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…
44 // -----------------------------------------------------------------------------
47   const CeedScalar *X = in[0], *J = in[1], *w = in[2];  in SetupMassGeoSphere()  local
61         {J[i + Q * 0], J[i + Q * 3]},  in SetupMassGeoSphere()
62         {J[i + Q * 1], J[i + Q * 4]},  in SetupMassGeoSphere()
63         {J[i + Q * 2], J[i + Q * 5]}  in SetupMassGeoSphere()
69     for (int j = 0; j < 3; j++) {  in SetupMassGeoSphere()  local
71         xx_sq[j][k] = 0;  in SetupMassGeoSphere()
72 …    for (int l = 0; l < 1; l++) xx_sq[j][k] += xx[j][l] * xx[k][l] / (sqrt(mod_xx_sq) * mod_xx_sq);  in SetupMassGeoSphere()
77 …{1. / sqrt(mod_xx_sq) - xx_sq[0][0], -xx_sq[0][1],                       -xx_sq[0][2]             …  in SetupMassGeoSphere()
78 …{-xx_sq[1][0],                       1. / sqrt(mod_xx_sq) - xx_sq[1][1], -xx_sq[1][2]             …  in SetupMassGeoSphere()
79 …{-xx_sq[2][0],                       -xx_sq[2][1],                       1. / sqrt(mod_xx_sq) - xx…  in SetupMassGeoSphere()
83     for (int j = 0; j < 3; j++) {  in SetupMassGeoSphere()  local
85         dxdX[j][k] = 0;  in SetupMassGeoSphere()
86         for (int l = 0; l < 3; l++) dxdX[j][k] += dxdxx[j][l] * dxxdX[l][k];  in SetupMassGeoSphere()
90     // J is given by the cross product of the columns of dxdX  in SetupMassGeoSphere()
91     const CeedScalar J[3][1] = {{dxdX[1][0] * dxdX[2][1] - dxdX[2][0] * dxdX[1][1]},  in SetupMassGeoSphere()  local
92                                 {dxdX[2][0] * dxdX[0][1] - dxdX[0][0] * dxdX[2][1]},  in SetupMassGeoSphere()
93                                 {dxdX[0][0] * dxdX[1][1] - dxdX[1][0] * dxdX[0][1]}};  in SetupMassGeoSphere()
94     // Use the magnitude of J as our detJ (volume scaling factor)  in SetupMassGeoSphere()
95     const CeedScalar mod_J = sqrt(J[0][0] * J[0][0] + J[1][0] * J[1][0] + J[2][0] * J[2][0]);  in SetupMassGeoSphere()
100 // -----------------------------------------------------------------------------