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