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 #ifndef bp3_h 46 #define bp3_h 47 #include <ceed.h> 48 49 #ifndef __CUDACC__ 50 # include <math.h> 51 #endif 52 53 // ----------------------------------------------------------------------------- 54 CEED_QFUNCTION(SetupDiffGeo)(void *ctx, CeedInt Q, 55 const CeedScalar *const *in, 56 CeedScalar *const *out) { 57 const CeedScalar *J = in[0], *w = in[1]; 58 CeedScalar *qd = out[0]; 59 60 // Quadrature Point Loop 61 CeedPragmaSIMD 62 for (CeedInt i=0; i<Q; i++) { 63 const CeedScalar J11 = J[i+Q*0]; 64 const CeedScalar J21 = J[i+Q*1]; 65 const CeedScalar J31 = J[i+Q*2]; 66 const CeedScalar J12 = J[i+Q*3]; 67 const CeedScalar J22 = J[i+Q*4]; 68 const CeedScalar J32 = J[i+Q*5]; 69 const CeedScalar J13 = J[i+Q*6]; 70 const CeedScalar J23 = J[i+Q*7]; 71 const CeedScalar J33 = J[i+Q*8]; 72 const CeedScalar A11 = J22*J33 - J23*J32; 73 const CeedScalar A12 = J13*J32 - J12*J33; 74 const CeedScalar A13 = J12*J23 - J13*J22; 75 const CeedScalar A21 = J23*J31 - J21*J33; 76 const CeedScalar A22 = J11*J33 - J13*J31; 77 const CeedScalar A23 = J13*J21 - J11*J23; 78 const CeedScalar A31 = J21*J32 - J22*J31; 79 const CeedScalar A32 = J12*J31 - J11*J32; 80 const CeedScalar A33 = J11*J22 - J12*J21; 81 const CeedScalar qw = w[i] / (J11*A11 + J21*A12 + J31*A13); 82 qd[i+Q*0] = qw * (A11*A11 + A12*A12 + A13*A13); 83 qd[i+Q*1] = qw * (A11*A21 + A12*A22 + A13*A23); 84 qd[i+Q*2] = qw * (A11*A31 + A12*A32 + A13*A33); 85 qd[i+Q*3] = qw * (A21*A21 + A22*A22 + A23*A23); 86 qd[i+Q*4] = qw * (A21*A31 + A22*A32 + A23*A33); 87 qd[i+Q*5] = qw * (A31*A31 + A32*A32 + A33*A33); 88 } // End of Quadrature Point Loop 89 90 return 0; 91 } 92 93 // ***************************************************************************** 94 // This QFunction sets up the rhs and true solution for the problem 95 // ***************************************************************************** 96 97 // ----------------------------------------------------------------------------- 98 CEED_QFUNCTION(SetupDiffRhs)(void *ctx, CeedInt Q, 99 const CeedScalar *const *in, 100 CeedScalar *const *out) { 101 #ifndef M_PI 102 # define M_PI 3.14159265358979323846 103 #endif 104 const CeedScalar *x = in[0], *J = in[1], *w = in[2]; 105 CeedScalar *true_soln = out[0], *rhs = out[1]; 106 107 // Quadrature Point Loop 108 CeedPragmaSIMD 109 for (CeedInt i=0; i<Q; i++) { 110 const CeedScalar J11 = J[i+Q*0]; 111 const CeedScalar J21 = J[i+Q*1]; 112 const CeedScalar J31 = J[i+Q*2]; 113 const CeedScalar J12 = J[i+Q*3]; 114 const CeedScalar J22 = J[i+Q*4]; 115 const CeedScalar J32 = J[i+Q*5]; 116 const CeedScalar J13 = J[i+Q*6]; 117 const CeedScalar J23 = J[i+Q*7]; 118 const CeedScalar J33 = J[i+Q*8]; 119 const CeedScalar A11 = J22*J33 - J23*J32; 120 const CeedScalar A12 = J13*J32 - J12*J33; 121 const CeedScalar A13 = J12*J23 - J13*J22; 122 123 const CeedScalar c[3] = { 0, 1., 2. }; 124 const CeedScalar k[3] = { 1., 2., 3. }; 125 126 true_soln[i] = sin(M_PI*(c[0] + k[0]*x[i+Q*0])) * 127 sin(M_PI*(c[1] + k[1]*x[i+Q*1])) * 128 sin(M_PI*(c[2] + k[2]*x[i+Q*2])); 129 130 const CeedScalar rho = w[i] * (J11*A11 + J21*A12 + J31*A13); 131 rhs[i] = rho * M_PI*M_PI * (k[0]*k[0] + k[1]*k[1] + k[2]*k[2]) * 132 true_soln[i]; 133 } // End of Quadrature Point Loop 134 135 return 0; 136 } 137 138 // ***************************************************************************** 139 // This QFunction applies the diffusion operator for a scalar field. 140 // 141 // Inputs: 142 // ug - Input vector gradient at quadrature points 143 // qdata - Geometric factors 144 // 145 // Output: 146 // vg - Output vector (test functions) gradient at quadrature points 147 // 148 // ***************************************************************************** 149 150 // ----------------------------------------------------------------------------- 151 CEED_QFUNCTION(Diff)(void *ctx, CeedInt Q, 152 const CeedScalar *const *in, CeedScalar *const *out) { 153 const CeedScalar *ug = in[0], *qdata = in[1]; 154 CeedScalar *vg = out[0]; 155 156 // Quadrature Point Loop 157 CeedPragmaSIMD 158 for (CeedInt i=0; i<Q; i++) { 159 // Read spatial derivatives of u 160 const CeedScalar du[3] = {ug[i+Q*0], 161 ug[i+Q*1], 162 ug[i+Q*2] 163 }; 164 // Read qdata (dXdxdXdxT symmetric matrix) 165 const CeedScalar dXdxdXdxT[3][3] = {{qdata[i+0*Q], 166 qdata[i+1*Q], 167 qdata[i+2*Q]}, 168 {qdata[i+1*Q], 169 qdata[i+3*Q], 170 qdata[i+4*Q]}, 171 {qdata[i+2*Q], 172 qdata[i+4*Q], 173 qdata[i+5*Q]} 174 }; 175 176 for (int j=0; j<3; j++) // j = direction of vg 177 vg[i+j*Q] = (du[0] * dXdxdXdxT[0][j] + 178 du[1] * dXdxdXdxT[1][j] + 179 du[2] * dXdxdXdxT[2][j]); 180 181 } // End of Quadrature Point Loop 182 return 0; 183 } 184 // ----------------------------------------------------------------------------- 185 186 #endif // bp3_h 187