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