1 // Copyright (c) 2017-2018, Lawrence Livermore National Security, LLC. 2 // Produced at the Lawrence Livermore National Laboratory. LLNL-CODE-734707. 3 // All Rights 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 18 /// A structure used to pass additional data to f_build_diff and f_apply_diff 19 struct BuildContext { CeedInt dim, space_dim; }; 20 21 /// libCEED Q-function for building quadrature data for a diffusion operator 22 CEED_QFUNCTION(f_build_diff)(void *ctx, const CeedInt Q, 23 const CeedScalar *const *in, CeedScalar *const *out) { 24 BuildContext *bc = (BuildContext *)ctx; 25 // in[0] is Jacobians with shape [dim, nc=dim, Q] 26 // in[1] is quadrature weights, size (Q) 27 // 28 // At every quadrature point, compute w/det(J).adj(J).adj(J)^T and store 29 // the symmetric part of the result. 30 const CeedScalar *J = in[0], *w = in[1]; 31 CeedScalar *qdata = out[0]; 32 33 switch (bc->dim + 10*bc->space_dim) { 34 case 11: 35 // Quadrature Point Loop 36 CeedPragmaSIMD 37 for (CeedInt i=0; i<Q; i++) { 38 qdata[i] = w[i] / J[i]; 39 } 40 break; 41 case 22: 42 // Quadrature Point Loop 43 CeedPragmaSIMD 44 for (CeedInt i=0; i<Q; i++) { 45 // J: 0 2 qdata: 0 2 adj(J): J22 -J12 46 // 1 3 2 1 -J21 J11 47 const CeedScalar J11 = J[i+Q*0]; 48 const CeedScalar J21 = J[i+Q*1]; 49 const CeedScalar J12 = J[i+Q*2]; 50 const CeedScalar J22 = J[i+Q*3]; 51 const CeedScalar qw = w[i] / (J11*J22 - J21*J12); 52 qdata[i+Q*0] = qw * (J12*J12 + J22*J22); 53 qdata[i+Q*1] = qw * (J11*J11 + J21*J21); 54 qdata[i+Q*2] = - qw * (J11*J12 + J21*J22); 55 } 56 break; 57 case 33: 58 // Quadrature Point Loop 59 CeedPragmaSIMD 60 for (CeedInt i=0; i<Q; i++) { 61 // J: 0 3 6 qdata: 0 5 4 62 // 1 4 7 5 1 3 63 // 2 5 8 4 3 2 64 const CeedScalar J11 = J[i+Q*0]; 65 const CeedScalar J21 = J[i+Q*1]; 66 const CeedScalar J31 = J[i+Q*2]; 67 const CeedScalar J12 = J[i+Q*3]; 68 const CeedScalar J22 = J[i+Q*4]; 69 const CeedScalar J32 = J[i+Q*5]; 70 const CeedScalar J13 = J[i+Q*6]; 71 const CeedScalar J23 = J[i+Q*7]; 72 const CeedScalar J33 = J[i+Q*8]; 73 const CeedScalar A11 = J22*J33 - J23*J32; 74 const CeedScalar A12 = J13*J32 - J12*J33; 75 const CeedScalar A13 = J12*J23 - J13*J22; 76 const CeedScalar A21 = J23*J31 - J21*J33; 77 const CeedScalar A22 = J11*J33 - J13*J31; 78 const CeedScalar A23 = J13*J21 - J11*J23; 79 const CeedScalar A31 = J21*J32 - J22*J31; 80 const CeedScalar A32 = J12*J31 - J11*J32; 81 const CeedScalar A33 = J11*J22 - J12*J21; 82 const CeedScalar qw = w[i] / (J11*A11 + J21*A12 + J31*A13); 83 qdata[i+Q*0] = qw * (A11*A11 + A12*A12 + A13*A13); 84 qdata[i+Q*1] = qw * (A21*A21 + A22*A22 + A23*A23); 85 qdata[i+Q*2] = qw * (A31*A31 + A32*A32 + A33*A33); 86 qdata[i+Q*3] = qw * (A21*A31 + A22*A32 + A23*A33); 87 qdata[i+Q*4] = qw * (A11*A31 + A12*A32 + A13*A33); 88 qdata[i+Q*5] = qw * (A11*A21 + A12*A22 + A13*A23); 89 } 90 break; 91 } 92 return 0; 93 } 94 95 /// libCEED Q-function for applying a diff operator 96 CEED_QFUNCTION(f_apply_diff)(void *ctx, const CeedInt Q, 97 const CeedScalar *const *in, CeedScalar *const *out) { 98 BuildContext *bc = (BuildContext *)ctx; 99 // in[0], out[0] have shape [dim, nc=1, Q] 100 const CeedScalar *ug = in[0], *qdata = in[1]; 101 CeedScalar *vg = out[0]; 102 103 switch (bc->dim) { 104 case 1: 105 // Quadrature Point Loop 106 CeedPragmaSIMD 107 for (CeedInt i=0; i<Q; i++) { 108 vg[i] = ug[i] * qdata[i]; 109 } 110 break; 111 case 2: 112 // Quadrature Point Loop 113 CeedPragmaSIMD 114 for (CeedInt i=0; i<Q; i++) { 115 const CeedScalar ug0 = ug[i+Q*0]; 116 const CeedScalar ug1 = ug[i+Q*1]; 117 vg[i+Q*0] = qdata[i+Q*0]*ug0 + qdata[i+Q*2]*ug1; 118 vg[i+Q*1] = qdata[i+Q*2]*ug0 + qdata[i+Q*1]*ug1; 119 } 120 break; 121 case 3: 122 // Quadrature Point Loop 123 CeedPragmaSIMD 124 for (CeedInt i=0; i<Q; i++) { 125 const CeedScalar ug0 = ug[i+Q*0]; 126 const CeedScalar ug1 = ug[i+Q*1]; 127 const CeedScalar ug2 = ug[i+Q*2]; 128 vg[i+Q*0] = qdata[i+Q*0]*ug0 + qdata[i+Q*5]*ug1 + qdata[i+Q*4]*ug2; 129 vg[i+Q*1] = qdata[i+Q*5]*ug0 + qdata[i+Q*1]*ug1 + qdata[i+Q*3]*ug2; 130 vg[i+Q*2] = qdata[i+Q*4]*ug0 + qdata[i+Q*3]*ug1 + qdata[i+Q*2]*ug2; 131 } 132 break; 133 } 134 return 0; 135 } 136 137