1 // Copyright (c) 2017-2026, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
4 // SPDX-License-Identifier: BSD-2-Clause
9 /// Geometric factors (3D) for Navier-Stokes example using PETSc
25  * Inverse of change of coordinate matrix: dXdx_{i,j} = (detJ^-1) * X_{i,j}
52   const CeedScalar A11     = dxdX_22 * dxdX_33 - dxdX_23 * dxdX_32;  in InvertMappingJacobian_3D()
53   const CeedScalar A12     = dxdX_13 * dxdX_32 - dxdX_12 * dxdX_33;  in InvertMappingJacobian_3D()
54   const CeedScalar A13     = dxdX_12 * dxdX_23 - dxdX_13 * dxdX_22;  in InvertMappingJacobian_3D()
55   const CeedScalar A21     = dxdX_23 * dxdX_31 - dxdX_21 * dxdX_33;  in InvertMappingJacobian_3D()
56   const CeedScalar A22     = dxdX_11 * dxdX_33 - dxdX_13 * dxdX_31;  in InvertMappingJacobian_3D()
57   const CeedScalar A23     = dxdX_13 * dxdX_21 - dxdX_11 * dxdX_23;  in InvertMappingJacobian_3D()
58   const CeedScalar A31     = dxdX_21 * dxdX_32 - dxdX_22 * dxdX_31;  in InvertMappingJacobian_3D()
59   const CeedScalar A32     = dxdX_12 * dxdX_31 - dxdX_11 * dxdX_32;  in InvertMappingJacobian_3D()
60   const CeedScalar A33     = dxdX_11 * dxdX_22 - dxdX_12 * dxdX_21;  in InvertMappingJacobian_3D()
81  * Inverse of change of coordinate matrix: dXdx_{i,j} = (detJ^-1) * X_{i,j}
103   const CeedScalar detJ    = dxdX_11 * dxdX_22 - dxdX_21 * dxdX_12;  in InvertMappingJacobian_2D()
106   dXdx[0][1] = -dxdX_12 / detJ;  in InvertMappingJacobian_2D()
107   dXdx[1][0] = -dxdX_21 / detJ;  in InvertMappingJacobian_2D()
122  * (J1,J2,J3) is given by the cross product of the columns of dxdX_{i,j}
124  * detJb is the magnitude of (J1,J2,J3)
126  * Normal vector = (J1,J2,J3) / detJb
141   // J1, J2, and J3 are given by the cross product of the columns of dxdX  in NormalVectorFromdxdX_3D()
142   const CeedScalar J1 = dxdX[1][0] * dxdX[2][1] - dxdX[2][0] * dxdX[1][1];  in NormalVectorFromdxdX_3D()
143   const CeedScalar J2 = dxdX[2][0] * dxdX[0][1] - dxdX[0][0] * dxdX[2][1];  in NormalVectorFromdxdX_3D()  local
144   const CeedScalar J3 = dxdX[0][0] * dxdX[1][1] - dxdX[1][0] * dxdX[0][1];  in NormalVectorFromdxdX_3D()
146   const CeedScalar detJ = sqrt(J1 * J1 + J2 * J2 + J3 * J3);  in NormalVectorFromdxdX_3D()
149   normal[1] = J2 / detJ;  in NormalVectorFromdxdX_3D()
161  *           J2 = dx_2/dX
163  * detJb is the magnitude of (J1,J2)
167  * Normal vector is given by the cross product of (J1,J2)/detJ and ẑ
178   const CeedScalar J2 = dxdX_q[1][i];  in NormalVectorFromdxdX_2D()  local
180   CeedScalar detJb = sqrt(J1 * J1 + J2 * J2);  in NormalVectorFromdxdX_2D()
181   normal[0]        = J2 / detJb;  in NormalVectorFromdxdX_2D()
182   normal[1]        = -J1 / detJb;  in NormalVectorFromdxdX_2D()
187  * @brief Calculate inverse of mapping Jacobian, (dxdX)^-1
198  *   dX_i/dx_j = (dxdX^T dxdX)^(-1) dxdX
199  *             = (dx_l/dX_i * dx_l/dX_k)^(-1) dx_j/dX_k
221 …const CeedScalar detdxdXTdxdX = dxdXTdxdX[0][0] * dxdXTdxdX[1][1] - dxdXTdxdX[1][0] * dxdXTdxdX[0]…  in InvertBoundaryMappingJacobian_3D()
226   dxdXTdxdX_inv[0][1] = -dxdXTdxdX[0][1] / detdxdXTdxdX;  in InvertBoundaryMappingJacobian_3D()
227   dxdXTdxdX_inv[1][0] = -dxdXTdxdX[1][0] / detdxdXTdxdX;  in InvertBoundaryMappingJacobian_3D()
230   // Compute dXdx from dxdXTdxdX^-1 and dxdX  in InvertBoundaryMappingJacobian_3D()