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