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/*=========================================================================
Program: Insight Segmentation & Registration Toolkit
Module: $RCSfile: itkFEMSolverHyperbolic.cxx,v $
Language: C++
Date: $Date: 2009-01-30 21:53:03 $
Version: $Revision: 1.7 $
Copyright (c) Insight Software Consortium. All rights reserved.
See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details.
This software is distributed WITHOUT ANY WARRANTY; without even
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
PURPOSE. See the above copyright notices for more information.
=========================================================================*/
// disable debug warnings in MS compiler
#ifdef _MSC_VER
#pragma warning(disable: 4786)
#endif
#include "itkFEMSolverHyperbolic.h"
namespace itk {
namespace fem {
SolverHyperbolic::SolverHyperbolic()
{
this->InitializeLinearSystemWrapper();
m_beta=0.25;
m_gamma=0.5;
m_deltaT=1.0;
}
void
SolverHyperbolic
::InitializeLinearSystemWrapper(void)
{
// set the maximum number of matrices and vectors that
// we will need to store inside.
m_ls->SetNumberOfMatrices(5);
m_ls->SetNumberOfVectors(6);
m_ls->SetNumberOfSolutions(3);
}
void
SolverHyperbolic
::AssembleElementMatrix(Element::Pointer e)
{
// Copy the element stiffness matrix for faster access.
Element::MatrixType Ke;
e->GetStiffnessMatrix(Ke);
Element::MatrixType Me;
e->GetMassMatrix(Me);
// ... same for number of DOF
int Ne=e->GetNumberOfDegreesOfFreedom();
// step over all rows in element matrix
for(int j=0; j<Ne; j++)
{
// step over all columns in element matrix
for(int k=0; k<Ne; k++)
{
// error checking. all GFN should be =>0 and <NGFN
if ( e->GetDegreeOfFreedom(j) >= NGFN ||
e->GetDegreeOfFreedom(k) >= NGFN )
{
throw FEMExceptionSolution(__FILE__,__LINE__,"Solver::AssembleElementMatrix()","Illegal GFN!");
}
/**
* Here we finaly update the corresponding element
* in the master stiffness matrix. We first check if
* element in Ke is zero, to prevent zeros from being
* allocated in sparse matrix.
*/
if ( Ke[j][k]!=Float(0.0) )
{
this->m_ls->AddMatrixValue( e->GetDegreeOfFreedom(j), e->GetDegreeOfFreedom(k), Ke[j][k], matrix_K );
}
if ( Me[j][k]!=Float(0.0) )
{
this->m_ls->AddMatrixValue( e->GetDegreeOfFreedom(j), e->GetDegreeOfFreedom(k), Me[j][k], matrix_M );
}
}
}
}
void
SolverHyperbolic
::InitializeMatrixForAssembly(unsigned int N)
{
this->m_ls->SetSystemOrder(N);
this->m_ls->InitializeMatrix();
this->m_ls->InitializeMatrix(matrix_K);
this->m_ls->InitializeMatrix(matrix_M);
this->m_ls->InitializeMatrix(matrix_C);
for(unsigned int i=0; i<N; i++)
{
m_ls->SetMatrixValue(i,i,1.0,matrix_C);
}
}
void
SolverHyperbolic
::FinalizeMatrixAfterAssembly( void )
{
// Apply the boundary conditions to the matrix
// FIXME: this doesn't work in general
this->ApplyBC(0,matrix_M);
this->ApplyBC(0,matrix_K);
// Calculate initial values of vector_a
// M*a0=F - C*v0 - K*d0
// FIXME: take into account the d0 and v0.
m_ls->InitializeSolution(0);
m_ls->InitializeSolution(solution_a);
m_ls->CopyMatrix(matrix_M,0);
this->AssembleF();
m_ls->Solve();
m_ls->InitializeVector(vector_tmp);
m_ls->CopySolution2Vector(0,vector_tmp);
m_ls->InitializeSolution(solution_a);
m_ls->CopyVector2Solution(vector_tmp,solution_a);
m_ls->DestroyVector(vector_tmp);
m_ls->InitializeSolution(solution_d);
m_ls->InitializeSolution(solution_v);
// Compose the lhs of system of lin. eq.
m_ls->InitializeMatrix(matrix_tmp);
m_ls->CopyMatrix(matrix_C,matrix_tmp);
m_ls->ScaleMatrix(this->m_gamma*this->m_deltaT, matrix_tmp);
m_ls->AddMatrixMatrix(0,matrix_tmp);
m_ls->CopyMatrix(matrix_K,matrix_tmp);
m_ls->ScaleMatrix(this->m_beta*this->m_deltaT*this->m_deltaT, matrix_tmp);
m_ls->AddMatrixMatrix(0,matrix_tmp);
m_ls->DestroyMatrix(matrix_tmp);
}
void
SolverHyperbolic
::Solve()
{
m_ls->InitializeVector(vector_tmp);
m_ls->InitializeVector(vector_dhat);
m_ls->InitializeVector(vector_vhat);
m_ls->InitializeVector(vector_ahat);
// We're using the Newmark method to obtain the solution
// Assume that vectors solution_a solution_v and solution_d contain
// solutions obtained at the previous time step.
// Calculate the predictors
for(unsigned int i=0; i<m_ls->GetSystemOrder(); i++)
{
Float d0=m_ls->GetSolutionValue(i,solution_d);
Float v0=m_ls->GetSolutionValue(i,solution_v);
Float a0=m_ls->GetSolutionValue(i,solution_a);
m_ls->SetVectorValue( i, -(d0+this->m_deltaT*v0+0.5*this->m_deltaT*this->m_deltaT*(1.0-2.0*this->m_beta)*a0), vector_dhat);
m_ls->SetVectorValue( i, -(v0+this->m_deltaT*(1.0-this->m_gamma)*a0), vector_vhat);
}
// Calculate the rhs of master equation
m_ls->MultiplyMatrixVector(vector_tmp,matrix_C,vector_vhat);
m_ls->AddVectorVector(0,vector_tmp);
m_ls->MultiplyMatrixVector(vector_tmp,matrix_K,vector_dhat);
m_ls->AddVectorVector(0,vector_tmp);
// Solve the system of linear equations for accelerations
m_ls->Solve();
// move the solution for a to the correct vector
m_ls->CopySolution2Vector(0,vector_tmp);
m_ls->CopyVector2Solution(vector_tmp,solution_a);
// Calculate displacements and velocities
for(unsigned int i=0; i<m_ls->GetSystemOrder(); i++)
{
Float dhat=-m_ls->GetVectorValue(i,vector_dhat);
Float vhat=-m_ls->GetVectorValue(i,vector_vhat);
Float a1=m_ls->GetSolutionValue(i,solution_a);
m_ls->SetSolutionValue(i, dhat +
this->m_beta*this->m_deltaT*this->m_deltaT*a1
, solution_d);
m_ls->SetSolutionValue(i, vhat +
this->m_gamma*this->m_deltaT*a1
, solution_v);
}
m_ls->DestroyVector(vector_tmp);
m_ls->DestroyVector(vector_dhat);
m_ls->DestroyVector(vector_vhat);
m_ls->DestroyVector(vector_ahat);
}
}} // end namespace itk::fem
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