1*b5404d5dSSebastian Grimberg // Copyright (c) 2017-2022, Lawrence Livermore National Security, LLC and other CEED contributors. 2*b5404d5dSSebastian Grimberg // All Rights Reserved. See the top-level LICENSE and NOTICE files for details. 3*b5404d5dSSebastian Grimberg // 4*b5404d5dSSebastian Grimberg // SPDX-License-Identifier: BSD-2-Clause 5*b5404d5dSSebastian Grimberg // 6*b5404d5dSSebastian Grimberg // This file is part of CEED: http://github.com/ceed 7*b5404d5dSSebastian Grimberg 8*b5404d5dSSebastian Grimberg #include <ceed.h> 9*b5404d5dSSebastian Grimberg 10*b5404d5dSSebastian Grimberg // H(curl) basis for order 2 Nédélec (first kind) triangle element in 2D 11*b5404d5dSSebastian Grimberg // See: https://defelement.com/elements/examples/triangle-N1curl-2.html 12*b5404d5dSSebastian Grimberg static void BuildHcurl2DSimplex(CeedScalar *q_ref, CeedScalar *q_weight, CeedScalar *interp, CeedScalar *curl) { 13*b5404d5dSSebastian Grimberg CeedInt P = 8, Q = 4; 14*b5404d5dSSebastian Grimberg 15*b5404d5dSSebastian Grimberg q_ref[0] = 1. / 3.; 16*b5404d5dSSebastian Grimberg q_ref[4] = 1. / 3.; 17*b5404d5dSSebastian Grimberg q_ref[1] = 0.2; 18*b5404d5dSSebastian Grimberg q_ref[5] = 0.2; 19*b5404d5dSSebastian Grimberg q_ref[2] = 0.2; 20*b5404d5dSSebastian Grimberg q_ref[6] = 0.6; 21*b5404d5dSSebastian Grimberg q_ref[3] = 0.6; 22*b5404d5dSSebastian Grimberg q_ref[7] = 0.2; 23*b5404d5dSSebastian Grimberg q_weight[0] = -25. / 96.; 24*b5404d5dSSebastian Grimberg q_weight[1] = 25. / 96.; 25*b5404d5dSSebastian Grimberg q_weight[2] = 27. / 96.; 26*b5404d5dSSebastian Grimberg q_weight[3] = 25. / 96.; 27*b5404d5dSSebastian Grimberg 28*b5404d5dSSebastian Grimberg // Loop over quadrature points 29*b5404d5dSSebastian Grimberg for (int i = 0; i < Q; i++) { 30*b5404d5dSSebastian Grimberg CeedScalar x1 = q_ref[0 * Q + i], x2 = q_ref[1 * Q + i]; 31*b5404d5dSSebastian Grimberg // Interp 32*b5404d5dSSebastian Grimberg interp[(i + 0) * P + 0] = 2. * x2 * (1. - 4. * x1); 33*b5404d5dSSebastian Grimberg interp[(i + Q) * P + 0] = 4. * x1 * (2. * x1 - 1.); 34*b5404d5dSSebastian Grimberg interp[(i + 0) * P + 1] = 4. * x2 * (1. - 2. * x2); 35*b5404d5dSSebastian Grimberg interp[(i + Q) * P + 1] = 2. * x1 * (4. * x2 - 1.); 36*b5404d5dSSebastian Grimberg interp[(i + 0) * P + 2] = 2. * x2 * (-4. * x1 - 4. * x2 + 3.); 37*b5404d5dSSebastian Grimberg interp[(i + Q) * P + 2] = 8. * x1 * x1 + 8. * x1 * x2 - 12. * x1 - 6. * x2 + 4.; 38*b5404d5dSSebastian Grimberg interp[(i + 0) * P + 3] = 4. * x2 * (2. * x2 - 1.); 39*b5404d5dSSebastian Grimberg interp[(i + Q) * P + 3] = -8. * x1 * x2 + 2. * x1 + 6. * x2 - 2.; 40*b5404d5dSSebastian Grimberg interp[(i + 0) * P + 4] = 8. * x1 * x2 - 6. * x1 + 8. * x2 * x2 - 12. * x2 + 4.; 41*b5404d5dSSebastian Grimberg interp[(i + Q) * P + 4] = 2. * x1 * (-4. * x1 - 4. * x2 + 3.); 42*b5404d5dSSebastian Grimberg interp[(i + 0) * P + 5] = -8. * x1 * x2 + 6. * x1 + 2. * x2 - 2.; 43*b5404d5dSSebastian Grimberg interp[(i + Q) * P + 5] = 4. * x1 * (2. * x1 - 1.); 44*b5404d5dSSebastian Grimberg interp[(i + 0) * P + 6] = 8. * x2 * (-x1 - 2. * x2 + 2.); 45*b5404d5dSSebastian Grimberg interp[(i + Q) * P + 6] = 8. * x1 * (x1 + 2. * x2 - 1.); 46*b5404d5dSSebastian Grimberg interp[(i + 0) * P + 7] = 8. * x2 * (2. * x1 + x2 - 1.); 47*b5404d5dSSebastian Grimberg interp[(i + Q) * P + 7] = 8. * x1 * (-2. * x1 - x2 + 2.); 48*b5404d5dSSebastian Grimberg // Curl 49*b5404d5dSSebastian Grimberg curl[i * P + 0] = 24. * x1 - 6.; 50*b5404d5dSSebastian Grimberg curl[i * P + 1] = 24. * x2 - 6.; 51*b5404d5dSSebastian Grimberg curl[i * P + 2] = 24. * x1 + 24. * x2 - 18.; 52*b5404d5dSSebastian Grimberg curl[i * P + 3] = -24. * x2 + 6.; 53*b5404d5dSSebastian Grimberg curl[i * P + 4] = -24. * x1 - 24. * x2 + 18.; 54*b5404d5dSSebastian Grimberg curl[i * P + 5] = 24. * x1 - 6.; 55*b5404d5dSSebastian Grimberg curl[i * P + 6] = 24. * x1 + 48. * x2 - 24.; 56*b5404d5dSSebastian Grimberg curl[i * P + 7] = -48. * x1 - 24. * x1 + 24.; 57*b5404d5dSSebastian Grimberg } 58*b5404d5dSSebastian Grimberg } 59