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