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 reference coordinates have a different dimension than the one of physical 19 // coordinates 20 // 21 // Reference (parent) 2D coordinates: X \in [-1, 1]^2 22 // 23 // Global physical coordinates given by the mesh (3D): xx \in [-l, l]^3 24 // 25 // Local physical coordinates on the manifold (2D): x \in [-l, l]^2 26 // 27 // Change of coordinates matrix computed by the library: 28 // (physical 3D coords relative to reference 2D coords) 29 // dxx_j/dX_i (indicial notation) [3 * 2] 30 // 31 // Change of coordinates x (physical 2D) relative to xx (phyiscal 3D): 32 // dx_i/dxx_j (indicial notation) [2 * 3] 33 // 34 // Change of coordinates x (physical 2D) relative to X (reference 2D): 35 // (by chain rule) 36 // dx_i/dX_j = dx_i/dxx_k * dxx_k/dX_j 37 // 38 // The quadrature data is stored in the array q_data. 39 // 40 // We require the determinant of the Jacobian to properly compute integrals of the form: int( u v ) 41 // 42 // Qdata: w * det(dx_i/dX_j) 43 // ----------------------------------------------------------------------------- 44 CEED_QFUNCTION(SetupMassGeoCube)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 45 // Inputs 46 const CeedScalar *J = in[1], *w = in[2]; 47 // Outputs 48 CeedScalar *q_data = out[0]; 49 50 // Quadrature Point Loop 51 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 52 // Read dxxdX Jacobian entries, stored as 53 // 0 3 54 // 1 4 55 // 2 5 56 const CeedScalar dxxdX[3][2] = { 57 {J[i + Q * 0], J[i + Q * 3]}, 58 {J[i + Q * 1], J[i + Q * 4]}, 59 {J[i + Q * 2], J[i + Q * 5]} 60 }; 61 62 // Modulus of dxxdX column vectors 63 const CeedScalar mod_g_1 = sqrt(dxxdX[0][0] * dxxdX[0][0] + dxxdX[1][0] * dxxdX[1][0] + dxxdX[2][0] * dxxdX[2][0]); 64 const CeedScalar mod_g_2 = sqrt(dxxdX[0][1] * dxxdX[0][1] + dxxdX[1][1] * dxxdX[1][1] + dxxdX[2][1] * dxxdX[2][1]); 65 66 // Use normalized column vectors of dxxdX as rows of dxdxx 67 const CeedScalar dxdxx[2][3] = { 68 {dxxdX[0][0] / mod_g_1, dxxdX[1][0] / mod_g_1, dxxdX[2][0] / mod_g_1}, 69 {dxxdX[0][1] / mod_g_2, dxxdX[1][1] / mod_g_2, dxxdX[2][1] / mod_g_2} 70 }; 71 72 CeedScalar dxdX[2][2]; 73 for (int j = 0; j < 2; j++) { 74 for (int k = 0; k < 2; k++) { 75 dxdX[j][k] = 0; 76 for (int l = 0; l < 3; l++) dxdX[j][k] += dxdxx[j][l] * dxxdX[l][k]; 77 } 78 } 79 80 q_data[i + Q * 0] = (dxdX[0][0] * dxdX[1][1] - dxdX[1][0] * dxdX[0][1]) * w[i]; 81 82 } // End of Quadrature Point Loop 83 return 0; 84 } 85 86 // ----------------------------------------------------------------------------- 87 // This QFunction applies the mass operator for a scalar field. 88 // 89 // Inputs: 90 // u - Input vector at quadrature points 91 // q_data - Geometric factors 92 // 93 // Output: 94 // v - Output vector (test function) at quadrature points 95 // ----------------------------------------------------------------------------- 96 CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 97 // Inputs 98 const CeedScalar *u = in[0], *q_data = in[1]; 99 // Outputs 100 CeedScalar *v = out[0]; 101 102 // Quadrature Point Loop 103 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) v[i] = q_data[i] * u[i]; 104 105 return 0; 106 } 107 // ----------------------------------------------------------------------------- 108 109 #endif // areacube_h 110