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 /// @file 9 /// libCEED QFunctions for mass operator example for a vector field on the sphere using PETSc 10 11 #ifndef bp4sphere_h 12 #define bp4sphere_h 13 14 #include <ceed.h> 15 #include <math.h> 16 17 // ----------------------------------------------------------------------------- 18 // This QFunction sets up the rhs and true solution for the problem 19 // ----------------------------------------------------------------------------- 20 CEED_QFUNCTION(SetupDiffRhs3)(void *ctx, const CeedInt Q, 21 const CeedScalar *const *in, 22 CeedScalar *const *out) { 23 // Inputs 24 const CeedScalar *X = in[0], *q_data = in[1]; 25 // Outputs 26 CeedScalar *true_soln = out[0], *rhs = out[1]; 27 28 // Context 29 const CeedScalar *context = (const CeedScalar*)ctx; 30 const CeedScalar R = context[0]; 31 32 // Quadrature Point Loop 33 CeedPragmaSIMD 34 for (CeedInt i=0; i<Q; i++) { 35 // Read global Cartesian coordinates 36 CeedScalar x = X[i+Q*0], y = X[i+Q*1], z = X[i+Q*2]; 37 // Normalize quadrature point coordinates to sphere 38 CeedScalar rad = sqrt(x*x + y*y + z*z); 39 x *= R / rad; 40 y *= R / rad; 41 z *= R / rad; 42 // Compute latitude and longitude 43 const CeedScalar theta = asin(z / R); // latitude 44 const CeedScalar lambda = atan2(y, x); // longitude 45 46 // Use absolute value of latitude for true solution 47 // Component 1 48 true_soln[i+0*Q] = sin(lambda) * cos(theta); 49 // Component 2 50 true_soln[i+1*Q] = 2 * true_soln[i+0*Q]; 51 // Component 3 52 true_soln[i+2*Q] = 3 * true_soln[i+0*Q]; 53 54 // Component 1 55 rhs[i+0*Q] = q_data[i+Q*0] * 2 * sin(lambda)*cos(theta) / (R*R); 56 // Component 2 57 rhs[i+1*Q] = 2 * rhs[i+0*Q]; 58 // Component 3 59 rhs[i+2*Q] = 3 * rhs[i+0*Q]; 60 } // End of Quadrature Point Loop 61 62 return 0; 63 } 64 65 // ----------------------------------------------------------------------------- 66 // This QFunction applies the diffusion operator for a vector field of 3 components. 67 // 68 // Inputs: 69 // ug - Input vector Jacobian at quadrature points 70 // q_data - Geometric factors 71 // 72 // Output: 73 // vJ - Output vector (test functions) Jacobian at quadrature points 74 // 75 // ----------------------------------------------------------------------------- 76 CEED_QFUNCTION(Diff3)(void *ctx, const CeedInt Q, 77 const CeedScalar *const *in, CeedScalar *const *out) { 78 const CeedScalar *ug = in[0], *q_data = in[1]; 79 CeedScalar *vJ = out[0]; 80 81 // Quadrature Point Loop 82 CeedPragmaSIMD 83 for (CeedInt i=0; i<Q; i++) { 84 // Read spatial derivatives of u 85 const CeedScalar uJ[3][2] = {{ug[i+(0+0*3)*Q], 86 ug[i+(0+1*3)*Q]}, 87 {ug[i+(1+0*3)*Q], 88 ug[i+(1+1*3)*Q]}, 89 {ug[i+(2+0*3)*Q], 90 ug[i+(2+1*3)*Q]} 91 }; 92 // Read q_data 93 const CeedScalar w_det_J = q_data[i+Q*0]; 94 // -- Grad-to-Grad q_data 95 // ---- dXdx_j,k * dXdx_k,j 96 const CeedScalar dXdxdXdx_T[2][2] = {{q_data[i+Q*1], 97 q_data[i+Q*3]}, 98 {q_data[i+Q*3], 99 q_data[i+Q*2]} 100 }; 101 102 for (int k=0; k<3; k++) // k = component 103 for (int j=0; j<2; j++) // j = direction of vg 104 vJ[i+(k+j*3)*Q] = w_det_J * (uJ[k][0] * dXdxdXdx_T[0][j] + 105 uJ[k][1] * dXdxdXdx_T[1][j]); 106 107 } // End of Quadrature Point Loop 108 109 return 0; 110 } 111 // ----------------------------------------------------------------------------- 112 113 #endif // bp4sphere_h 114