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
16 // -----------------------------------------------------------------------------
20 // Reference (parent) 2D coordinates: X \in [-1, 1]^2
22 // Global 3D physical coordinates given by the mesh: xx \in [-R, R]^3 with R radius of the sphere
24 // Local 3D physical coordinates on the 2D manifold: x \in [-l, l]^3 with l half edge of the cube i…
48 // dX_i/dx_j [2 * 3] = (dx_i/dX_j)+ = (dxdX^T dxdX)^(-1) dxdX
52 // g^{ij} = dX_i/dx_k dX_j/dx_k = (dxdX^T dxdX)^{-1}
58 // -----------------------------------------------------------------------------
79     // x = xx (xx^T xx)^{-1/2}  in SetupDiffGeo()
80     // dx/dxx = I (xx^T xx)^{-1/2} - xx xx^T (xx^T xx)^{-3/2}  in SetupDiffGeo()
88 …{1. / sqrt(mod_xx_sq) - xx_sq[0][0], -xx_sq[0][1],                       -xx_sq[0][2]             …  in SetupDiffGeo()
89 …{-xx_sq[1][0],                       1. / sqrt(mod_xx_sq) - xx_sq[1][1], -xx_sq[1][2]             …  in SetupDiffGeo()
90 …{-xx_sq[2][0],                       -xx_sq[2][1],                       1. / sqrt(mod_xx_sq) - xx…  in SetupDiffGeo()
102 …const CeedScalar J[3] = {dxdX[1][0] * dxdX[2][1] - dxdX[2][0] * dxdX[1][1], dxdX[2][0] * dxdX[0][1…  in SetupDiffGeo()
103                              dxdX[0][0] * dxdX[1][1] - dxdX[1][0] * dxdX[0][1]};  in SetupDiffGeo()
108     // Interp-to-Interp q_data  in SetupDiffGeo()
120 …const CeedScalar detdxdXTdxdX = dxdXTdxdX[0][0] * dxdXTdxdX[1][1] - dxdXTdxdX[1][0] * dxdXTdxdX[0]…  in SetupDiffGeo()
125     dxdXTdxdX_inv[0][1] = -dxdXTdxdX[0][1] / detdxdXTdxdX;  in SetupDiffGeo()
126     dxdXTdxdX_inv[1][0] = -dxdXTdxdX[1][0] / detdxdXTdxdX;  in SetupDiffGeo()
139 // -----------------------------------------------------------------------------
141 // -----------------------------------------------------------------------------
150   const CeedScalar  R       = context[0];  in SetupDiffRhs()  local
158     x *= R / rad;  in SetupDiffRhs()
159     y *= R / rad;  in SetupDiffRhs()
160     z *= R / rad;  in SetupDiffRhs()
162     const CeedScalar theta  = asin(z / R);  // latitude  in SetupDiffRhs()
167     rhs[i + Q * 0] = q_data[i + Q * 0] * 2 * sin(lambda) * cos(theta) / (R * R);  in SetupDiffRhs()
173 // -----------------------------------------------------------------------------
177 //   ug      - Input vector gradient at quadrature points
178 //   q_data  - Geometric factors
181 //   vg     - Output vector (test functions) gradient at quadrature points
182 // -----------------------------------------------------------------------------
195     // -- Grad-to-Grad q_data  in Diff()
196     // ---- dXdx_j,k * dXdx_k,j  in Diff()
209 // -----------------------------------------------------------------------------