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