SimpleNonlinearEllipticAssembler.cpp

00001 /*
00002 
00003 Copyright (C) University of Oxford, 2005-2009
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 
00030 #include "SimpleNonlinearEllipticAssembler.hpp"
00031 
00032 
00033 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
00034 SimpleNonlinearEllipticAssembler<ELEMENT_DIM, SPACE_DIM>::SimpleNonlinearEllipticAssembler(
00035             AbstractMesh<ELEMENT_DIM, SPACE_DIM>* pMesh,
00036             AbstractNonlinearEllipticPde<SPACE_DIM>* pPde,
00037             BoundaryConditionsContainer<ELEMENT_DIM, SPACE_DIM, 1>* pBoundaryConditions,
00038             unsigned numQuadPoints)
00039     : AbstractAssembler<ELEMENT_DIM,SPACE_DIM,1>(),
00040       SimpleNonlinearEllipticAssembler<ELEMENT_DIM, SPACE_DIM>::BaseClassType(numQuadPoints)
00041 {
00042     assert(pMesh!=NULL);
00043     assert(pPde!=NULL);
00044     assert(pBoundaryConditions!=NULL);
00045 
00046     // Store data structures
00047     this->SetMesh(pMesh);
00048     mpNonlinearEllipticPde = pPde;
00049     this->SetBoundaryConditionsContainer(pBoundaryConditions);
00050 }
00051 
00052 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
00053 c_matrix<double,1*(ELEMENT_DIM+1),1*(ELEMENT_DIM+1)>
00054     SimpleNonlinearEllipticAssembler<ELEMENT_DIM, SPACE_DIM>::ComputeMatrixTerm(
00055             c_vector<double, ELEMENT_DIM+1> &rPhi,
00056             c_matrix<double, ELEMENT_DIM, ELEMENT_DIM+1> &rGradPhi,
00057             ChastePoint<SPACE_DIM> &rX,
00058             c_vector<double,1> &u,
00059             c_matrix<double,1,SPACE_DIM> &rGradU,
00060             Element<ELEMENT_DIM,SPACE_DIM>* pElement)
00061 {
00062     c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> ret;
00063 
00064     c_matrix<double, ELEMENT_DIM, ELEMENT_DIM> f_of_u = mpNonlinearEllipticPde->ComputeDiffusionTerm(rX,u(0));
00065     c_matrix<double, ELEMENT_DIM, ELEMENT_DIM> f_of_u_prime = mpNonlinearEllipticPde->ComputeDiffusionTermPrime(rX,u(0));
00066 
00067     //LinearSourceTerm(x)   not needed as it is a constant wrt u
00068     double forcing_term_prime = mpNonlinearEllipticPde->ComputeNonlinearSourceTermPrime(rX, u(0));
00069 
00070     // note rGradU is a 1 by SPACE_DIM matrix, the 1 representing the dimension of
00071     // u (ie in this problem the unknown is a scalar). rGradU0 is rGradU as a vector
00072     matrix_row< c_matrix<double, 1, SPACE_DIM> > rGradU0( rGradU, 0);
00073     c_vector<double, ELEMENT_DIM> temp1 = prod(f_of_u_prime,rGradU0);
00074     c_vector<double, ELEMENT_DIM+1> temp1a = prod(temp1, rGradPhi);
00075 
00076     c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> integrand_values1 = outer_prod(temp1a, rPhi);
00077     c_matrix<double, ELEMENT_DIM, ELEMENT_DIM+1> temp2 = prod(f_of_u, rGradPhi);
00078     c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> integrand_values2 = prod(trans(rGradPhi), temp2);
00079     c_vector<double, ELEMENT_DIM+1> integrand_values3 = forcing_term_prime * rPhi;
00080 
00081     ret = integrand_values1 + integrand_values2 - outer_prod( scalar_vector<double>(ELEMENT_DIM+1), integrand_values3);
00082 
00083     return ret;
00084 }
00085 
00086 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
00087 c_vector<double,1*(ELEMENT_DIM+1)>
00088     SimpleNonlinearEllipticAssembler<ELEMENT_DIM, SPACE_DIM>::ComputeVectorTerm(
00089             c_vector<double, ELEMENT_DIM+1> &rPhi,
00090             c_matrix<double, ELEMENT_DIM, ELEMENT_DIM+1> &rGradPhi,
00091             ChastePoint<SPACE_DIM> &rX,
00092             c_vector<double,1> &u,
00093             c_matrix<double,1,SPACE_DIM> &rGradU,
00094             Element<ELEMENT_DIM,SPACE_DIM>* pElement)
00095 {
00096     c_vector<double, 1*(ELEMENT_DIM+1)> ret;
00097 
00098     //c_vector<double, SPACE_DIM> gradU = prod(grad_phi, Ui);
00099 
00100     // For solving NonlinearEllipticEquation
00101     // which should be defined in/by NonlinearEllipticEquation.hpp:
00102     // d/dx [f(U,x) du/dx ] = -g
00103     // where g(x,U) is the forcing term
00104     double ForcingTerm = mpNonlinearEllipticPde->ComputeLinearSourceTerm(rX);
00105     ForcingTerm += mpNonlinearEllipticPde->ComputeNonlinearSourceTerm(rX, u(0));
00106     //make RHS general: consists of linear and nonlinear source terms
00107 
00108     c_matrix<double, ELEMENT_DIM, ELEMENT_DIM> FOfU = mpNonlinearEllipticPde->ComputeDiffusionTerm(rX,u(0));
00109 
00110     // note rGradU is a 1 by SPACE_DIM matrix, the 1 representing the dimension of
00111     // u (ie in this problem the unknown is a scalar). rGradU0 is rGradU as a vector.
00112     matrix_row< c_matrix<double, 1, SPACE_DIM> > rGradU0( rGradU, 0);
00113     c_vector<double, ELEMENT_DIM+1> integrand_values1 =
00114         prod(c_vector<double, ELEMENT_DIM>(prod(rGradU0, FOfU)), rGradPhi);
00115 
00116     ret = integrand_values1 - (ForcingTerm * rPhi);
00117     return ret;
00118 }
00119 
00120 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
00121 c_vector<double, 1*ELEMENT_DIM>
00122     SimpleNonlinearEllipticAssembler<ELEMENT_DIM, SPACE_DIM>::ComputeVectorSurfaceTerm(
00123             const BoundaryElement<ELEMENT_DIM-1,SPACE_DIM> &rSurfaceElement,
00124             c_vector<double, ELEMENT_DIM> &rPhi,
00125             ChastePoint<SPACE_DIM> &rX)
00126 {
00127     double Dgradu_dot_n = this->mpBoundaryConditions->GetNeumannBCValue(&rSurfaceElement, rX);
00128 
00129     // I'm not sure why we want -phi, but it seems to work:)
00130     return  (-Dgradu_dot_n)* rPhi;
00131 }
00132 
00133 
00134 
00136 // Explicit instantiation
00138 
00139 template class SimpleNonlinearEllipticAssembler<1,1>;
00140 template class SimpleNonlinearEllipticAssembler<2,2>;
00141 template class SimpleNonlinearEllipticAssembler<3,3>;

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