Chaste  Release::2018.1
SimpleNonlinearEllipticSolver.cpp
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35 
36 #include "SimpleNonlinearEllipticSolver.hpp"
37 
38 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
39 c_matrix<double,1*(ELEMENT_DIM+1),1*(ELEMENT_DIM+1)> SimpleNonlinearEllipticSolver<ELEMENT_DIM,SPACE_DIM>::ComputeMatrixTerm(
40  c_vector<double, ELEMENT_DIM+1>& rPhi,
41  c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>& rGradPhi,
43  c_vector<double,1>& rU,
44  c_matrix<double,1,SPACE_DIM>& rGradU,
46 {
47  c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> ret;
48 
49  c_matrix<double, SPACE_DIM, SPACE_DIM> f_of_u = mpNonlinearEllipticPde->ComputeDiffusionTerm(rX, rU(0));
50  c_matrix<double, SPACE_DIM, SPACE_DIM> f_of_u_prime = mpNonlinearEllipticPde->ComputeDiffusionTermPrime(rX, rU(0));
51 
52  // LinearSourceTerm(x) not needed as it is a constant wrt u
53  double forcing_term_prime = mpNonlinearEllipticPde->ComputeNonlinearSourceTermPrime(rX, rU(0));
54 
55  // Note rGradU is a 1 by SPACE_DIM matrix, the 1 representing the dimension of
56  // u (ie in this problem the unknown is a scalar). r_gradu_0 is rGradU as a vector
57  matrix_row< c_matrix<double, 1, SPACE_DIM> > r_gradu_0(rGradU, 0);
58  c_vector<double, SPACE_DIM> temp1 = prod(f_of_u_prime, r_gradu_0);
59  c_vector<double, ELEMENT_DIM+1> temp1a = prod(temp1, rGradPhi);
60 
61  c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> integrand_values1 = outer_prod(temp1a, rPhi);
62  c_matrix<double, SPACE_DIM, ELEMENT_DIM+1> temp2 = prod(f_of_u, rGradPhi);
63  c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> integrand_values2 = prod(trans(rGradPhi), temp2);
64  c_vector<double, ELEMENT_DIM+1> integrand_values3 = forcing_term_prime * rPhi;
65 
66  ret = integrand_values1 + integrand_values2 - outer_prod( scalar_vector<double>(ELEMENT_DIM+1), integrand_values3);
67 
68  return ret;
69 }
70 
71 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
73  c_vector<double, ELEMENT_DIM+1>& rPhi,
74  c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>& rGradPhi,
76  c_vector<double,1>& rU,
77  c_matrix<double,1,SPACE_DIM>& rGradU,
79 {
80  c_vector<double, 1*(ELEMENT_DIM+1)> ret;
81 
82  // For solving an AbstractNonlinearEllipticEquation
83  // d/dx [f(U,x) du/dx ] = -g
84  // where g(x,U) is the forcing term
85  double forcing_term = mpNonlinearEllipticPde->ComputeLinearSourceTerm(rX);
86  forcing_term += mpNonlinearEllipticPde->ComputeNonlinearSourceTerm(rX, rU(0));
87 
88  c_matrix<double, ELEMENT_DIM, ELEMENT_DIM> FOfU = mpNonlinearEllipticPde->ComputeDiffusionTerm(rX, rU(0));
89 
90  // Note rGradU is a 1 by SPACE_DIM matrix, the 1 representing the dimension of
91  // u (ie in this problem the unknown is a scalar). rGradU0 is rGradU as a vector.
92  matrix_row< c_matrix<double, 1, SPACE_DIM> > rGradU0(rGradU, 0);
93  c_vector<double, ELEMENT_DIM+1> integrand_values1 =
94  prod(c_vector<double, ELEMENT_DIM>(prod(rGradU0, FOfU)), rGradPhi);
95 
96  ret = integrand_values1 - (forcing_term * rPhi);
97  return ret;
98 }
99 
100 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
105  : AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM,SPACE_DIM,1>(pMesh,pBoundaryConditions),
106  mpNonlinearEllipticPde(pPde)
107 {
108  assert(pPde!=nullptr);
109 }
110 
111 // Explicit instantiation
virtual c_matrix< double, 1 *(ELEMENT_DIM+1), 1 *(ELEMENT_DIM+1)> ComputeMatrixTerm(c_vector< double, ELEMENT_DIM+1 > &rPhi, c_matrix< double, SPACE_DIM, ELEMENT_DIM+1 > &rGradPhi, ChastePoint< SPACE_DIM > &rX, c_vector< double, 1 > &rU, c_matrix< double, 1, SPACE_DIM > &rGradU, Element< ELEMENT_DIM, SPACE_DIM > *pElement)
virtual c_vector< double, 1 *(ELEMENT_DIM+1)> ComputeVectorTerm(c_vector< double, ELEMENT_DIM+1 > &rPhi, c_matrix< double, SPACE_DIM, ELEMENT_DIM+1 > &rGradPhi, ChastePoint< SPACE_DIM > &rX, c_vector< double, 1 > &rU, c_matrix< double, 1, SPACE_DIM > &rGradU, Element< ELEMENT_DIM, SPACE_DIM > *pElement)
SimpleNonlinearEllipticSolver(AbstractTetrahedralMesh< ELEMENT_DIM, SPACE_DIM > *pMesh, AbstractNonlinearEllipticPde< SPACE_DIM > *pPde, BoundaryConditionsContainer< ELEMENT_DIM, SPACE_DIM, 1 > *pBoundaryConditions)