Detailed Description

Backward differentiation formula.

Definition at line 452 of file TimeDiscretization.h.

#include <TimeDiscretization.h>

Inheritance diagram for NumLib::BackwardDifferentiationFormula:

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Collaboration diagram for NumLib::BackwardDifferentiationFormula:

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Public Member Functions
	BackwardDifferentiationFormula (const unsigned num_steps)

	~BackwardDifferentiationFormula () override

void	setInitialState (const double t0, GlobalVector const &x0) override
	Sets the initial condition. More...

double	getRelativeChangeFromPreviousTimestep (GlobalVector const &x, MathLib::VecNormType norm_type) override

void	pushState (const double, GlobalVector const &x, InternalMatrixStorage const &) override

void	popState (GlobalVector &x) override

void	nextTimestep (const double t, const double delta_t) override

double	getCurrentTime () const override

double	getNewXWeight () const override
	Returns $\alpha = \partial \hat x / \partial x_N$ . More...

void	getWeightedOldX (GlobalVector &y) const override
	Returns . More...

Public Member Functions inherited from NumLib::TimeDiscretization
	TimeDiscretization ()=default

void	getXdot (GlobalVector const &x_at_new_timestep, GlobalVector &xdot) const

virtual	~TimeDiscretization ()=default

virtual bool	isLinearTimeDisc () const

virtual double	getDxDx () const

virtual GlobalVector const &	getCurrentX (GlobalVector const &x_at_new_timestep) const

virtual bool	needsPreload () const

Private Member Functions
std::size_t	eff_num_steps () const

Private Attributes
const unsigned	_num_steps
	The order of the BDF method. More...

double	_t
	More...

double	_delta_t
	the timestep size More...

std::vector< GlobalVector * >	_xs_old
	solutions from the preceding timesteps More...

unsigned	_offset = 0
	allows treating `_xs_old` as circular buffer More...

Additional Inherited Members
Protected Member Functions inherited from NumLib::TimeDiscretization
double	computeRelativeChangeFromPreviousTimestep (GlobalVector const &x, GlobalVector const &x_old, MathLib::VecNormType norm_type)

Protected Attributes inherited from NumLib::TimeDiscretization
std::unique_ptr< GlobalVector >	_dx
	Used to store $u_{n+1}-u_{n}$ . More...

Constructor & Destructor Documentation

◆ BackwardDifferentiationFormula()

NumLib::BackwardDifferentiationFormula::BackwardDifferentiationFormula ( const unsigned num_steps )

inlineexplicit

Constructs a new instance.

Parameters

num_steps The order of the BDF to be used (= the number of timesteps kept in the internal history buffer). Valid range: 1 through 6.

Note: Until a sufficient number of timesteps has been computed to be able to use the full num_steps order BDF, lower order BDFs are used in the first timesteps.

Definition at line 467 of file TimeDiscretization.h.

         : _num_steps(num_steps)
     {
         assert(1 <= num_steps && num_steps <= 6);
         _xs_old.reserve(num_steps);
     }

◆ ~BackwardDifferentiationFormula()

NumLib::BackwardDifferentiationFormula::~BackwardDifferentiationFormula ( )

inlineoverride

Definition at line 474 of file TimeDiscretization.h.

References NumLib::GlobalVectorProvider::provider, and NumLib::VectorProvider::releaseVector().

     {
         for (auto* x : _xs_old)
             NumLib::GlobalVectorProvider::provider.releaseVector(*x);
     }

Member Function Documentation

◆ eff_num_steps()

std::size_t NumLib::BackwardDifferentiationFormula::eff_num_steps ( ) const

inlineprivate

Definition at line 511 of file TimeDiscretization.h.

511 { return _xs_old.size(); }

NumLib::BackwardDifferentiationFormula::_xs_old

std::vector< GlobalVector * > _xs_old

solutions from the preceding timesteps

Definition: TimeDiscretization.h:516

◆ getCurrentTime()

double NumLib::BackwardDifferentiationFormula::getCurrentTime ( ) const

inlineoverridevirtual

Returns $ t_C $ , i.e., the time at which the equation will be assembled.

Implements NumLib::TimeDiscretization.

Definition at line 504 of file TimeDiscretization.h.

504 { return _t; }

NumLib::BackwardDifferentiationFormula::_t

double _t

Definition: TimeDiscretization.h:513

◆ getNewXWeight()

double NumLib::BackwardDifferentiationFormula::getNewXWeight ( ) const

overridevirtual

Returns $\alpha = \partial \hat x / \partial x_N$ .

Implements NumLib::TimeDiscretization.

Definition at line 112 of file TimeDiscretization.cpp.

References NumLib::detail::BDF_Coeffs.

 {
     auto const k = eff_num_steps();
     return detail::BDF_Coeffs[k - 1][0] / _delta_t;
 }

◆ getRelativeChangeFromPreviousTimestep()

double NumLib::BackwardDifferentiationFormula::getRelativeChangeFromPreviousTimestep	(	GlobalVector const &	x,
		MathLib::VecNormType	norm_type
	)

overridevirtual

Get the relative change of solutions between two successive time steps by $e_n = \|u^{n+1}-u^{n}\|/\|u^{n+1}\|$ .

Parameters

x	The solution at the current timestep.
norm_type	The type of global vector norm.

Implements NumLib::TimeDiscretization.

Definition at line 68 of file TimeDiscretization.cpp.

References NumLib::TimeDiscretization::computeRelativeChangeFromPreviousTimestep().

 {
     return computeRelativeChangeFromPreviousTimestep(
         x, *_xs_old[_offset], norm_type);
 }

◆ getWeightedOldX()

void NumLib::BackwardDifferentiationFormula::getWeightedOldX ( GlobalVector & y ) const

overridevirtual

Returns $ x_O $ .

Implements NumLib::TimeDiscretization.

Definition at line 118 of file TimeDiscretization.cpp.

References MathLib::LinAlg::axpy(), NumLib::detail::BDF_Coeffs, MathLib::LinAlg::copy(), and MathLib::LinAlg::scale().

 {
     namespace LinAlg = MathLib::LinAlg;
 
     auto const k = eff_num_steps();
     auto const* const BDFk = detail::BDF_Coeffs[k - 1];
 
     // compute linear combination \sum_{i=0}^{k-1} BDFk_{k-i} \cdot x_{n+i}
     LinAlg::copy(*_xs_old[_offset], y);  // _xs_old[offset] = x_n
     LinAlg::scale(y, BDFk[k]);
 
     for (unsigned i = 1; i < k; ++i)
     {
         auto const off = (_offset + i) % k;
         LinAlg::axpy(y, BDFk[k - i], *_xs_old[off]);
     }
 
     LinAlg::scale(y, 1.0 / _delta_t);
 }

◆ nextTimestep()

void NumLib::BackwardDifferentiationFormula::nextTimestep	(	const double	t,
		const double	delta_t
	)

inlineoverridevirtual

Indicate that the computation of a new timestep is being started now.

Warning: Currently changing timestep sizes are not supported. Thus, delta_t must not change throughout the entire time integration process! This is not checked by this code!

Implements NumLib::TimeDiscretization.

Definition at line 498 of file TimeDiscretization.h.

     {
         _t = t;
         _delta_t = delta_t;
     }

◆ popState()

void NumLib::BackwardDifferentiationFormula::popState ( GlobalVector & x )

inlineoverridevirtual

Restores the given vector x to its old value. Used only for repeating of the time step with new time step size when the current time step is rejected. The restored x is only used as an initial guess for linear solver in the first Picard nonlinear iteration.

Parameters

x	The solution at the current time step, which is going to be reset to its previous value.

Implements NumLib::TimeDiscretization.

Definition at line 493 of file TimeDiscretization.h.

References MathLib::LinAlg::copy().

     {
         MathLib::LinAlg::copy(*_xs_old[_xs_old.size()-1], x);
     }

◆ pushState()

void NumLib::BackwardDifferentiationFormula::pushState	(	const double	t,
		GlobalVector const &	x,
		InternalMatrixStorage const &	strg
	)

overridevirtual

Indicate that the current timestep is done and that you will proceed to the next one.

Warning: Do not use this method for setting the initial condition, rather use setInitialState()!

Parameters

t	The current timestep.
x	The solution at the current timestep.
strg	Trigger storing some internal state. Currently only used by the CrankNicolson scheme.

Implements NumLib::TimeDiscretization.

Definition at line 75 of file TimeDiscretization.cpp.

References MathLib::LinAlg::copy(), and NumLib::GlobalVectorProvider::provider.

 {
     namespace LinAlg = MathLib::LinAlg;
     // TODO use boost circular buffer?
 
     // until _xs_old is filled, lower-order BDF formulas are used.
     if (_xs_old.size() < _num_steps)
     {
         _xs_old.push_back(&NumLib::GlobalVectorProvider::provider.getVector(x));
     }
     else
     {
         LinAlg::copy(x, *_xs_old[_offset]);
         _offset =
             (_offset + 1) % _num_steps;  // treat _xs_old as a circular buffer
     }
 }

◆ setInitialState()

void NumLib::BackwardDifferentiationFormula::setInitialState	(	const double	t0,
		GlobalVector const &	x0
	)

inlineoverridevirtual

Sets the initial condition.

Implements NumLib::TimeDiscretization.

Definition at line 480 of file TimeDiscretization.h.

References NumLib::GlobalVectorProvider::provider.

     {
         _t = t0;
         _xs_old.push_back(
             &NumLib::GlobalVectorProvider::provider.getVector(x0));
     }

Member Data Documentation

◆ _delta_t

double NumLib::BackwardDifferentiationFormula::_delta_t

private

the timestep size

Definition at line 514 of file TimeDiscretization.h.

◆ _num_steps

const unsigned NumLib::BackwardDifferentiationFormula::_num_steps

private

The order of the BDF method.

Definition at line 512 of file TimeDiscretization.h.

◆ _offset

unsigned NumLib::BackwardDifferentiationFormula::_offset = 0

private

allows treating _xs_old as circular buffer

Definition at line 517 of file TimeDiscretization.h.

◆ _t

double NumLib::BackwardDifferentiationFormula::_t

private

$ t_C $

Definition at line 513 of file TimeDiscretization.h.

◆ _xs_old

std::vector<GlobalVector*> NumLib::BackwardDifferentiationFormula::_xs_old

private

solutions from the preceding timesteps

Definition at line 516 of file TimeDiscretization.h.

The documentation for this class was generated from the following files:

NumLib/ODESolver/TimeDiscretization.h
NumLib/ODESolver/TimeDiscretization.cpp

Detailed Description

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ BackwardDifferentiationFormula()

◆ ~BackwardDifferentiationFormula()

Member Function Documentation

◆ eff_num_steps()

◆ getCurrentTime()

◆ getNewXWeight()

◆ getRelativeChangeFromPreviousTimestep()

◆ getWeightedOldX()

◆ nextTimestep()

◆ popState()

◆ pushState()

◆ setInitialState()

Member Data Documentation

◆ _delta_t

◆ _num_steps

◆ _offset

◆ _t

◆ _xs_old