itkFEMSolverCrankNicolson.h

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/*=========================================================================

  Program:   Insight Segmentation & Registration Toolkit
  Module:    $RCSfile: itkFEMSolverCrankNicolson.h,v $
  Language:  C++
  Date:      $Date: 2009-01-30 21:53:03 $
  Version:   $Revision: 1.19 $

  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.

=========================================================================*/

#ifndef __itkFEMSolverCrankNicolson_h
#define __itkFEMSolverCrankNicolson_h

#include "itkFEMSolver.h"
#include "itkFEMElementBase.h"
#include "itkFEMMaterialBase.h"
#include "itkFEMLoadBase.h"
#include "itkFEMLinearSystemWrapperVNL.h"

#include "vnl/vnl_sparse_matrix.h"
#include "vnl/vnl_matrix.h"
#include "vnl/vnl_vector.h"
#include "vnl/algo/vnl_svd.h"
#include "vnl/algo/vnl_cholesky.h"
#include <vnl/vnl_sparse_matrix_linear_system.h>
#include <vnl/algo/vnl_lsqr.h>
#include <math.h>


namespace itk {
namespace fem {


class SolverCrankNicolson : public Solver
{
public:

  void InitializeForSolution(); 

  void AssembleKandM();

  void AssembleFforTimeStep(int dim=0);

  void Solve();

  void AddToDisplacements(Float optimum=1.0);
  void AverageLastTwoDisplacements(Float t=0.5);
  void ZeroVector(int which=0);
  void PrintDisplacements(); 
  void PrintForce();

  inline void SetAlpha(Float a = 0.5) { m_alpha=a; }

  inline void SetDeltatT(Float T) { m_deltaT=T; }

  inline void SetRho(Float rho) { m_rho=rho;  }

  void RecomputeForceVector(unsigned int index);

  /* Finds a triplet that brackets the energy minimum.  From Numerical Recipes.*/
  void FindBracketingTriplet(Float* a,Float* b,Float* c);

  Float GoldenSection(Float tol=0.01,unsigned int MaxIters=25);
  /* Brents method from Numerical Recipes. */
  Float BrentsMethod(Float tol=0.01,unsigned int MaxIters=25);
  Float EvaluateResidual(Float t=1.0);
  Float GetDeformationEnergy(Float t=1.0);
  inline Float GSSign(Float a,Float b) { return (b > 0.0 ? vcl_fabs(a) : -1.*vcl_fabs(a)); }
  inline Float GSMax(Float a,Float b) { return (a > b ? a : b); }

  void SetEnergyToMin(Float xmin);
  inline LinearSystemWrapper* GetLS(){ return m_ls;}

  Float GetCurrentMaxSolution() { return m_CurrentMaxSolution; }

  void PrintMinMaxOfSolution();

  SolverCrankNicolson() 
    { 
    m_deltaT=0.5; 
    m_rho=1.; 
    m_alpha=0.5;
    // BUG FIXME NOT SURE IF SOLVER IS USING VECTOR INDEX 1 FOR BCs
    ForceTIndex=0;                        // vector
    ForceTMinus1Index=2;                  // vector
    SolutionVectorTMinus1Index=3;         // vector
    DiffMatrixBySolutionTMinus1Index=4;   // vector
    ForceTotalIndex=5;                    // vector
    SolutionTIndex=0;                   // solution
    TotalSolutionIndex=1;               // solution
    SolutionTMinus1Index=2;       // solution
    SumMatrixIndex=0;                   // matrix
    DifferenceMatrixIndex=1;            // matrix
    m_CurrentMaxSolution=1.0;
    }

 
  ~SolverCrankNicolson() { }

  Float m_deltaT;
  Float m_rho;
  Float m_alpha;
  Float m_CurrentMaxSolution;

  unsigned int ForceTIndex;
  unsigned int ForceTotalIndex;
  unsigned int ForceTMinus1Index;
  unsigned int SolutionTIndex;
  unsigned int SolutionTMinus1Index;
  unsigned int SolutionVectorTMinus1Index;
  unsigned int TotalSolutionIndex;
  unsigned int DifferenceMatrixIndex;
  unsigned int SumMatrixIndex;
  unsigned int DiffMatrixBySolutionTMinus1Index;
  
};

}} // end namespace itk::fem

#endif // #ifndef __itkFEMSolverCrankNicolson_h