1 // Copyright (c) 2017-2022, Lawrence Livermore National Security, LLC and other CEED contributors. 2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details. 3 // 4 // SPDX-License-Identifier: BSD-2-Clause 5 // 6 // This file is part of CEED: http://github.com/ceed 7 8 /// @file 9 /// libCEED QFunctions for mass operator example for a scalar field on the sphere using PETSc 10 11 #ifndef areasphere_h 12 #define areasphere_h 13 14 #include <ceed.h> 15 #include <math.h> 16 17 // ----------------------------------------------------------------------------- 18 // This QFunction sets up the geometric factor required for integration when 19 // reference coordinates have a different dimension than the one of 20 // physical coordinates 21 // 22 // Reference (parent) 2D coordinates: X \in [-1, 1]^2 23 // 24 // Global 3D physical coordinates given by the mesh: xx \in [-R, R]^3 25 // with R radius of the sphere 26 // 27 // Local 3D physical coordinates on the 2D manifold: x \in [-l, l]^3 28 // with l half edge of the cube inscribed in the sphere 29 // 30 // Change of coordinates matrix computed by the library: 31 // (physical 3D coords relative to reference 2D coords) 32 // dxx_j/dX_i (indicial notation) [3 * 2] 33 // 34 // Change of coordinates x (on the 2D manifold) relative to xx (phyisical 3D): 35 // dx_i/dxx_j (indicial notation) [3 * 3] 36 // 37 // Change of coordinates x (on the 2D manifold) relative to X (reference 2D): 38 // (by chain rule) 39 // dx_i/dX_j = dx_i/dxx_k * dxx_k/dX_j [3 * 2] 40 // 41 // mod_J is given by the magnitude of the cross product of the columns of dx_i/dX_j 42 // 43 // The quadrature data is stored in the array q_data. 44 // 45 // We require the determinant of the Jacobian to properly compute integrals of 46 // the form: int( u v ) 47 // 48 // Qdata: mod_J * w 49 // 50 // ----------------------------------------------------------------------------- 51 CEED_QFUNCTION(SetupMassGeoSphere)(void *ctx, const CeedInt Q, 52 const CeedScalar *const *in, 53 CeedScalar *const *out) { 54 // Inputs 55 const CeedScalar *X = in[0], *J = in[1], *w = in[2]; 56 // Outputs 57 CeedScalar *q_data = out[0]; 58 59 // Quadrature Point Loop 60 CeedPragmaSIMD 61 for (CeedInt i=0; i<Q; i++) { 62 // Read global Cartesian coordinates 63 const CeedScalar xx[3][1] = {{X[i+0*Q]}, 64 {X[i+1*Q]}, 65 {X[i+2*Q]} 66 }; 67 68 // Read dxxdX Jacobian entries, stored as 69 // 0 3 70 // 1 4 71 // 2 5 72 const CeedScalar dxxdX[3][2] = {{J[i+Q*0], 73 J[i+Q*3]}, 74 {J[i+Q*1], 75 J[i+Q*4]}, 76 {J[i+Q*2], 77 J[i+Q*5]} 78 }; 79 80 // Setup 81 const CeedScalar mod_xx_sq = xx[0][0]*xx[0][0]+xx[1][0]*xx[1][0]+xx[2][0]*xx[2][0]; 82 CeedScalar xx_sq[3][3]; 83 for (int j=0; j<3; j++) 84 for (int k=0; k<3; k++) { 85 xx_sq[j][k] = 0; 86 for (int l=0; l<1; l++) 87 xx_sq[j][k] += xx[j][l]*xx[k][l] / (sqrt(mod_xx_sq) * mod_xx_sq); 88 } 89 90 const CeedScalar dxdxx[3][3] = {{1./sqrt(mod_xx_sq) - xx_sq[0][0], 91 -xx_sq[0][1], 92 -xx_sq[0][2]}, 93 {-xx_sq[1][0], 94 1./sqrt(mod_xx_sq) - xx_sq[1][1], 95 -xx_sq[1][2]}, 96 {-xx_sq[2][0], 97 -xx_sq[2][1], 98 1./sqrt(mod_xx_sq) - xx_sq[2][2]} 99 }; 100 101 CeedScalar dxdX[3][2]; 102 for (int j=0; j<3; j++) 103 for (int k=0; k<2; k++) { 104 dxdX[j][k] = 0; 105 for (int l=0; l<3; l++) 106 dxdX[j][k] += dxdxx[j][l]*dxxdX[l][k]; 107 } 108 109 // J is given by the cross product of the columns of dxdX 110 const CeedScalar J[3][1] = {{dxdX[1][0]*dxdX[2][1] - dxdX[2][0]*dxdX[1][1]}, 111 {dxdX[2][0]*dxdX[0][1] - dxdX[0][0]*dxdX[2][1]}, 112 {dxdX[0][0]*dxdX[1][1] - dxdX[1][0]*dxdX[0][1]} 113 }; 114 // Use the magnitude of J as our detJ (volume scaling factor) 115 const CeedScalar mod_J = sqrt(J[0][0]*J[0][0]+J[1][0]*J[1][0]+J[2][0]*J[2][0]); 116 q_data[i+Q*0] = mod_J * w[i]; 117 } // End of Quadrature Point Loop 118 return 0; 119 } 120 // ----------------------------------------------------------------------------- 121 122 #endif // areasphere_h 123