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 mass operator example for a scalar field on the sphere using PETSc 19 20 #ifndef areacube_h 21 #define areacube_h 22 23 #include <math.h> 24 25 // ----------------------------------------------------------------------------- 26 // This QFunction sets up the geometric factor required for integration when 27 // reference coordinates have a different dimension than the one of 28 // physical coordinates 29 // 30 // Reference (parent) 2D coordinates: X \in [-1, 1]^2 31 // 32 // Global physical coordinates given by the mesh (3D): xx \in [-l, l]^3 33 // 34 // Local physical coordinates on the manifold (2D): x \in [-l, l]^2 35 // 36 // Change of coordinates matrix computed by the library: 37 // (physical 3D coords relative to reference 2D coords) 38 // dxx_j/dX_i (indicial notation) [3 * 2] 39 // 40 // Change of coordinates x (physical 2D) relative to xx (phyisical 3D): 41 // dx_i/dxx_j (indicial notation) [2 * 3] 42 // 43 // Change of coordinates x (physical 2D) relative to X (reference 2D): 44 // (by chain rule) 45 // dx_i/dX_j = dx_i/dxx_k * dxx_k/dX_j 46 // 47 // The quadrature data is stored in the array q_data. 48 // 49 // We require the determinant of the Jacobian to properly compute integrals of 50 // the form: int( u v ) 51 // 52 // Qdata: w * det(dx_i/dX_j) 53 // 54 // ----------------------------------------------------------------------------- 55 CEED_QFUNCTION(SetupMassGeoCube)(void *ctx, const CeedInt Q, 56 const CeedScalar *const *in, 57 CeedScalar *const *out) { 58 // Inputs 59 const CeedScalar *J = in[1], *w = in[2]; 60 // Outputs 61 CeedScalar *q_data = out[0]; 62 63 // Quadrature Point Loop 64 CeedPragmaSIMD 65 for (CeedInt i=0; i<Q; i++) { 66 // Read dxxdX Jacobian entries, stored as 67 // 0 3 68 // 1 4 69 // 2 5 70 const CeedScalar dxxdX[3][2] = {{J[i+Q*0], 71 J[i+Q*3]}, 72 {J[i+Q*1], 73 J[i+Q*4]}, 74 {J[i+Q*2], 75 J[i+Q*5]} 76 }; 77 78 // Modulus of dxxdX column vectors 79 const CeedScalar mod_g_1 = sqrt(dxxdX[0][0]*dxxdX[0][0] + 80 dxxdX[1][0]*dxxdX[1][0] + 81 dxxdX[2][0]*dxxdX[2][0]); 82 const CeedScalar mod_g_2 = sqrt(dxxdX[0][1]*dxxdX[0][1] + 83 dxxdX[1][1]*dxxdX[1][1] + 84 dxxdX[2][1]*dxxdX[2][1]); 85 86 // Use normalized column vectors of dxxdX as rows of dxdxx 87 const CeedScalar dxdxx[2][3] = {{dxxdX[0][0] / mod_g_1, 88 dxxdX[1][0] / mod_g_1, 89 dxxdX[2][0] / mod_g_1}, 90 {dxxdX[0][1] / mod_g_2, 91 dxxdX[1][1] / mod_g_2, 92 dxxdX[2][1] / mod_g_2} 93 }; 94 95 CeedScalar dxdX[2][2]; 96 for (int j=0; j<2; j++) 97 for (int k=0; k<2; k++) { 98 dxdX[j][k] = 0; 99 for (int l=0; l<3; l++) 100 dxdX[j][k] += dxdxx[j][l]*dxxdX[l][k]; 101 } 102 103 q_data[i+Q*0] = (dxdX[0][0]*dxdX[1][1] - dxdX[1][0]*dxdX[0][1]) * w[i]; 104 105 } // End of Quadrature Point Loop 106 return 0; 107 } 108 109 // ----------------------------------------------------------------------------- 110 // This QFunction applies the mass operator for a scalar field. 111 // 112 // Inputs: 113 // u - Input vector at quadrature points 114 // q_data - Geometric factors 115 // 116 // Output: 117 // v - Output vector (test function) at quadrature points 118 // 119 // ----------------------------------------------------------------------------- 120 CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q, 121 const CeedScalar *const *in, CeedScalar *const *out) { 122 // Inputs 123 const CeedScalar *u = in[0], *q_data = in[1]; 124 // Outputs 125 CeedScalar *v = out[0]; 126 127 // Quadrature Point Loop 128 CeedPragmaSIMD 129 for (CeedInt i=0; i<Q; i++) 130 v[i] = q_data[i] * u[i]; 131 132 return 0; 133 } 134 // ----------------------------------------------------------------------------- 135 136 #endif // areacube_h 137