xref: /libCEED/examples/petsc/qfunctions/area/areacube.h (revision caee03026e6576cbf7a399c2fc51bb918c77f451)
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, const CeedScalar *const *in, CeedScalar *const *out) {
48   // Inputs
49   const CeedScalar *J = in[1], *w = in[2];
50   // Outputs
51   CeedScalar *q_data = out[0];
52 
53   // Quadrature Point Loop
54   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) {
55     // Read dxxdX Jacobian entries, stored as
56     // 0 3
57     // 1 4
58     // 2 5
59     const CeedScalar dxxdX[3][2] = {
60         {J[i + Q * 0], J[i + Q * 3]},
61         {J[i + Q * 1], J[i + Q * 4]},
62         {J[i + Q * 2], J[i + Q * 5]}
63     };
64 
65     // Modulus of dxxdX column vectors
66     const CeedScalar mod_g_1 = sqrt(dxxdX[0][0] * dxxdX[0][0] + dxxdX[1][0] * dxxdX[1][0] + dxxdX[2][0] * dxxdX[2][0]);
67     const CeedScalar mod_g_2 = sqrt(dxxdX[0][1] * dxxdX[0][1] + dxxdX[1][1] * dxxdX[1][1] + dxxdX[2][1] * dxxdX[2][1]);
68 
69     // Use normalized column vectors of dxxdX as rows of dxdxx
70     const CeedScalar dxdxx[2][3] = {
71         {dxxdX[0][0] / mod_g_1, dxxdX[1][0] / mod_g_1, dxxdX[2][0] / mod_g_1},
72         {dxxdX[0][1] / mod_g_2, dxxdX[1][1] / mod_g_2, dxxdX[2][1] / mod_g_2}
73     };
74 
75     CeedScalar dxdX[2][2];
76     for (int j = 0; j < 2; j++) {
77       for (int k = 0; k < 2; k++) {
78         dxdX[j][k] = 0;
79         for (int l = 0; l < 3; l++) dxdX[j][k] += dxdxx[j][l] * dxxdX[l][k];
80       }
81     }
82 
83     q_data[i + Q * 0] = (dxdX[0][0] * dxdX[1][1] - dxdX[1][0] * dxdX[0][1]) * w[i];
84 
85   }  // End of Quadrature Point Loop
86   return 0;
87 }
88 
89 // -----------------------------------------------------------------------------
90 // This QFunction applies the mass operator for a scalar field.
91 //
92 // Inputs:
93 //   u     - Input vector at quadrature points
94 //   q_data - Geometric factors
95 //
96 // Output:
97 //   v     - Output vector (test function) at quadrature points
98 //
99 // -----------------------------------------------------------------------------
100 CEED_QFUNCTION(Mass)(void *ctx, const CeedInt Q, const CeedScalar *const *in, CeedScalar *const *out) {
101   // Inputs
102   const CeedScalar *u = in[0], *q_data = in[1];
103   // Outputs
104   CeedScalar *v = out[0];
105 
106   // Quadrature Point Loop
107   CeedPragmaSIMD for (CeedInt i = 0; i < Q; i++) v[i] = q_data[i] * u[i];
108 
109   return 0;
110 }
111 // -----------------------------------------------------------------------------
112 
113 #endif  // areacube_h
114