar *ug = in[0], *qdata = in[1]; 146 CeedScalar *vg = out[0]; 147 148 // Quadrature Point Loop 149 CeedPragmaSIMD 150 for (CeedInt i=0; i<Q; i++) { 151 // Read spatial derivatives of u 152 const CeedScalar du[3] = {ug[i+Q*0], 153 ug[i+Q*1], 154 ug[i+Q*2] 155 }; 156 // Read qdata (dXdxdXdxT symmetric matrix) 157 const CeedScalar dXdxdXdxT[3][3] = {{qdata[i+0*Q], 158 qdata[i+1*Q], 159 qdata[i+2*Q]}, 160 {qdata[i+1*Q], 161 qdata[i+3*Q], 162 qdata[i+4*Q]}, 163 {qdata[i+2*Q], 164 qdata[i+4*Q], 165 qdata[i+5*Q]} 166 }; 167 168 for (int j=0; j<3; j++) // j = direction of vg 169 vg[i+j*Q] = (du[0] * dXdxdXdxT[0][j] + 170 du[1] * dXdxdXdxT[1][j] + 171 du[2] * dXdxdXdxT[2][j]); 172 173 } // End of Quadrature Point Loop 174 return 0; 175 } 176 // ----------------------------------------------------------------------------- 177