BidomainAssembler.cpp

00001 
00002 /*
00003 
00004 Copyright (C) University of Oxford, 2005-2011
00005 
00006 University of Oxford means the Chancellor, Masters and Scholars of the
00007 University of Oxford, having an administrative office at Wellington
00008 Square, Oxford OX1 2JD, UK.
00009 
00010 This file is part of Chaste.
00011 
00012 Chaste is free software: you can redistribute it and/or modify it
00013 under the terms of the GNU Lesser General Public License as published
00014 by the Free Software Foundation, either version 2.1 of the License, or
00015 (at your option) any later version.
00016 
00017 Chaste is distributed in the hope that it will be useful, but WITHOUT
00018 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
00019 FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
00020 License for more details. The offer of Chaste under the terms of the
00021 License is subject to the License being interpreted in accordance with
00022 English Law and subject to any action against the University of Oxford
00023 being under the jurisdiction of the English Courts.
00024 
00025 You should have received a copy of the GNU Lesser General Public License
00026 along with Chaste. If not, see <http://www.gnu.org/licenses/>.
00027 
00028 */
00029 
00030 #include "BidomainAssembler.hpp"
00031 #include "PdeSimulationTime.hpp"
00032 #include "UblasIncludes.hpp"
00033 #include <boost/numeric/ublas/vector_proxy.hpp>
00034 
00035 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
00036 void BidomainAssembler<ELEMENT_DIM,SPACE_DIM>::ResetInterpolatedQuantities()
00037 {
00038     mIionic = 0;
00039     mIIntracellularStimulus = 0;
00040 }
00041 
00042 
00043 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
00044 void BidomainAssembler<ELEMENT_DIM,SPACE_DIM>::IncrementInterpolatedQuantities(
00045         double phiI,
00046         const Node<SPACE_DIM>* pNode)
00047 {
00048     unsigned node_global_index = pNode->GetIndex();
00049 
00050     mIionic                 += phiI * this->mpCardiacTissue->rGetIionicCacheReplicated()[ node_global_index ];
00051     mIIntracellularStimulus += phiI * this->mpCardiacTissue->rGetIntracellularStimulusCacheReplicated()[ node_global_index ];
00052 }
00053 
00054 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
00055 c_matrix<double,2*(ELEMENT_DIM+1),2*(ELEMENT_DIM+1)>
00056     BidomainAssembler<ELEMENT_DIM,SPACE_DIM>::ComputeMatrixTerm(
00057             c_vector<double, ELEMENT_DIM+1> &rPhi,
00058             c_matrix<double, SPACE_DIM, ELEMENT_DIM+1> &rGradPhi,
00059             ChastePoint<SPACE_DIM> &rX,
00060             c_vector<double,2> &rU,
00061             c_matrix<double, 2, SPACE_DIM> &rGradU /* not used */,
00062             Element<ELEMENT_DIM,SPACE_DIM>* pElement)
00063 {
00064     // get bidomain parameters
00065     double Am = mpConfig->GetSurfaceAreaToVolumeRatio();
00066     double Cm = mpConfig->GetCapacitance();
00067 
00068     const c_matrix<double, SPACE_DIM, SPACE_DIM>& sigma_i = this->mpCardiacTissue->rGetIntracellularConductivityTensor(pElement->GetIndex());
00069     const c_matrix<double, SPACE_DIM, SPACE_DIM>& sigma_e = this->mpCardiacTissue->rGetExtracellularConductivityTensor(pElement->GetIndex());
00070 
00071 
00072     c_matrix<double, SPACE_DIM, ELEMENT_DIM+1> temp = prod(sigma_i, rGradPhi);
00073     c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> grad_phi_sigma_i_grad_phi =
00074         prod(trans(rGradPhi), temp);
00075 
00076     c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> basis_outer_prod =
00077         outer_prod(rPhi, rPhi);
00078 
00079     c_matrix<double, SPACE_DIM, ELEMENT_DIM+1> temp2 = prod(sigma_e, rGradPhi);
00080     c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> grad_phi_sigma_e_grad_phi =
00081         prod(trans(rGradPhi), temp2);
00082 
00083 
00084     c_matrix<double,2*(ELEMENT_DIM+1),2*(ELEMENT_DIM+1)> ret;
00085 
00086     // even rows, even columns
00087     matrix_slice<c_matrix<double, 2*ELEMENT_DIM+2, 2*ELEMENT_DIM+2> >
00088     slice00(ret, slice (0, 2, ELEMENT_DIM+1), slice (0, 2, ELEMENT_DIM+1));
00089     slice00 = (Am*Cm*PdeSimulationTime::GetPdeTimeStepInverse())*basis_outer_prod + grad_phi_sigma_i_grad_phi;
00090 
00091     // odd rows, even columns
00092     matrix_slice<c_matrix<double, 2*ELEMENT_DIM+2, 2*ELEMENT_DIM+2> >
00093     slice10(ret, slice (1, 2, ELEMENT_DIM+1), slice (0, 2, ELEMENT_DIM+1));
00094     slice10 = grad_phi_sigma_i_grad_phi;
00095 
00096     // even rows, odd columns
00097     matrix_slice<c_matrix<double, 2*ELEMENT_DIM+2, 2*ELEMENT_DIM+2> >
00098     slice01(ret, slice (0, 2, ELEMENT_DIM+1), slice (1, 2, ELEMENT_DIM+1));
00099     slice01 = grad_phi_sigma_i_grad_phi;
00100 
00101     // odd rows, odd columns
00102     matrix_slice<c_matrix<double, 2*ELEMENT_DIM+2, 2*ELEMENT_DIM+2> >
00103     slice11(ret, slice (1, 2, ELEMENT_DIM+1), slice (1, 2, ELEMENT_DIM+1));
00104     slice11 = grad_phi_sigma_i_grad_phi + grad_phi_sigma_e_grad_phi;
00105 
00106     return ret;
00107 }
00108 
00109 
00110 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
00111 c_vector<double,2*(ELEMENT_DIM+1)>
00112     BidomainAssembler<ELEMENT_DIM,SPACE_DIM>::ComputeVectorTerm(
00113             c_vector<double, ELEMENT_DIM+1> &rPhi,
00114             c_matrix<double, SPACE_DIM, ELEMENT_DIM+1> &rGradPhi,
00115             ChastePoint<SPACE_DIM> &rX,
00116             c_vector<double,2> &u,
00117             c_matrix<double, 2, SPACE_DIM> &rGradU /* not used */,
00118             Element<ELEMENT_DIM,SPACE_DIM>* pElement)
00119 {
00120     // get bidomain parameters
00121     double Am = mpConfig->GetSurfaceAreaToVolumeRatio();
00122     double Cm = mpConfig->GetCapacitance();
00123 
00124     c_vector<double,2*(ELEMENT_DIM+1)> ret;
00125 
00126     vector_slice<c_vector<double, 2*(ELEMENT_DIM+1)> > slice_V  (ret, slice (0, 2, ELEMENT_DIM+1));
00127     vector_slice<c_vector<double, 2*(ELEMENT_DIM+1)> > slice_Phi(ret, slice (1, 2, ELEMENT_DIM+1));
00128 
00129     // u(0) = voltage
00130     noalias(slice_V)   = (Am*Cm*u(0)*PdeSimulationTime::GetPdeTimeStepInverse() - Am*mIionic - mIIntracellularStimulus) * rPhi;
00131     noalias(slice_Phi) = zero_vector<double>(ELEMENT_DIM+1);
00132 
00133     return ret;
00134 }
00135 
00136 
00137 
00138 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
00139 c_vector<double, 2*ELEMENT_DIM> BidomainAssembler<ELEMENT_DIM,SPACE_DIM>::ComputeVectorSurfaceTerm(
00140         const BoundaryElement<ELEMENT_DIM-1,SPACE_DIM> &rSurfaceElement,
00141         c_vector<double,ELEMENT_DIM> &rPhi,
00142         ChastePoint<SPACE_DIM> &rX)
00143 {
00144     // D_times_gradu_dot_n = [D grad(u)].n, D=diffusion matrix
00145     double sigma_i_times_grad_phi_i_dot_n = this->mpBoundaryConditions->GetNeumannBCValue(&rSurfaceElement, rX, 0);
00146     double sigma_e_times_grad_phi_e_dot_n = this->mpBoundaryConditions->GetNeumannBCValue(&rSurfaceElement, rX, 1);
00147 
00148     c_vector<double, 2*ELEMENT_DIM> ret;
00149     for (unsigned i=0; i<ELEMENT_DIM; i++)
00150     {
00151         ret(2*i)   = rPhi(i)*sigma_i_times_grad_phi_i_dot_n;
00152         ret(2*i+1) = rPhi(i)*(sigma_i_times_grad_phi_i_dot_n + sigma_e_times_grad_phi_e_dot_n);
00153     }
00154 
00155     return ret;
00156 }
00157 
00158 
00159 
00160 template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
00161 BidomainAssembler<ELEMENT_DIM,SPACE_DIM>::BidomainAssembler(
00162             AbstractTetrahedralMesh<ELEMENT_DIM,SPACE_DIM>* pMesh,
00163             BidomainTissue<SPACE_DIM>* pTissue,
00164             unsigned numQuadPoints)
00165     : AbstractCardiacFeObjectAssembler<ELEMENT_DIM,SPACE_DIM,2,true,true,CARDIAC>(pMesh,pTissue,numQuadPoints)
00166 {
00167     assert(pTissue != NULL);
00168     mpConfig = HeartConfig::Instance();
00169 }
00170 
00171 
00172 
00174 // explicit instantiation
00176 
00177 template class BidomainAssembler<1,1>;
00178 template class BidomainAssembler<2,2>;
00179 template class BidomainAssembler<3,3>;

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