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