xref: /libCEED/examples/fluids/qfunctions/setupgeo.h (revision 9ef220489445f31398d6e42662820ac48a00a591)
1 // Copyright (c) 2017-2024, 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 (3D) for Navier-Stokes example using PETSc
10 #include <ceed.h>
11 #include <math.h>
12 
13 #include "setupgeo_helpers.h"
14 #include "utils.h"
15 
16 // *****************************************************************************
17 // This QFunction sets up the geometric factors required for integration and coordinate transformations
18 //
19 // Reference (parent) coordinates: X
20 // Physical (current) coordinates: x
21 // Change of coordinate matrix: dxdX_{i,j} = x_{i,j} (indicial notation)
22 // Inverse of change of coordinate matrix: dXdx_{i,j} = (detJ^-1) * X_{i,j}
23 //
24 // All quadrature data is stored in 10 field vector of quadrature data.
25 //
26 // We require the determinant of the Jacobian to properly compute integrals of the form: int( v u )
27 //
28 // Determinant of Jacobian:
29 //   detJ = J11*A11 + J21*A12 + J31*A13
30 //     Jij = Jacobian entry ij
31 //     Aij = Adjugate ij
32 //
33 // Stored: w detJ
34 //   in q_data[0]
35 //
36 // We require the transpose of the inverse of the Jacobian to properly compute integrals of the form: int( gradv u )
37 //
38 // Inverse of Jacobian:
39 //   dXdx_i,j = Aij / detJ
40 //
41 // Stored: Aij / detJ
42 //   in q_data[1:9] as
43 //   (detJ^-1) * [A11 A12 A13]
44 //               [A21 A22 A23]
45 //               [A31 A32 A33]
46 // *****************************************************************************
47 CEED_QFUNCTION(Setup)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
48   const CeedScalar(*J)[3][CEED_Q_VLA] = (const CeedScalar(*)[3][CEED_Q_VLA])in[0];
49   const CeedScalar(*w)                = in[1];
50   CeedScalar(*q_data)                 = out[0];
51 
52   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
53     CeedScalar detJ, dXdx[3][3];
54     InvertMappingJacobian_3D(Q, i, J, dXdx, &detJ);
55     const CeedScalar wdetJ = w[i] * detJ;
56 
57     StoredValuesPack(Q, i, 0, 1, &wdetJ, q_data);
58     StoredValuesPack(Q, i, 1, 9, (const CeedScalar *)dXdx, q_data);
59   }
60   return 0;
61 }
62 
63 // *****************************************************************************
64 // This QFunction sets up the geometric factor required for integration when reference coordinates are in 2D and the physical coordinates are in 3D
65 //
66 // Reference (parent) 2D coordinates: X
67 // Physical (current) 3D coordinates: x
68 // Change of coordinate matrix:
69 //   dxdX_{i,j} = dx_i/dX_j (indicial notation) [3 * 2]
70 // Inverse change of coordinate matrix:
71 //   dXdx_{i,j} = dX_i/dx_j (indicial notation) [2 * 3]
72 //
73 // (J1,J2,J3) is given by the cross product of the columns of dxdX_{i,j}
74 //
75 // detJb is the magnitude of (J1,J2,J3)
76 //
77 // dXdx is calculated via Moore–Penrose inverse:
78 //
79 //   dX_i/dx_j = (dxdX^T dxdX)^(-1) dxdX
80 //             = (dx_l/dX_i * dx_l/dX_k)^(-1) dx_j/dX_k
81 //
82 // All quadrature data is stored in 10 field vector of quadrature data.
83 //
84 // We require the determinant of the Jacobian to properly compute integrals of
85 //   the form: int( u v )
86 //
87 // Stored: w detJb
88 //   in q_data_sur[0]
89 //
90 // Normal vector = (J1,J2,J3) / detJb
91 //
92 //   - TODO Could possibly remove normal vector, as it could be calculated in the Qfunction from dXdx
93 //    See https://github.com/CEED/libCEED/pull/868#discussion_r871979484
94 // Stored: (J1,J2,J3) / detJb
95 //   in q_data_sur[1:3] as
96 //   (detJb^-1) * [ J1 ]
97 //                [ J2 ]
98 //                [ J3 ]
99 //
100 // Stored: dXdx_{i,j}
101 //   in q_data_sur[4:9] as
102 //    [dXdx_11 dXdx_12 dXdx_13]
103 //    [dXdx_21 dXdx_22 dXdx_23]
104 // *****************************************************************************
105 CEED_QFUNCTION(SetupBoundary)(void *ctx, CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
106   const CeedScalar(*J)[3][CEED_Q_VLA] = (const CeedScalar(*)[3][CEED_Q_VLA])in[0];
107   const CeedScalar(*w)                = in[1];
108   CeedScalar(*q_data_sur)             = out[0];
109 
110   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
111     CeedScalar detJb, normal[3], dXdx[2][3];
112 
113     NormalVectorFromdxdX_3D(Q, i, J, normal, &detJb);
114     InvertBoundaryMappingJacobian_3D(Q, i, J, dXdx);
115     const CeedScalar wdetJ = w[i] * detJb;
116 
117     StoredValuesPack(Q, i, 0, 1, &wdetJ, q_data_sur);
118     StoredValuesPack(Q, i, 1, 3, normal, q_data_sur);
119     StoredValuesPack(Q, i, 4, 6, (const CeedScalar *)dXdx, q_data_sur);
120   }
121   return 0;
122 }
123