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 /// Geometric factors (2D) for Navier-Stokes example using PETSc 10 11 #ifndef setup_geo_2d_h 12 #define setup_geo_2d_h 13 14 #include <ceed.h> 15 #include <math.h> 16 #include "setupgeo_helpers.h" 17 #include "utils.h" 18 19 // ***************************************************************************** 20 // This QFunction sets up the geometric factors required for integration and coordinate transformations 21 // 22 // Reference (parent) coordinates: X 23 // Physical (current) coordinates: x 24 // Change of coordinate matrix: dxdX_{i,j} = x_{i,j} (indicial notation) 25 // Inverse of change of coordinate matrix: dXdx_{i,j} = (detJ^-1) * X_{i,j} 26 // 27 // All quadrature data is stored in 10 field vector of quadrature data. 28 // 29 // We require the determinant of the Jacobian to properly compute integrals of the form: int( v u ) 30 // 31 // Determinant of Jacobian: 32 // detJ = J11*J22 - J21*J12 33 // Jij = Jacobian entry ij 34 // 35 // Stored: w detJ 36 // in q_data[0] 37 // 38 // We require the transpose of the inverse of the Jacobian to properly compute integrals of the form: int( gradv u ) 39 // 40 // Inverse of Jacobian: 41 // dXdx_i,j = Aij / detJ 42 // Aij = Adjugate ij 43 // 44 // Stored: Aij / detJ 45 // in q_data[1:4] as 46 // (detJ^-1) * [A11 A12] 47 // [A21 A22] 48 // ***************************************************************************** 49 CEED_QFUNCTION(Setup2d)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 50 const CeedScalar(*J)[2][CEED_Q_VLA] = (const CeedScalar(*)[2][CEED_Q_VLA])in[0]; 51 const CeedScalar(*w) = in[1]; 52 CeedScalar(*q_data) = out[0]; 53 54 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 55 CeedScalar dXdx[2][2], detJ; 56 InvertMappingJacobian_2D(Q, i, J, dXdx, &detJ); 57 const CeedScalar wdetJ = w[i] * detJ; 58 59 StoredValuesPack(Q, i, 0, 1, &wdetJ, q_data); 60 StoredValuesPack(Q, i, 1, 4, (const CeedScalar *)dXdx, q_data); 61 } 62 return 0; 63 } 64 65 // ***************************************************************************** 66 // This QFunction sets up the geometric factor required for integration when reference coordinates are in 1D and the physical coordinates are in 2D 67 // 68 // Reference (parent) 1D coordinates: X 69 // Physical (current) 2D coordinates: x 70 // Change of coordinate vector: 71 // J1 = dx_1/dX 72 // J2 = dx_2/dX 73 // 74 // detJb is the magnitude of (J1,J2) 75 // 76 // All quadrature data is stored in 3 field vector of quadrature data. 77 // 78 // We require the determinant of the Jacobian to properly compute integrals of the form: int( u v ) 79 // 80 // Stored: w detJb 81 // in q_data_sur[0] 82 // 83 // Normal vector is given by the cross product of (J1,J2)/detJ and ẑ 84 // 85 // Stored: (J1,J2,0) x (0,0,1) / detJb 86 // in q_data_sur[1:2] as 87 // (detJb^-1) * [ J2 ] 88 // [-J1 ] 89 // ***************************************************************************** 90 CEED_QFUNCTION(SetupBoundary2d)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) { 91 const CeedScalar(*J)[CEED_Q_VLA] = (const CeedScalar(*)[CEED_Q_VLA])in[0]; 92 const CeedScalar(*w) = in[1]; 93 CeedScalar(*q_data_sur) = out[0]; 94 95 CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) { 96 CeedScalar normal[2], detJb; 97 NormalVectorFromdxdX_2D(Q, i, J, normal, &detJb); 98 const CeedScalar wdetJ = w[i] * detJb; 99 100 StoredValuesPack(Q, i, 0, 1, &wdetJ, q_data_sur); 101 StoredValuesPack(Q, i, 1, 2, normal, q_data_sur); 102 } 103 return 0; 104 } 105 106 // ***************************************************************************** 107 108 #endif // setup_geo_2d_h 109