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 areacube_h 12 #define areacube_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 physical coordinates given by the mesh (3D): xx \in [-l, l]^3 25 // 26 // Local physical coordinates on the manifold (2D): x \in [-l, l]^2 27 // 28 // Change of coordinates matrix computed by the library: 29 // (physical 3D coords relative to reference 2D coords) 30 // dxx_j/dX_i (indicial notation) [3 * 2] 31 // 32 // Change of coordinates x (physical 2D) relative to xx (phyisical 3D): 33 // dx_i/dxx_j (indicial notation) [2 * 3] 34 // 35 // Change of coordinates x (physical 2D) relative to X (reference 2D): 36 // (by chain rule) 37 // dx_i/dX_j = dx_i/dxx_k * dxx_k/dX_j 38 // 39 // The quadrature data is stored in the array q_data. 40 // 41 // We require the determinant of the Jacobian to properly compute integrals of 42 // the form: int( u v ) 43 // 44 // Qdata: w * det(dx_i/dX_j) 45 // 46 // ----------------------------------------------------------------------------- 47 CEED_QFUNCTION(SetupMassGeoCube)(void *ctx, const CeedInt Q, 48 const CeedScalar *const *in, 49 CeedScalar *const *out) { 50 // Inputs 51 const CeedScalar *J = in[1], *w = in[2]; 52 // Outputs 53 CeedScalar *q_data = out[0]; 54 55 // Quadrature Point Loop 56 CeedPragmaSIMD 57 for (CeedInt i=0; i<Q; i++) { 58 // Read dxxdX Jacobian entries, stored as 59 // 0 3 60 // 1 4 61 // 2 5 62 const CeedScalar dxxdX[3][2] = {{J[i+Q*0], 63 J[i+Q*3]}, 64 {J[i+Q*1], 65 J[i+Q*4]}, 66 {J[i+Q*2], 67 J[i+Q*5]} 68 }; 69 70 // Modulus of dxxdX column vectors 71 const CeedScalar mod_g_1 = sqrt(dxxdX[0][0]*dxxdX[0][0] + 72 dxxdX[1][0]*dxxdX[1][0] + 73 dxxdX[2][0]*dxxdX[2][0]); 74 const CeedScalar mod_g_2 = sqrt(dxxdX[0][1]*dxxdX[0][1] + 75 dxxdX[1][1]*dxxdX[1][1] + 76 dxxdX[2][1]*dxxdX[2][1]); 77 78 // Use normalized column vectors of dxxdX as rows of dxdxx 79 const CeedScalar dxdxx[2][3] = {{dxxdX[0][0] / mod_g_1, 80 dxxdX[1][0] / mod_g_1, 81 dxxdX[2][0] / mod_g_1}, 82 {dxxdX[0][1] / mod_g_2, 83 dxxdX[1][1] / mod_g_2, 84 dxxdX[2][1] / mod_g_2} 85 }; 86 87 CeedScalar dxdX[2][2]; 88 for (int j=0; j<2; j++) 89 for (int k=0; k<2; k++) { 90 dxdX[j][k] = 0; 91 for (int l=0; l<3; l++) 92 dxdX[j][k] += dxdxx[j][l]*dxxdX[l][k]; 93 } 94 95 q_data[i+Q*0] = (dxdX[0][0]*dxdX[1][1] - dxdX[1][0]*dxdX[0][1]) * w[i]; 96 97 } // End of Quadrature Point Loop 98 return 0; 99 } 100 101 // ----------------------------------------------------------------------------- 102 // This QFunction applies the mass operator for a scalar field. 103 // 104 // Inputs: 105 // u - Input vector at quadrature points 106 // q_data - Geometric factors 107 // 108 // Output: 109 // v - Output vector (test function) at quadrature points 110 // 111 // ----------------------------------------------------------------------------- 112 CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q, 113 const CeedScalar *const *in, CeedScalar *const *out) { 114 // Inputs 115 const CeedScalar *u = in[0], *q_data = in[1]; 116 // Outputs 117 CeedScalar *v = out[0]; 118 119 // Quadrature Point Loop 120 CeedPragmaSIMD 121 for (CeedInt i=0; i<Q; i++) 122 v[i] = q_data[i] * u[i]; 123 124 return 0; 125 } 126 // ----------------------------------------------------------------------------- 127 128 #endif // areacube_h 129