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 #include <ceed.h> 9 10 // H(curl) basis for order 2 Nédélec (first kind) triangle element in 2D 11 // See: https://defelement.com/elements/examples/triangle-N1curl-2.html 12 static void BuildHcurl2DSimplex(CeedScalar *q_ref, CeedScalar *q_weight, CeedScalar *interp, CeedScalar *curl) { 13 CeedInt P = 8, Q = 4; 14 15 q_ref[0] = 1. / 3.; 16 q_ref[4] = 1. / 3.; 17 q_ref[1] = 0.2; 18 q_ref[5] = 0.2; 19 q_ref[2] = 0.2; 20 q_ref[6] = 0.6; 21 q_ref[3] = 0.6; 22 q_ref[7] = 0.2; 23 q_weight[0] = -25. / 96.; 24 q_weight[1] = 25. / 96.; 25 q_weight[2] = 27. / 96.; 26 q_weight[3] = 25. / 96.; 27 28 // Loop over quadrature points 29 for (int i = 0; i < Q; i++) { 30 CeedScalar x1 = q_ref[0 * Q + i], x2 = q_ref[1 * Q + i]; 31 // Interp 32 interp[(i + 0) * P + 0] = 2. * x2 * (1. - 4. * x1); 33 interp[(i + Q) * P + 0] = 4. * x1 * (2. * x1 - 1.); 34 interp[(i + 0) * P + 1] = 4. * x2 * (1. - 2. * x2); 35 interp[(i + Q) * P + 1] = 2. * x1 * (4. * x2 - 1.); 36 interp[(i + 0) * P + 2] = 2. * x2 * (-4. * x1 - 4. * x2 + 3.); 37 interp[(i + Q) * P + 2] = 8. * x1 * x1 + 8. * x1 * x2 - 12. * x1 - 6. * x2 + 4.; 38 interp[(i + 0) * P + 3] = 4. * x2 * (2. * x2 - 1.); 39 interp[(i + Q) * P + 3] = -8. * x1 * x2 + 2. * x1 + 6. * x2 - 2.; 40 interp[(i + 0) * P + 4] = 8. * x1 * x2 - 6. * x1 + 8. * x2 * x2 - 12. * x2 + 4.; 41 interp[(i + Q) * P + 4] = 2. * x1 * (-4. * x1 - 4. * x2 + 3.); 42 interp[(i + 0) * P + 5] = -8. * x1 * x2 + 6. * x1 + 2. * x2 - 2.; 43 interp[(i + Q) * P + 5] = 4. * x1 * (2. * x1 - 1.); 44 interp[(i + 0) * P + 6] = 8. * x2 * (-x1 - 2. * x2 + 2.); 45 interp[(i + Q) * P + 6] = 8. * x1 * (x1 + 2. * x2 - 1.); 46 interp[(i + 0) * P + 7] = 8. * x2 * (2. * x1 + x2 - 1.); 47 interp[(i + Q) * P + 7] = 8. * x1 * (-2. * x1 - x2 + 2.); 48 // Curl 49 curl[i * P + 0] = 24. * x1 - 6.; 50 curl[i * P + 1] = 24. * x2 - 6.; 51 curl[i * P + 2] = 24. * x1 + 24. * x2 - 18.; 52 curl[i * P + 3] = -24. * x2 + 6.; 53 curl[i * P + 4] = -24. * x1 - 24. * x2 + 18.; 54 curl[i * P + 5] = 24. * x1 - 6.; 55 curl[i * P + 6] = 24. * x1 + 48. * x2 - 24.; 56 curl[i * P + 7] = -48. * x1 - 24. * x1 + 24.; 57 } 58 } 59