xref: /libCEED/examples/petsc/qfunctions/area/areacube.h (revision d83cf49fece5d7d5441d5b92eb712b904329a4d2)
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 /// libCEED QFunctions for mass operator example for a scalar field on the sphere using PETSc
10 
11 #include <ceed.h>
12 #include <math.h>
13 
14 // -----------------------------------------------------------------------------
15 // This QFunction sets up the geometric factor required for integration when reference coordinates have a different dimension than the one of physical
16 // coordinates
17 //
18 // Reference (parent) 2D coordinates: X \in [-1, 1]^2
19 //
20 // Global physical coordinates given by the mesh (3D): xx \in [-l, l]^3
21 //
22 // Local physical coordinates on the manifold (2D): x \in [-l, l]^2
23 //
24 // Change of coordinates matrix computed by the library:
25 //   (physical 3D coords relative to reference 2D coords)
26 //   dxx_j/dX_i (indicial notation) [3 * 2]
27 //
28 // Change of coordinates x (physical 2D) relative to xx (phyiscal 3D):
29 //   dx_i/dxx_j (indicial notation) [2 * 3]
30 //
31 // Change of coordinates x (physical 2D) relative to X (reference 2D):
32 //   (by chain rule)
33 //   dx_i/dX_j = dx_i/dxx_k * dxx_k/dX_j
34 //
35 // The quadrature data is stored in the array q_data.
36 //
37 // We require the determinant of the Jacobian to properly compute integrals of the form: int( u v )
38 //
39 // Qdata: w * det(dx_i/dX_j)
40 // -----------------------------------------------------------------------------
41 CEED_QFUNCTION(SetupMassGeoCube)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
42   // Inputs
43   const CeedScalar *J = in[1], *w = in[2];
44   // Outputs
45   CeedScalar *q_data = out[0];
46 
47   // Quadrature Point Loop
48   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
49     // Read dxxdX Jacobian entries, stored as
50     // 0 3
51     // 1 4
52     // 2 5
53     const CeedScalar dxxdX[3][2] = {
54         {J[i + Q * 0], J[i + Q * 3]},
55         {J[i + Q * 1], J[i + Q * 4]},
56         {J[i + Q * 2], J[i + Q * 5]}
57     };
58 
59     // Modulus of dxxdX column vectors
60     const CeedScalar mod_g_1 = sqrt(dxxdX[0][0] * dxxdX[0][0] + dxxdX[1][0] * dxxdX[1][0] + dxxdX[2][0] * dxxdX[2][0]);
61     const CeedScalar mod_g_2 = sqrt(dxxdX[0][1] * dxxdX[0][1] + dxxdX[1][1] * dxxdX[1][1] + dxxdX[2][1] * dxxdX[2][1]);
62 
63     // Use normalized column vectors of dxxdX as rows of dxdxx
64     const CeedScalar dxdxx[2][3] = {
65         {dxxdX[0][0] / mod_g_1, dxxdX[1][0] / mod_g_1, dxxdX[2][0] / mod_g_1},
66         {dxxdX[0][1] / mod_g_2, dxxdX[1][1] / mod_g_2, dxxdX[2][1] / mod_g_2}
67     };
68 
69     CeedScalar dxdX[2][2];
70     for (int j = 0; j < 2; j++) {
71       for (int k = 0; k < 2; k++) {
72         dxdX[j][k] = 0;
73         for (int l = 0; l < 3; l++) dxdX[j][k] += dxdxx[j][l] * dxxdX[l][k];
74       }
75     }
76 
77     q_data[i + Q * 0] = (dxdX[0][0] * dxdX[1][1] - dxdX[1][0] * dxdX[0][1]) * w[i];
78 
79   }  // End of Quadrature Point Loop
80   return 0;
81 }
82 
83 // -----------------------------------------------------------------------------
84 // This QFunction applies the mass operator for a scalar field.
85 //
86 // Inputs:
87 //   u      - Input vector at quadrature points
88 //   q_data - Geometric factors
89 //
90 // Output:
91 //   v     - Output vector (test function) at quadrature points
92 // -----------------------------------------------------------------------------
93 CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
94   // Inputs
95   const CeedScalar *u = in[0], *q_data = in[1];
96   // Outputs
97   CeedScalar *v = out[0];
98 
99   // Quadrature Point Loop
100   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) v[i] = q_data[i] * u[i];
101 
102   return 0;
103 }
104 // -----------------------------------------------------------------------------
105