SimpleNonlinearEllipticSolver.cpp

00001 /*
00002 
00003 Copyright (C) University of Oxford, 2005-2011
00004 
00005 University of Oxford means the Chancellor, Masters and Scholars of the
00006 University of Oxford, having an administrative office at Wellington
00007 Square, Oxford OX1 2JD, UK.
00008 
00009 This file is part of Chaste.
00010 
00011 Chaste is free software: you can redistribute it and/or modify it
00012 under the terms of the GNU Lesser General Public License as published
00013 by the Free Software Foundation, either version 2.1 of the License, or
00014 (at your option) any later version.
00015 
00016 Chaste is distributed in the hope that it will be useful, but WITHOUT
00017 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
00018 FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
00019 License for more details. The offer of Chaste under the terms of the
00020 License is subject to the License being interpreted in accordance with
00021 English Law and subject to any action against the University of Oxford
00022 being under the jurisdiction of the English Courts.
00023 
00024 You should have received a copy of the GNU Lesser General Public License
00025 along with Chaste. If not, see <http://www.gnu.org/licenses/>.
00026 
00027 */
00028 
00029 #include "SimpleNonlinearEllipticSolver.hpp"
00030 
00031 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
00032 c_matrix<double,1*(ELEMENT_DIM+1),1*(ELEMENT_DIM+1)> SimpleNonlinearEllipticSolver<ELEMENT_DIM,SPACE_DIM>::ComputeMatrixTerm(
00033         c_vector<double, ELEMENT_DIM+1>& rPhi,
00034         c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>& rGradPhi,
00035         ChastePoint<SPACE_DIM>& rX,
00036         c_vector<double,1>& rU,
00037         c_matrix<double,1,SPACE_DIM>& rGradU,
00038         Element<ELEMENT_DIM,SPACE_DIM>* pElement)
00039 {
00040     c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> ret;
00041 
00042     c_matrix<double, SPACE_DIM, SPACE_DIM> f_of_u = mpNonlinearEllipticPde->ComputeDiffusionTerm(rX, rU(0));
00043     c_matrix<double, SPACE_DIM, SPACE_DIM> f_of_u_prime = mpNonlinearEllipticPde->ComputeDiffusionTermPrime(rX, rU(0));
00044 
00045     // LinearSourceTerm(x) not needed as it is a constant wrt u
00046     double forcing_term_prime = mpNonlinearEllipticPde->ComputeNonlinearSourceTermPrime(rX, rU(0));
00047 
00048     // Note rGradU is a 1 by SPACE_DIM matrix, the 1 representing the dimension of
00049     // u (ie in this problem the unknown is a scalar). r_gradu_0 is rGradU as a vector
00050     matrix_row< c_matrix<double, 1, SPACE_DIM> > r_gradu_0(rGradU, 0);
00051     c_vector<double, SPACE_DIM> temp1 = prod(f_of_u_prime, r_gradu_0);
00052     c_vector<double, ELEMENT_DIM+1> temp1a = prod(temp1, rGradPhi);
00053 
00054     c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> integrand_values1 = outer_prod(temp1a, rPhi);
00055     c_matrix<double, SPACE_DIM, ELEMENT_DIM+1> temp2 = prod(f_of_u, rGradPhi);
00056     c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> integrand_values2 = prod(trans(rGradPhi), temp2);
00057     c_vector<double, ELEMENT_DIM+1> integrand_values3 = forcing_term_prime * rPhi;
00058 
00059     ret = integrand_values1 + integrand_values2 - outer_prod( scalar_vector<double>(ELEMENT_DIM+1), integrand_values3);
00060 
00061     return ret;
00062 }
00063 
00064 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
00065 c_vector<double,1*(ELEMENT_DIM+1)> SimpleNonlinearEllipticSolver<ELEMENT_DIM,SPACE_DIM>::ComputeVectorTerm(
00066         c_vector<double, ELEMENT_DIM+1>& rPhi,
00067         c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>& rGradPhi,
00068         ChastePoint<SPACE_DIM>& rX,
00069         c_vector<double,1>& rU,
00070         c_matrix<double,1,SPACE_DIM>& rGradU,
00071         Element<ELEMENT_DIM,SPACE_DIM>* pElement)
00072 {
00073     c_vector<double, 1*(ELEMENT_DIM+1)> ret;
00074 
00075     // For solving an AbstractNonlinearEllipticEquation
00076     // d/dx [f(U,x) du/dx ] = -g
00077     // where g(x,U) is the forcing term
00078     double forcing_term = mpNonlinearEllipticPde->ComputeLinearSourceTerm(rX);
00079     forcing_term += mpNonlinearEllipticPde->ComputeNonlinearSourceTerm(rX, rU(0));
00080 
00081     c_matrix<double, ELEMENT_DIM, ELEMENT_DIM> FOfU = mpNonlinearEllipticPde->ComputeDiffusionTerm(rX, rU(0));
00082 
00083     // Note rGradU is a 1 by SPACE_DIM matrix, the 1 representing the dimension of
00084     // u (ie in this problem the unknown is a scalar). rGradU0 is rGradU as a vector.
00085     matrix_row< c_matrix<double, 1, SPACE_DIM> > rGradU0(rGradU, 0);
00086     c_vector<double, ELEMENT_DIM+1> integrand_values1 =
00087         prod(c_vector<double, ELEMENT_DIM>(prod(rGradU0, FOfU)), rGradPhi);
00088 
00089     ret = integrand_values1 - (forcing_term * rPhi);
00090     return ret;
00091 }
00092 
00093 
00094 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
00095 SimpleNonlinearEllipticSolver<ELEMENT_DIM,SPACE_DIM>::SimpleNonlinearEllipticSolver(
00096                               AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>* pMesh,
00097                               AbstractNonlinearEllipticPde<SPACE_DIM>* pPde,
00098                               BoundaryConditionsContainer<ELEMENT_DIM, SPACE_DIM, 1>* pBoundaryConditions,
00099                               unsigned numQuadPoints)
00100     :  AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM,SPACE_DIM,1>(pMesh,pBoundaryConditions,numQuadPoints),
00101        mpNonlinearEllipticPde(pPde)
00102 {
00103     assert(pPde!=NULL);
00104 }
00105 
00107 // Explicit instantiation
00109 
00110 template class SimpleNonlinearEllipticSolver<1,1>;
00111 template class SimpleNonlinearEllipticSolver<2,2>;
00112 template class SimpleNonlinearEllipticSolver<3,3>;