#include <DriverModifiedArnoldi.h>

Inheritance diagram for Nektar::SolverUtils::DriverModifiedArnoldi:

Static Public Member Functions
static DriverSharedPtr	create (const LibUtilities::SessionReaderSharedPtr &pSession, const SpatialDomains::MeshGraphSharedPtr &pGraph)
	Creates an instance of this class. More...

Static Public Attributes
static std::string	className
	Name of the class. More...

Protected Member Functions
	DriverModifiedArnoldi (const LibUtilities::SessionReaderSharedPtr pSession, const SpatialDomains::MeshGraphSharedPtr pGraph)
	Constructor. More...

virtual	~DriverModifiedArnoldi ()
	Destructor. More...

virtual void	v_InitObject (std::ostream &out=std::cout)
	Virtual function for initialisation implementation. More...

virtual void	v_Execute (std::ostream &out=std::cout)
	Virtual function for solve implementation. More...

Protected Member Functions inherited from Nektar::SolverUtils::DriverArnoldi
	DriverArnoldi (const LibUtilities::SessionReaderSharedPtr pSession, const SpatialDomains::MeshGraphSharedPtr pGraph)
	Constructor. More...

virtual	~DriverArnoldi ()
	Destructor. More...

void	CopyArnoldiArrayToField (Array< OneD, NekDouble > &array)
	Copy Arnoldi storage to fields. More...

void	CopyFieldToArnoldiArray (Array< OneD, NekDouble > &array)
	Copy fields to Arnoldi storage. More...

void	CopyFwdToAdj ()
	Copy the forward field to the adjoint system in transient growth calculations. More...

void	WriteFld (std::string file, std::vector< Array< OneD, NekDouble > > coeffs)
	Write coefficients to file. More...

void	WriteFld (std::string file, Array< OneD, NekDouble > coeffs)

void	WriteEvs (std::ostream &evlout, const int k, const NekDouble real, const NekDouble imag, NekDouble resid=NekConstants::kNekUnsetDouble, bool DumpInverse=true)

void	MaskInit ()
	init mask More...

void	GetUnmaskFunction (std::vector< std::vector< LibUtilities::EquationSharedPtr > > &unmaskfun)

virtual Array< OneD, NekDouble >	v_GetRealEvl (void)

virtual Array< OneD, NekDouble >	v_GetImagEvl (void)

Protected Member Functions inherited from Nektar::SolverUtils::Driver
	Driver (const LibUtilities::SessionReaderSharedPtr pSession, const SpatialDomains::MeshGraphSharedPtr pGraph)
	Initialises EquationSystem class members. More...

Private Member Functions
void	EV_update (Array< OneD, NekDouble > &src, Array< OneD, NekDouble > &tgt)
	Generates a new vector in the sequence by applying the linear operator. More...

void	EV_small (Array< OneD, Array< OneD, NekDouble > > &Kseq, Array< OneD, Array< OneD, NekDouble > > &Kseqcopy, const int ntot, const Array< OneD, NekDouble > &alpha, const int kdim, Array< OneD, NekDouble > &zvec, Array< OneD, NekDouble > &wr, Array< OneD, NekDouble > &wi, NekDouble &resnorm)
	Generates the upper Hessenberg matrix H and computes its eigenvalues. More...

int	EV_test (const int itrn, const int kdim, Array< OneD, NekDouble > &zvec, Array< OneD, NekDouble > &wr, Array< OneD, NekDouble > &wi, const NekDouble resnorm, int nvec, std::ofstream &evlout, NekDouble &resid0)
	Tests for convergence of eigenvalues of H. More...

void	EV_sort (Array< OneD, NekDouble > &evec, Array< OneD, NekDouble > &wr, Array< OneD, NekDouble > &wi, Array< OneD, NekDouble > &test, const int dim)
	Sorts a sequence of eigenvectors/eigenvalues by magnitude. More...

void	EV_post (Array< OneD, Array< OneD, NekDouble > > &Tseq, Array< OneD, Array< OneD, NekDouble > > &Kseq, const int ntot, const int kdim, const int nvec, Array< OneD, NekDouble > &zvec, Array< OneD, NekDouble > &wr, Array< OneD, NekDouble > &wi, const int icon)

void	EV_big (Array< OneD, Array< OneD, NekDouble > > &bvecs, Array< OneD, Array< OneD, NekDouble > > &evecs, const int ntot, const int kdim, const int nvec, Array< OneD, NekDouble > &zvec, Array< OneD, NekDouble > &wr, Array< OneD, NekDouble > &wi)

Static Private Attributes
static std::string	driverLookupId

Friends
class	MemoryManager< DriverModifiedArnoldi >

Additional Inherited Members
Public Member Functions inherited from Nektar::SolverUtils::DriverArnoldi
SOLVER_UTILS_EXPORT void	ArnoldiSummary (std::ostream &out)

SOLVER_UTILS_EXPORT const Array< OneD, const NekDouble > &	GetMaskCoeff () const

SOLVER_UTILS_EXPORT const Array< OneD, const NekDouble > &	GetMaskPhys () const

Public Member Functions inherited from Nektar::SolverUtils::Driver
virtual	~Driver ()
	Destructor. More...

SOLVER_UTILS_EXPORT void	InitObject (std::ostream &out=std::cout)
	Initialise Object. More...

SOLVER_UTILS_EXPORT void	Execute (std::ostream &out=std::cout)
	Execute driver. More...

SOLVER_UTILS_EXPORT Array< OneD, EquationSystemSharedPtr >	GetEqu ()

SOLVER_UTILS_EXPORT Array< OneD, NekDouble >	GetRealEvl (void)

SOLVER_UTILS_EXPORT Array< OneD, NekDouble >	GetImagEvl (void)

Protected Attributes inherited from Nektar::SolverUtils::DriverArnoldi
int	m_kdim

int	m_nvec
	Dimension of Krylov subspace. More...

int	m_nits
	Number of vectors to test. More...

NekDouble	m_evtol
	Maxmum number of iterations. More...

NekDouble	m_period
	Tolerance of iteratiosn. More...

bool	m_timeSteppingAlgorithm
	Period of time stepping algorithm. More...

int	m_infosteps
	underlying operator is time stepping More...

int	m_nfields
	interval to dump information if required. More...

NekDouble	m_realShift

NekDouble	m_imagShift

int	m_negatedOp

Array< OneD, NekDouble >	m_real_evl
	Operator in solve call is negated. More...

Array< OneD, NekDouble >	m_imag_evl

bool	m_useMask

Array< OneD, NekDouble >	m_maskCoeffs

Array< OneD, NekDouble >	m_maskPhys

Protected Attributes inherited from Nektar::SolverUtils::Driver
LibUtilities::CommSharedPtr	m_comm
	Communication object. More...

LibUtilities::SessionReaderSharedPtr	m_session
	Session reader object. More...

LibUtilities::SessionReaderSharedPtr	session_LinNS
	I the Coupling between SFD and arnoldi. More...

SpatialDomains::MeshGraphSharedPtr	m_graph
	MeshGraph object. More...

Array< OneD, EquationSystemSharedPtr >	m_equ
	Equation system to solve. More...

int	m_nequ
	number of equations More...

enum EvolutionOperatorType	m_EvolutionOperator
	Evolution Operator. More...

Static Protected Attributes inherited from Nektar::SolverUtils::Driver
static std::string	evolutionOperatorLookupIds []

static std::string	evolutionOperatorDef

static std::string	driverDefault

Detailed Description

Definition at line 46 of file DriverModifiedArnoldi.h.

Constructor & Destructor Documentation

◆ DriverModifiedArnoldi()

Nektar::SolverUtils::DriverModifiedArnoldi::DriverModifiedArnoldi	(	const LibUtilities::SessionReaderSharedPtr	pSession,
		const SpatialDomains::MeshGraphSharedPtr	pGraph
	)

protected

Constructor.

Definition at line 59 of file DriverModifiedArnoldi.cpp.

     : DriverArnoldi(pSession, pGraph)
 {
 }

◆ ~DriverModifiedArnoldi()

Nektar::SolverUtils::DriverModifiedArnoldi::~DriverModifiedArnoldi ( )

protectedvirtual

Destructor.

Definition at line 70 of file DriverModifiedArnoldi.cpp.

71 {

72 }

Member Function Documentation

◆ create()

static DriverSharedPtr Nektar::SolverUtils::DriverModifiedArnoldi::create	(	const LibUtilities::SessionReaderSharedPtr &	pSession,
		const SpatialDomains::MeshGraphSharedPtr &	pGraph
	)

inlinestatic

Creates an instance of this class.

Definition at line 52 of file DriverModifiedArnoldi.h.

         {
             DriverSharedPtr p = MemoryManager<DriverModifiedArnoldi>
                 ::AllocateSharedPtr(pSession, pGraph);
             p->InitObject();
             return p;
         }

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), and CellMLToNektar.cellml_metadata::p.

◆ EV_big()

void Nektar::SolverUtils::DriverModifiedArnoldi::EV_big	(	Array< OneD, Array< OneD, NekDouble > > &	bvecs,
		Array< OneD, Array< OneD, NekDouble > > &	evecs,
		const int	ntot,
		const int	kdim,
		const int	nvec,
		Array< OneD, NekDouble > &	zvec,
		Array< OneD, NekDouble > &	wr,
		Array< OneD, NekDouble > &	wi
	)

private

Compute estimates of the eigenvalues/eigenvectors of the original system.

Definition at line 617 of file DriverModifiedArnoldi.cpp.

 {
     boost::ignore_unused(wr);
  
     NekDouble wgt, norm;
     Array<OneD, Array<OneD, NekDouble> > btmp(nvec);
     Array<OneD, Array<OneD, NekDouble> > etmp(nvec);
     for(int i=0; i<nvec; ++i)
     {
         if (m_useMask)
         {
             btmp[i] = Array<OneD, NekDouble>(ntot, 0.);
             etmp[i] = Array<OneD, NekDouble>(ntot, 0.);
         }
         else
         {
             btmp[i] = evecs[i];
         }
     }
  
     // Generate big eigenvectors
     for (int j = 0; j < nvec; ++j)
     {
         Vmath::Zero(ntot, btmp[j], 1);
         if (m_useMask)
         {
             Vmath::Zero(ntot, etmp[j], 1);
         }
         for (int i = 0; i < kdim; ++i)
         {
             wgt = zvec[i + j*kdim];
             Vmath::Svtvp(ntot, wgt, bvecs[i], 1, btmp[j], 1, btmp[j], 1);
             if (m_useMask)
             {
                 Vmath::Svtvp(ntot, wgt, evecs[i], 1, etmp[j], 1, etmp[j], 1);
             }
         }
     }
  
     // Normalise the big eigenvectors
     for (int i = 0; i < nvec; ++i)
     {
         if (wi[i] == 0.0)   // Real mode
         {
             if (m_session->GetComm()->GetRank() == 0)
             {
                 cout << "eigenvalue " << i << ": real mode" << endl;
             }
             norm = Blas::Ddot(ntot, &btmp[i][0], 1, &btmp[i][0], 1);
             m_comm->AllReduce(norm, Nektar::LibUtilities::ReduceSum);
             norm = std::sqrt(norm);
             if (m_useMask)
             {
                 Vmath::Smul(ntot, 1.0/norm, btmp[i], 1, bvecs[i], 1);
                 Vmath::Smul(ntot, 1.0/norm, etmp[i], 1, evecs[i], 1);
             }
             else
             {
                 Vmath::Smul(ntot, 1.0/norm, btmp[i], 1, evecs[i], 1);
             }
         }
         else
         {
             if (m_session->GetComm()->GetRank() == 0)
             {
                 cout << "eigenvalues " << i << ", " << i+1
                      <<  ": complex modes" << endl;
             }
             norm  = Blas::Ddot(ntot, &btmp[i][0],   1, &btmp[i][0],   1);
             norm += Blas::Ddot(ntot, &btmp[i+1][0], 1, &btmp[i+1][0], 1);
             m_comm->AllReduce(norm, Nektar::LibUtilities::ReduceSum);
             norm = std::sqrt(norm);
  
             if (m_useMask)
             {
                 Vmath::Smul(ntot, 1.0/norm, btmp[i],   1, bvecs[i],   1);
                 Vmath::Smul(ntot, 1.0/norm, btmp[i+1], 1, bvecs[i+1], 1);
                 Vmath::Smul(ntot, 1.0/norm, etmp[i],   1, evecs[i],   1);
                 Vmath::Smul(ntot, 1.0/norm, etmp[i+1], 1, evecs[i+1], 1);
             }
             else
             {
                 Vmath::Smul(ntot, 1.0/norm, btmp[i],   1, evecs[i],   1);
                 Vmath::Smul(ntot, 1.0/norm, btmp[i+1], 1, evecs[i+1], 1);
             }
  
             i++;
         }
     }
 }

References Blas::Ddot(), Nektar::SolverUtils::Driver::m_comm, Nektar::SolverUtils::Driver::m_session, Nektar::SolverUtils::DriverArnoldi::m_useMask, Nektar::LibUtilities::ReduceSum, Vmath::Smul(), tinysimd::sqrt(), Vmath::Svtvp(), and Vmath::Zero().

Referenced by EV_post().

◆ EV_post()

void Nektar::SolverUtils::DriverModifiedArnoldi::EV_post	(	Array< OneD, Array< OneD, NekDouble > > &	Tseq,
		Array< OneD, Array< OneD, NekDouble > > &	Kseq,
		const int	ntot,
		const int	kdim,
		const int	nvec,
		Array< OneD, NekDouble > &	zvec,
		Array< OneD, NekDouble > &	wr,
		Array< OneD, NekDouble > &	wi,
		const int	icon
	)

private

Post-process the Ritz eigenvalues/eigenvectors of the matrix H, to compute estimations of the leading eigenvalues and eigenvectors of the original matrix.

Definition at line 557 of file DriverModifiedArnoldi.cpp.

 {
     if (icon == 0)
     {
         // Not converged, write final Krylov vector
         ASSERTL0(false, "Convergence was not achieved within the "
                         "prescribed number of iterations.");
     }
     else if (icon < 0)
     {
         // Minimum residual reached
         ASSERTL0(false, "Minimum residual reached.");
     }
     else if (icon == nvec)
     {
         // Converged, write out eigenvectors
         EV_big(Tseq, Kseq, ntot, kdim, icon, zvec, wr, wi);
         Array<OneD, MultiRegions::ExpListSharedPtr> fields
                 = m_equ[0]->UpdateFields();
  
         for (int j = 0; j < icon; ++j)
         {
             std::string file = m_session->GetSessionName() + "_eig_"
                 + boost::lexical_cast<std::string>(j)
                 + ".fld";
  
             if (m_comm->GetRank() == 0)
             {
                 WriteEvs(cout, j, wr[j], wi[j]);
             }
             WriteFld(file,Kseq[j]);
             if (m_useMask)
             {
                 std::string fileunmask = m_session->GetSessionName() + "_eig_masked_"
                     + boost::lexical_cast<std::string>(j)
                     + ".fld";
                 WriteFld(fileunmask,Tseq[j]);
             }
         }
     }
     else
     {
         // Not recognised
         ASSERTL0(false, "Unrecognised value.");
     }
 }

References ASSERTL0, EV_big(), Nektar::SolverUtils::Driver::m_comm, Nektar::SolverUtils::Driver::m_equ, Nektar::SolverUtils::Driver::m_session, Nektar::SolverUtils::DriverArnoldi::m_useMask, Nektar::SolverUtils::DriverArnoldi::WriteEvs(), and Nektar::SolverUtils::DriverArnoldi::WriteFld().

Referenced by v_Execute().

◆ EV_small()

void Nektar::SolverUtils::DriverModifiedArnoldi::EV_small	(	Array< OneD, Array< OneD, NekDouble > > &	Kseq,
		Array< OneD, Array< OneD, NekDouble > > &	Kseqcopy,
		const int	ntot,
		const Array< OneD, NekDouble > &	alpha,
		const int	kdim,
		Array< OneD, NekDouble > &	zvec,
		Array< OneD, NekDouble > &	wr,
		Array< OneD, NekDouble > &	wi,
		NekDouble &	resnorm
	)

private

Generates the upper Hessenberg matrix H and computes its eigenvalues.

Computes the Ritz eigenvalues and eigenvectors of the Hessenberg matrix constructed from the Krylov sequence.

Definition at line 382 of file DriverModifiedArnoldi.cpp.

 {
     int kdimp = kdim + 1;
     int lwork = 10*kdim;
     int ier;
     Array<OneD, NekDouble> R(kdimp * kdimp, 0.0);
     Array<OneD, NekDouble> H(kdimp * kdim, 0.0);
     Array<OneD, NekDouble> rwork(lwork, 0.0);
  
     // Modified G-S orthonormalisation
     for (int i = 0; i < kdimp; ++i)
     {
         NekDouble gsc = Blas::Ddot(ntot, &Kseq[i][0], 1, &Kseq[i][0], 1);
         m_comm->AllReduce(gsc, Nektar::LibUtilities::ReduceSum);
         gsc = std::sqrt(gsc);
         ASSERTL0(gsc != 0.0, "Vectors are linearly independent.");
  
         R[i*kdimp+i] = gsc;
         Vmath::Smul(ntot, 1.0/gsc, Kseq[i], 1, Kseq[i], 1);
         if (m_useMask)
         {
             Vmath::Smul(ntot, 1.0/gsc, Kseqcopy[i], 1, Kseqcopy[i], 1);
         }
  
         for (int j = i + 1; j < kdimp; ++j)
         {
             gsc = Blas::Ddot(ntot, &Kseq[i][0], 1, &Kseq[j][0], 1);
             m_comm->AllReduce(gsc, Nektar::LibUtilities::ReduceSum);
             Vmath::Svtvp(ntot, -gsc, Kseq[i], 1, Kseq[j], 1, Kseq[j], 1);
             if (m_useMask)
             {
                 Vmath::Svtvp(ntot, -gsc, Kseqcopy[i], 1, Kseqcopy[j], 1, Kseqcopy[j], 1);
             }
             R[j*kdimp+i] = gsc;
         }
     }
  
     // Compute H matrix
     for (int i = 0; i < kdim; ++i)
     {
         for (int j = 0; j < kdim; ++j)
         {
             H[j*kdim+i] = alpha[j+1] * R[(j+1)*kdimp+i]
             - Vmath::Dot(j, &H[0] + i, kdim, &R[0] + j*kdimp, 1);
             H[j*kdim+i] /= R[j*kdimp+j];
         }
     }
  
     H[(kdim-1)*kdim+kdim] = alpha[kdim]
                   * std::fabs(R[kdim*kdimp+kdim] / R[(kdim-1)*kdimp + kdim-1]);
  
     Lapack::dgeev_('N', 'V', kdim, &H[0], kdim, &wr[0], &wi[0], 0, 1,
                    &zvec[0], kdim, &rwork[0], lwork, ier);
  
     ASSERTL0(!ier, "Error with dgeev");
  
     resnorm = H[(kdim-1)*kdim + kdim];
 }

References ASSERTL0, Blas::Ddot(), Vmath::Dot(), Nektar::SolverUtils::Driver::m_comm, Nektar::SolverUtils::DriverArnoldi::m_useMask, Nektar::LibUtilities::ReduceSum, Vmath::Smul(), tinysimd::sqrt(), and Vmath::Svtvp().

Referenced by v_Execute().

◆ EV_sort()

void Nektar::SolverUtils::DriverModifiedArnoldi::EV_sort	(	Array< OneD, NekDouble > &	evec,
		Array< OneD, NekDouble > &	wr,
		Array< OneD, NekDouble > &	wi,
		Array< OneD, NekDouble > &	test,
		const int	dim
	)

private

Sorts a sequence of eigenvectors/eigenvalues by magnitude.

Sorts the computed eigenvalues by smallest residual first.

Definition at line 520 of file DriverModifiedArnoldi.cpp.

 {
     Array<OneD, NekDouble> z_tmp(dim,0.0);
     NekDouble wr_tmp, wi_tmp, te_tmp;
     for (int j = 1; j < dim; ++j)
     {
         wr_tmp = wr[j];
         wi_tmp = wi[j];
         te_tmp = test[j];
         Vmath::Vcopy(dim, &evec[0] + j*dim, 1, &z_tmp[0], 1);
         int i = j - 1;
         while (i >= 0 && test[i] > te_tmp)
         {
             wr[i+1] = wr[i];
             wi[i+1] = wi[i];
             test[i+1] = test[i];
             Vmath::Vcopy(dim, &evec[0] + i*dim, 1, &evec[0] + (i+1)*dim, 1);
             i--;
         }
         wr[i+1] = wr_tmp;
         wi[i+1] = wi_tmp;
         test[i+1] = te_tmp;
         Vmath::Vcopy(dim, &z_tmp[0], 1, &evec[0] + (i+1)*dim, 1);
     }
 }

References Vmath::Vcopy().

Referenced by EV_test().

◆ EV_test()

int Nektar::SolverUtils::DriverModifiedArnoldi::EV_test	(	const int	itrn,
		const int	kdim,
		Array< OneD, NekDouble > &	zvec,
		Array< OneD, NekDouble > &	wr,
		Array< OneD, NekDouble > &	wi,
		const NekDouble	resnorm,
		int	nvec,
		std::ofstream &	evlout,
		NekDouble &	resid0
	)

private

Tests for convergence of eigenvalues of H.

Check for convergence of the residuals of the eigenvalues of H.

Definition at line 454 of file DriverModifiedArnoldi.cpp.

 {
     int idone = 0;
     // NekDouble period = 0.1;
  
     Array<OneD, NekDouble> resid(kdim);
     for (int i = 0; i < kdim; ++i)
     {
         NekDouble tmp = std::sqrt(Vmath::Dot(kdim, &zvec[0] + i*kdim, 1,
                                              &zvec[0] + i*kdim, 1));
         resid[i] = resnorm * std::fabs(zvec[kdim - 1 + i*kdim]) / tmp;
         if (wi[i] < 0.0)
         {
             resid[i-1] = resid[i] = hypot(resid[i-1], resid[i]);
         }
     }
  
     EV_sort(zvec, wr, wi, resid, kdim);
  
     while (nvec <= kdim && resid[nvec-1] < m_evtol)
     {
         idone = nvec;
         ++nvec;
     }
     nvec -= (idone > 0);
  
     if (m_comm->GetRank() == 0)
     {
         evlout << "-- Iteration = " << itrn << ", H(k+1, k) = "
                << resnorm << endl;
         evlout.precision(4);
         evlout.setf(ios::scientific, ios::floatfield);
         if(m_timeSteppingAlgorithm)
         {
             evlout << "        Magnitude   Angle       Growth      "
                    << "Frequency   Residual" << endl;
         }
         else
         {
             evlout << "        Real        Imaginary   inverse real  "
                    << "inverse imag  Residual" << endl;
         }
  
         for (int i = 0; i < kdim; i++)
         {
             WriteEvs(evlout,i,wr[i],wi[i],resid[i]);
         }
     }
  
     resid0 = resid[nvec-1];
     return idone;
 }

References Vmath::Dot(), EV_sort(), Nektar::SolverUtils::Driver::m_comm, Nektar::SolverUtils::DriverArnoldi::m_evtol, Nektar::SolverUtils::DriverArnoldi::m_timeSteppingAlgorithm, tinysimd::sqrt(), and Nektar::SolverUtils::DriverArnoldi::WriteEvs().

Referenced by v_Execute().

◆ EV_update()

void Nektar::SolverUtils::DriverModifiedArnoldi::EV_update	(	Array< OneD, NekDouble > &	src,
		Array< OneD, NekDouble > &	tgt
	)

private

Generates a new vector in the sequence by applying the linear operator.

Definition at line 349 of file DriverModifiedArnoldi.cpp.

 {
     // Copy starting vector into first sequence element.
     CopyArnoldiArrayToField(src);
     m_equ[0]->TransCoeffToPhys();
  
     m_equ[0]->SetTime(0.);
     m_equ[0]->DoSolve();
  
     if(m_EvolutionOperator == eTransientGrowth)
     {
         Array<OneD, MultiRegions::ExpListSharedPtr> fields;
         fields = m_equ[0]->UpdateFields();
  
         //start Adjoint with latest fields of direct
         CopyFwdToAdj();
         m_equ[1]->TransCoeffToPhys();
  
         m_equ[1]->SetTime(0.);
         m_equ[1]->DoSolve();
     }
  
     // Copy starting vector into first sequence element.
     CopyFieldToArnoldiArray(tgt);
 }

References Nektar::SolverUtils::DriverArnoldi::CopyArnoldiArrayToField(), Nektar::SolverUtils::DriverArnoldi::CopyFieldToArnoldiArray(), Nektar::SolverUtils::DriverArnoldi::CopyFwdToAdj(), Nektar::SolverUtils::eTransientGrowth, Nektar::SolverUtils::Driver::m_equ, and Nektar::SolverUtils::Driver::m_EvolutionOperator.

Referenced by v_Execute().

◆ v_Execute()

void Nektar::SolverUtils::DriverModifiedArnoldi::v_Execute ( std::ostream & out = std::cout )

protectedvirtual

Virtual function for solve implementation.

Implements Nektar::SolverUtils::Driver.

Reimplemented in Nektar::SolverUtils::DriverSteadyState.

Definition at line 106 of file DriverModifiedArnoldi.cpp.

 {
     int i               = 0;
     int j               = 0;
     int nq              = m_equ[0]->UpdateFields()[0]->GetNcoeffs();
     int ntot            = m_nfields*nq;
     int converged       = 0;
     NekDouble resnorm   = 0.0;
     ofstream evlout;
     std::string evlFile = m_session->GetSessionName() + ".evl";
  
     if (m_comm->GetRank() == 0)
     {
         evlout.open(evlFile.c_str());
     }
  
     // Allocate memory
     Array<OneD, NekDouble> alpha = Array<OneD, NekDouble> (m_kdim+1,      0.0);
     Array<OneD, NekDouble> wr    = Array<OneD, NekDouble> (m_kdim,        0.0);
     Array<OneD, NekDouble> wi    = Array<OneD, NekDouble> (m_kdim,        0.0);
     Array<OneD, NekDouble> zvec  = Array<OneD, NekDouble> (m_kdim*m_kdim, 0.0);
  
     Array<OneD, Array<OneD, NekDouble> > Kseq
             = Array<OneD, Array<OneD, NekDouble> > (m_kdim + 1);
     Array<OneD, Array<OneD, NekDouble> > Kseqcopy
             = Array<OneD, Array<OneD, NekDouble> > (m_kdim + 1);
     Array<OneD, Array<OneD, NekDouble> > Tseq
             = Array<OneD, Array<OneD, NekDouble> > (m_kdim + 1);
     for (i = 0; i < m_kdim + 1; ++i)
     {
         Kseq[i] = Array<OneD, NekDouble>(ntot, 0.0);
         if (m_useMask)
         {
             Kseqcopy[i] = Array<OneD, NekDouble>(ntot, 0.0);
         }
         else
         {
             Kseqcopy[i] = Kseq[i];
         }
         Tseq[i] = Array<OneD, NekDouble>(ntot, 0.0);
     }
  
     // Copy starting vector into second sequence element (temporary).
     if(m_session->DefinesFunction("InitialConditions"))
     {
         if (m_comm->GetRank() == 0)
         {
             out << "\tInital vector       : specified in input file " << endl;
         }
         m_equ[0]->SetInitialConditions(0.0,false);
  
         CopyFieldToArnoldiArray(Kseq[1]);
     }
     else
     {
         if (m_comm->GetRank() == 0)
         {
             out << "\tInital vector       : random  " << endl;
         }
  
         NekDouble eps=0.0001;
         Vmath::FillWhiteNoise(ntot, eps , &Kseq[1][0], 1);
         if (m_useMask)
         {
             Vmath::Vmul(ntot, Kseq[1], 1, GetMaskCoeff(), 1, Kseq[1], 1);
         }
     }
  
     // Perform one iteration to enforce boundary conditions.
     // Set this as the initial value in the sequence.
     EV_update(Kseq[1], Kseq[0]);
     if (m_comm->GetRank() == 0)
     {
         out << "Iteration: " << 0 <<  endl;
     }
  
     // Normalise first vector in sequence
     if (m_useMask)
     {
         Vmath::Vmul(ntot, Kseq[0], 1, GetMaskCoeff(), 1, Kseqcopy[0], 1);
     }
     alpha[0] = Blas::Ddot(ntot, &Kseqcopy[0][0], 1, &Kseqcopy[0][0], 1);
     m_comm->AllReduce(alpha[0], Nektar::LibUtilities::ReduceSum);
     alpha[0] = std::sqrt(alpha[0]);
     Vmath::Smul(ntot, 1.0/alpha[0], Kseq[0], 1, Kseq[0], 1);
  
     // Fill initial krylov sequence
     NekDouble resid0;
     for (i = 1; !converged && i <= m_kdim; ++i)
     {
         // Compute next vector
         EV_update(Kseq[i-1], Kseq[i]);
  
         // Normalise
         if (m_useMask)
         {
             Vmath::Vmul(ntot, Kseq[i], 1, GetMaskCoeff(), 1, Kseqcopy[i], 1);
         }
         alpha[i] = Blas::Ddot(ntot, &Kseqcopy[i][0], 1, &Kseqcopy[i][0], 1);
         m_comm->AllReduce(alpha[i], Nektar::LibUtilities::ReduceSum);
         alpha[i] = std::sqrt(alpha[i]);
  
         //alpha[i] = std::sqrt(alpha[i]);
         Vmath::Smul(ntot, 1.0/alpha[i], Kseq[i], 1, Kseq[i], 1);
  
         // Copy Krylov sequence into temporary storage
         for (int k = 0; k < i + 1; ++k)
         {
             if (m_useMask)
             {
                 Vmath::Vmul(ntot, Kseq[k], 1, GetMaskCoeff(), 1, Tseq[k], 1);
                 Vmath::Vcopy(ntot, Kseq[k], 1, Kseqcopy[k], 1);
             }
             else
             {
                 Vmath::Vcopy(ntot, Kseq[k], 1, Tseq[k], 1);;
             }
         }
  
         // Generate Hessenberg matrix and compute eigenvalues of it.
         EV_small(Tseq, Kseqcopy, ntot, alpha, i, zvec, wr, wi, resnorm);
  
         // Test for convergence.
         converged = EV_test(i, i, zvec, wr, wi, resnorm,
             std::min(i, m_nvec), evlout, resid0);
         if ( i >= m_nvec)
         {
             converged = max (converged, 0);
         }
         else
         {
             converged = 0;
         }
  
         if (m_comm->GetRank() == 0)
         {
             out << "Iteration: " <<  i << " (residual : " << resid0
             << ")" <<endl;
         }
     }
  
     // Continue with full sequence
     if (!converged)
     {
         for (i = m_kdim + 1; !converged && i <= m_nits; ++i)
         {
             // Shift all the vectors in the sequence.
             // First vector is removed.
             for (int j = 1; j <= m_kdim; ++j)
             {
                 alpha[j-1] = alpha[j];
                 Vmath::Vcopy(ntot, Kseq[j], 1, Kseq[j-1], 1);
             }
  
             // Compute next vector
             EV_update(Kseq[m_kdim - 1], Kseq[m_kdim]);
  
             // Compute new scale factor
             if (m_useMask)
             {
                 Vmath::Vmul(ntot, Kseq[m_kdim], 1, GetMaskCoeff(), 1,
                                   Kseqcopy[m_kdim], 1);
             }
             alpha[m_kdim] = Blas::Ddot(ntot, &Kseqcopy[m_kdim][0], 1,
                                              &Kseqcopy[m_kdim][0], 1);
             m_comm->AllReduce(alpha[m_kdim], Nektar::LibUtilities::ReduceSum);
             alpha[m_kdim] = std::sqrt(alpha[m_kdim]);
             Vmath::Smul(ntot, 1.0/alpha[m_kdim], Kseq[m_kdim], 1,
                                                  Kseq[m_kdim], 1);
  
             // Copy Krylov sequence into temporary storage
             for (int k = 0; k < m_kdim + 1; ++k)
             {
                 if (m_useMask)
                 {
                     Vmath::Vmul(ntot, Kseq[k], 1, GetMaskCoeff(), 1, Tseq[k], 1);
                     Vmath::Vcopy(ntot, Kseq[k], 1, Kseqcopy[k], 1);
                 }
                 else
                 {
                     Vmath::Vcopy(ntot, Kseq[k], 1, Tseq[k], 1);;
                 }
             }
  
             // Generate Hessenberg matrix and compute eigenvalues of it
             EV_small(Tseq, Kseqcopy, ntot, alpha, m_kdim, zvec, wr, wi, resnorm);
  
             // Test for convergence.
             converged = EV_test(i, m_kdim, zvec, wr, wi, resnorm,
                                 m_nvec, evlout, resid0);
  
             if (m_comm->GetRank() == 0)
             {
                 out << "Iteration: " <<  i << " (residual : "
                     << resid0 << ")" <<endl;
             }
         }
     }
  
     m_equ[0]->Output();
  
     // Evaluate and output computation time and solution accuracy.
     // The specific format of the error output is essential for the
     // regression tests to work.
     // Evaluate L2 Error
     for(j = 0; j < m_equ[0]->GetNvariables(); ++j)
     {
         NekDouble vL2Error = m_equ[0]->L2Error(j,false);
         NekDouble vLinfError = m_equ[0]->LinfError(j);
         if (m_comm->GetRank() == 0)
         {
             out << "L 2 error (variable " << m_equ[0]->GetVariable(j)
             << ") : " << vL2Error << endl;
             out << "L inf error (variable " << m_equ[0]->GetVariable(j)
             << ") : " << vLinfError << endl;
         }
     }
  
     // Process eigenvectors and write out.
     m_nvec = converged;
     EV_post(Tseq, Kseqcopy, ntot, min(--i, m_kdim), m_nvec, zvec, wr, wi,
             converged);
  
     WARNINGL0(m_imagShift == 0,"Complex Shift applied. "
               "Need to implement Ritz re-evaluation of"
               "eigenvalue. Only one half of complex "
               "value will be correct");
  
     // store eigenvalues so they can be accessed from driver class
     m_real_evl = wr;
     m_imag_evl = wi;
  
     // Close the runtime info file.
     if (m_comm->GetRank() == 0)
     {
         evlout.close();
     }
 }

Referenced by Nektar::SolverUtils::DriverSteadyState::v_Execute().

◆ v_InitObject()

void Nektar::SolverUtils::DriverModifiedArnoldi::v_InitObject ( std::ostream & out = std::cout )

protectedvirtual

Virtual function for initialisation implementation.

Reimplemented from Nektar::SolverUtils::DriverArnoldi.

Reimplemented in Nektar::SolverUtils::DriverSteadyState.

Definition at line 78 of file DriverModifiedArnoldi.cpp.

 {
     DriverArnoldi::v_InitObject(out);
  
     m_equ[0]->PrintSummary(out);
  
     // Print session parameters
     if (m_comm->GetRank() == 0)
     {
         out << "\tArnoldi solver type    : Modified Arnoldi" << endl;
     }
  
     DriverArnoldi::ArnoldiSummary(out);
  
     for( int i = 0; i < m_nequ; ++i)
     {
         m_equ[i]->DoInitialise();
     }
  
     //FwdTrans Initial conditions to be in Coefficient Space
     m_equ[m_nequ-1] ->TransPhysToCoeff();
  
 }

References Nektar::SolverUtils::DriverArnoldi::ArnoldiSummary(), Nektar::SolverUtils::Driver::m_comm, Nektar::SolverUtils::Driver::m_equ, Nektar::SolverUtils::Driver::m_nequ, and Nektar::SolverUtils::DriverArnoldi::v_InitObject().

Referenced by Nektar::SolverUtils::DriverSteadyState::v_InitObject().

Friends And Related Function Documentation

◆ MemoryManager< DriverModifiedArnoldi >

friend class MemoryManager< DriverModifiedArnoldi >

friend

Definition at line 1 of file DriverModifiedArnoldi.h.

Member Data Documentation

◆ className

string Nektar::SolverUtils::DriverModifiedArnoldi::className

static

Initial value:

=
        GetDriverFactory().RegisterCreatorFunction("ModifiedArnoldi",
                                    DriverModifiedArnoldi::create)

Name of the class.

Definition at line 63 of file DriverModifiedArnoldi.h.

◆ driverLookupId

string Nektar::SolverUtils::DriverModifiedArnoldi::driverLookupId

staticprivate

Initial value:

=
        LibUtilities::SessionReader::RegisterEnumValue("Driver",
                                    "ModifiedArnoldi",0)

Definition at line 135 of file DriverModifiedArnoldi.h.

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Private Member Functions

Static Private Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ DriverModifiedArnoldi()

◆ ~DriverModifiedArnoldi()

Member Function Documentation

◆ create()

◆ EV_big()

◆ EV_post()

◆ EV_small()

◆ EV_sort()

◆ EV_test()

◆ EV_update()

◆ v_Execute()

◆ v_InitObject()

Friends And Related Function Documentation

◆ MemoryManager< DriverModifiedArnoldi >

Member Data Documentation

◆ className

◆ driverLookupId