BDF integration scheme (for dynamic problems) More...

#include <residual_based_bdf_scheme.h>

Inheritance diagram for Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >:

Collaboration diagram for Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >:

Classes
struct	GeneralVectors

Public Member Functions
Life Cycle
	ResidualBasedBDFScheme (const std::size_t Order=2)
	Constructor. The BDF method. More...

	ResidualBasedBDFScheme (ResidualBasedBDFScheme &rOther)

BaseTypePointer	Clone () override

	~ResidualBasedBDFScheme () override

Operations
void	Update (ModelPart &rModelPart, DofsArrayType &rDofSet, TSystemMatrixType &rA, TSystemVectorType &rDx, TSystemVectorType &rb) override
	Performing the update of the solution. More...

void	Predict (ModelPart &rModelPart, DofsArrayType &rDofSet, TSystemMatrixType &rA, TSystemVectorType &rDx, TSystemVectorType &rb) override
	Performing the prediction of the solution. More...

void	InitializeSolutionStep (ModelPart &rModelPart, TSystemMatrixType &rA, TSystemVectorType &rDx, TSystemVectorType &rb) override
	It initializes time step solution. Only for reasons if the time step solution is restarted. More...

int	Check (const ModelPart &rModelPart) const override
	This function is designed to be called once to perform all the checks needed on the input provided. More...

void	Clear () override
	Free memory allocated by this class. More...

Input and output
Parameters	GetDefaultParameters () const override
	This method provides the defaults parameters to avoid conflicts between the different constructors. More...

std::string	Info () const override
	Turn back information as a string. More...

void	PrintInfo (std::ostream &rOStream) const override
	Print information about this object. More...

void	PrintData (std::ostream &rOStream) const override
	Print object's data. More...

Public Member Functions inherited from Kratos::ResidualBasedImplicitTimeScheme< TSparseSpace, TDenseSpace >
	ResidualBasedImplicitTimeScheme ()

	ResidualBasedImplicitTimeScheme (Parameters ThisParameters)
	Constructor. The implicit method method. More...

	ResidualBasedImplicitTimeScheme (ResidualBasedImplicitTimeScheme &rOther)

BaseType::Pointer	Clone () override

	~ResidualBasedImplicitTimeScheme () override

void	CalculateSystemContributions (Element &rCurrentElement, LocalSystemMatrixType &rLHSContribution, LocalSystemVectorType &rRHSContribution, Element::EquationIdVectorType &rEquationId, const ProcessInfo &rCurrentProcessInfo) override
	This function is designed to be called in the builder and solver to introduce the selected time integration scheme. More...

void	CalculateRHSContribution (Element &rCurrentElement, LocalSystemVectorType &rRHSContribution, Element::EquationIdVectorType &rEquationId, const ProcessInfo &rCurrentProcessInfo) override
	This function is designed to calculate just the RHS contribution. More...

void	CalculateSystemContributions (Condition &rCurrentCondition, LocalSystemMatrixType &rLHSContribution, LocalSystemVectorType &rRHSContribution, Element::EquationIdVectorType &rEquationId, const ProcessInfo &rCurrentProcessInfo) override
	Functions totally analogous to the precedent but applied to the "condition" objects. More...

void	CalculateRHSContribution (Condition &rCurrentCondition, LocalSystemVectorType &rRHSContribution, Element::EquationIdVectorType &rEquationId, const ProcessInfo &rCurrentProcessInfo) override
	Functions that calculates the RHS of a "condition" object. More...

void	InitializeSolutionStep (ModelPart &rModelPart, TSystemMatrixType &rA, TSystemVectorType &rDx, TSystemVectorType &rb) override
	It initializes time step solution. Only for reasons if the time step solution is restarted. More...

int	Check (const ModelPart &rModelPart) const override
	This function is designed to be called once to perform all the checks needed on the input provided. More...

Parameters	GetDefaultParameters () const override
	This method provides the defaults parameters to avoid conflicts between the different constructors. More...

std::string	Info () const override
	Turn back information as a string. More...

void	PrintInfo (std::ostream &rOStream) const override
	Print information about this object. More...

void	PrintData (std::ostream &rOStream) const override
	Print object's data. More...

	KRATOS_CLASS_POINTER_DEFINITION (ResidualBasedImplicitTimeScheme)

Public Member Functions inherited from Kratos::Scheme< TSparseSpace, TDenseSpace >
	Scheme ()
	Default Constructor. More...

	Scheme (Parameters ThisParameters)
	Constructor with Parameters. More...

	Scheme (Scheme &rOther)

virtual	~Scheme ()

	KRATOS_CLASS_POINTER_DEFINITION (Scheme)
	Pointer definition of Scheme. More...

virtual ClassType::Pointer	Create (Parameters ThisParameters) const
	Create method. More...

virtual void	Initialize (ModelPart &rModelPart)
	This is the place to initialize the Scheme. More...

bool	SchemeIsInitialized ()
	This method returns if the scheme is initialized. More...

void	SetSchemeIsInitialized (bool SchemeIsInitializedFlag=true)
	This method sets if the elements have been initialized or not (true by default) More...

bool	ElementsAreInitialized ()
	This method returns if the elements are initialized. More...

void	SetElementsAreInitialized (bool ElementsAreInitializedFlag=true)
	This method sets if the elements have been initialized or not (true by default) More...

bool	ConditionsAreInitialized ()
	This method returns if the conditions are initialized. More...

void	SetConditionsAreInitialized (bool ConditionsAreInitializedFlag=true)
	This method sets if the conditions have been initialized or not (true by default) More...

virtual void	InitializeElements (ModelPart &rModelPart)
	This is the place to initialize the elements. More...

virtual void	InitializeConditions (ModelPart &rModelPart)
	This is the place to initialize the conditions. More...

virtual void	FinalizeSolutionStep (ModelPart &rModelPart, TSystemMatrixType &A, TSystemVectorType &Dx, TSystemVectorType &b)
	Function called once at the end of a solution step, after convergence is reached if an iterative process is needed. More...

virtual void	InitializeNonLinIteration (ModelPart &rModelPart, TSystemMatrixType &A, TSystemVectorType &Dx, TSystemVectorType &b)
	unction to be called when it is needed to initialize an iteration. It is designed to be called at the beginning of each non linear iteration More...

virtual void	FinalizeNonLinIteration (ModelPart &rModelPart, TSystemMatrixType &A, TSystemVectorType &Dx, TSystemVectorType &b)
	Function to be called when it is needed to finalize an iteration. It is designed to be called at the end of each non linear iteration. More...

virtual void	CalculateOutputData (ModelPart &rModelPart, DofsArrayType &rDofSet, TSystemMatrixType &A, TSystemVectorType &Dx, TSystemVectorType &b)
	Functions to be called to prepare the data needed for the output of results. More...

virtual void	CleanOutputData ()
	Functions that cleans the results data. More...

virtual void	Clean ()
	This function is intended to be called at the end of the solution step to clean up memory storage not needed after the end of the solution step. More...

virtual int	Check (ModelPart &rModelPart)

virtual void	CalculateLHSContribution (Element &rElement, LocalSystemMatrixType &LHS_Contribution, Element::EquationIdVectorType &rEquationIdVector, const ProcessInfo &rCurrentProcessInfo)
	This function is designed to calculate just the LHS contribution. More...

virtual void	CalculateLHSContribution (Condition &rCondition, LocalSystemMatrixType &LHS_Contribution, Element::EquationIdVectorType &rEquationIdVector, const ProcessInfo &rCurrentProcessInfo)
	Functions totally analogous to the precedent but applied to the "condition" objects. More...

virtual void	EquationId (const Element &rElement, Element::EquationIdVectorType &rEquationId, const ProcessInfo &rCurrentProcessInfo)
	This method gets the eqaution id corresponding to the current element. More...

virtual void	EquationId (const Condition &rCondition, Element::EquationIdVectorType &rEquationId, const ProcessInfo &rCurrentProcessInfo)
	Functions totally analogous to the precedent but applied to the "condition" objects. More...

virtual void	GetDofList (const Element &rElement, Element::DofsVectorType &rDofList, const ProcessInfo &rCurrentProcessInfo)
	Function that returns the list of Degrees of freedom to be assembled in the system for a Given element. More...

virtual void	GetDofList (const Condition &rCondition, Element::DofsVectorType &rDofList, const ProcessInfo &rCurrentProcessInfo)
	Function that returns the list of Degrees of freedom to be assembled in the system for a Given condition. More...

Protected Member Functions
Protected Operations
void	UpdateDerivatives (ModelPart &rModelPart, DofsArrayType &rDofSet, TSystemMatrixType &rA, TSystemVectorType &rDx, TSystemVectorType &rb)
	Performing the update of the derivatives. More...

virtual void	UpdateFirstDerivative (NodesArrayType::iterator itNode)
	Updating first time derivative (velocity) More...

virtual void	UpdateSecondDerivative (NodesArrayType::iterator itNode)
	Updating second time derivative (acceleration) More...

void	AddDynamicsToLHS (LocalSystemMatrixType &rLHS_Contribution, LocalSystemMatrixType &rD, LocalSystemMatrixType &rM, const ProcessInfo &rCurrentProcessInfo) override
	It adds the dynamic LHS contribution of the elements. More...

template<class TObjectType >
void	TemplateAddDynamicsToRHS (TObjectType &rObject, LocalSystemVectorType &rRHS_Contribution, LocalSystemMatrixType &rD, LocalSystemMatrixType &rM, const ProcessInfo &rCurrentProcessInfo)
	It adds the dynamic RHS contribution of the objects. More...

void	AddDynamicsToRHS (Element &rElement, LocalSystemVectorType &rRHS_Contribution, LocalSystemMatrixType &rD, LocalSystemMatrixType &rM, const ProcessInfo &rCurrentProcessInfo) override
	It adds the dynamic RHS contribution of the elements. More...

void	AddDynamicsToRHS (Condition &rCondition, LocalSystemVectorType &rRHS_Contribution, LocalSystemMatrixType &rD, LocalSystemMatrixType &rM, const ProcessInfo &rCurrentProcessInfo) override
	It adds the dynamic RHS contribution of the condition. More...

Protected Operations
Protected Member Functions inherited from Kratos::Scheme< TSparseSpace, TDenseSpace >
virtual Parameters	ValidateAndAssignParameters (Parameters ThisParameters, const Parameters DefaultParameters) const
	This method validate and assign default parameters. More...

virtual void	AssignSettings (const Parameters ThisParameters)
	This method assigns settings to member variables. More...

Protected Attributes
Protected member Variables
const std::size_t	mOrder

Vector	mBDF
	The integration order. More...

GeneralVectors	mVector
	The BDF coefficients. More...

Kratos::unique_ptr< TimeDiscretization::BDF >	mpBDFUtility
	The structure containing the derivatives. More...

Protected Attributes inherited from Kratos::ResidualBasedImplicitTimeScheme< TSparseSpace, TDenseSpace >
GeneralMatrices	mMatrix

Protected Attributes inherited from Kratos::Scheme< TSparseSpace, TDenseSpace >
bool	mSchemeIsInitialized

bool	mElementsAreInitialized
	Flag to be used in controlling if the Scheme has been initialized or not. More...

bool	mConditionsAreInitialized
	Flag taking in account if the elements were initialized correctly or not. More...

Type Definitions
typedef Scheme< TSparseSpace, TDenseSpace >	BaseType

typedef BaseType::Pointer	BaseTypePointer

typedef ResidualBasedImplicitTimeScheme< TSparseSpace, TDenseSpace >	ImplicitBaseType

typedef ImplicitBaseType::TDataType	TDataType

typedef ImplicitBaseType::DofsArrayType	DofsArrayType

typedef Element::DofsVectorType	DofsVectorType

typedef ImplicitBaseType::TSystemMatrixType	TSystemMatrixType

typedef ImplicitBaseType::TSystemVectorType	TSystemVectorType

typedef ImplicitBaseType::LocalSystemVectorType	LocalSystemVectorType

typedef ImplicitBaseType::LocalSystemMatrixType	LocalSystemMatrixType

typedef ModelPart::NodesContainerType	NodesArrayType

static constexpr double	ZeroTolerance = std::numeric_limits<double>::epsilon()
	Definition of epsilon. More...

	KRATOS_CLASS_POINTER_DEFINITION (ResidualBasedBDFScheme)

Additional Inherited Members
Public Types inherited from Kratos::ResidualBasedImplicitTimeScheme< TSparseSpace, TDenseSpace >
typedef Scheme< TSparseSpace, TDenseSpace >	BaseType
	Base class definition. More...

typedef BaseType::DofsArrayType	DofsArrayType
	DoF array type definition. More...

typedef Element::DofsVectorType	DofsVectorType
	DoF vector type definition. More...

typedef BaseType::TDataType	TDataType
	Data type definition. More...

typedef BaseType::TSystemMatrixType	TSystemMatrixType
	Matrix type definition. More...

typedef BaseType::TSystemVectorType	TSystemVectorType
	Vector type definition. More...

typedef BaseType::LocalSystemVectorType	LocalSystemVectorType
	Local system matrix type definition. More...

typedef BaseType::LocalSystemMatrixType	LocalSystemMatrixType
	Local system vector type definition. More...

typedef ModelPart::NodesContainerType	NodesArrayType
	Nodes containers definition. More...

typedef ModelPart::ElementsContainerType	ElementsArrayType
	Elements containers definition. More...

typedef ModelPart::ConditionsContainerType	ConditionsArrayType
	Conditions containers definition. More...

typedef std::size_t	IndexType
	Index type definition. More...

Public Types inherited from Kratos::Scheme< TSparseSpace, TDenseSpace >
using	ClassType = Scheme< TSparseSpace, TDenseSpace >
	The definition of the current class. More...

using	TDataType = typename TSparseSpace::DataType
	Data type definition. More...

using	TSystemMatrixType = typename TSparseSpace::MatrixType
	Matrix type definition. More...

using	TSystemVectorType = typename TSparseSpace::VectorType
	Vector type definition. More...

using	LocalSystemMatrixType = typename TDenseSpace::MatrixType
	Local system matrix type definition. More...

using	LocalSystemVectorType = typename TDenseSpace::VectorType
	Local system vector type definition. More...

using	TDofType = Dof< double >
	DoF type definition. More...

using	DofsArrayType = ModelPart::DofsArrayType
	DoF array type definition. More...

using	ElementsArrayType = ModelPart::ElementsContainerType
	Elements containers definition. More...

using	ConditionsArrayType = ModelPart::ConditionsContainerType
	Conditions containers definition. More...

Static Public Member Functions inherited from Kratos::Scheme< TSparseSpace, TDenseSpace >
static std::string	Name ()
	Returns the name of the class as used in the settings (snake_case format) More...

Detailed Description

template<class TSparseSpace, class TDenseSpace>
class Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >

BDF integration scheme (for dynamic problems)

The \( n \) order Backward Differentiation Formula (BDF) method is a two step \( n \) order accurate method. This scheme is designed to solve a system of the type:

\[ \mathbf{M} \frac{d^2(u_{n0})}{dt^2} + \mathbf{D} \frac{d(un0)}{dt} + \mathbf{K} u_{n0} = \mathbf{f}_{ext} \]

If we call:

Second derivative:
1. \( \ddot{u}_{ni} \) the second derivative at the step i
First derivative:
1. \( \dot{u}_{ni} \) the first derivative at the step i
Third derivative:
1. \( u_{ni} \) the variable at the step i

Then we assume:

\[ \frac{d^2(u_{n0})}{dt^2} \|t_{n0} = \sum_i c_i \dot{u}_{ni} \]

\[ \frac{d(u_{n0})}{dt} \|t_{n0} = \sum_i c_i u_{n0} \]

with for order 2 (BDF2):

\( c_0 = \frac{1.5}{dt} \)
\( c_1 = \frac{-2.0}{dt} \)
\( c_2 = \frac{0.5}{dt} \)

The LHS and RHS can be defined as:

\[ RHS = \mathbf{f}_{ext} - \mathbf{M} \frac{d(\dot{u}_{n0})}{dt} - \mathbf{D} \frac{d(u_{n0})}{dt} - \mathbf{K} u_{n0} \]

and

\[ LHS = \frac{d(-RHS)}{d(u_{n0})} = c_0^2 \mathbf{M} + c_0 \mathbf{D} + K \]

Note: This implies that elements are expected to be written in terms of a variable with two time derivatives Main reference

Todo:: Create a BibTeX file https://www.stack.nl/~dimitri/doxygen/manual/commands.html#cmdcite

Author: Vicente Mataix Ferrandiz

Member Typedef Documentation

◆ BaseType

template<class TSparseSpace , class TDenseSpace >

typedef Scheme<TSparseSpace,TDenseSpace> Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::BaseType

◆ BaseTypePointer

template<class TSparseSpace , class TDenseSpace >

typedef BaseType::Pointer Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::BaseTypePointer

◆ DofsArrayType

template<class TSparseSpace , class TDenseSpace >

typedef ImplicitBaseType::DofsArrayType Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::DofsArrayType

◆ DofsVectorType

template<class TSparseSpace , class TDenseSpace >

typedef Element::DofsVectorType Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::DofsVectorType

◆ ImplicitBaseType

template<class TSparseSpace , class TDenseSpace >

typedef ResidualBasedImplicitTimeScheme<TSparseSpace,TDenseSpace> Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::ImplicitBaseType

◆ LocalSystemMatrixType

template<class TSparseSpace , class TDenseSpace >

typedef ImplicitBaseType::LocalSystemMatrixType Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::LocalSystemMatrixType

◆ LocalSystemVectorType

template<class TSparseSpace , class TDenseSpace >

typedef ImplicitBaseType::LocalSystemVectorType Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::LocalSystemVectorType

◆ NodesArrayType

template<class TSparseSpace , class TDenseSpace >

typedef ModelPart::NodesContainerType Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::NodesArrayType

◆ TDataType

template<class TSparseSpace , class TDenseSpace >

typedef ImplicitBaseType::TDataType Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::TDataType

◆ TSystemMatrixType

template<class TSparseSpace , class TDenseSpace >

typedef ImplicitBaseType::TSystemMatrixType Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::TSystemMatrixType

◆ TSystemVectorType

template<class TSparseSpace , class TDenseSpace >

typedef ImplicitBaseType::TSystemVectorType Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::TSystemVectorType

Constructor & Destructor Documentation

◆ ResidualBasedBDFScheme() [1/2]

template<class TSparseSpace , class TDenseSpace >

Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::ResidualBasedBDFScheme ( const std::size_t Order = 2 )

inlineexplicit

Constructor. The BDF method.

Parameters

Order The integration order

Todo:: The ideal would be to use directly the dof or the variable itself to identify the type of variable and is derivatives

◆ ResidualBasedBDFScheme() [2/2]

template<class TSparseSpace , class TDenseSpace >

Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::ResidualBasedBDFScheme ( ResidualBasedBDFScheme< TSparseSpace, TDenseSpace > & rOther )

inlineexplicit

Copy Constructor.

◆ ~ResidualBasedBDFScheme()

template<class TSparseSpace , class TDenseSpace >

Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::~ResidualBasedBDFScheme ( )

inlineoverride

Destructor.

Member Function Documentation

◆ AddDynamicsToLHS()

template<class TSparseSpace , class TDenseSpace >

void Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::AddDynamicsToLHS	(	LocalSystemMatrixType &	rLHS_Contribution,
		LocalSystemMatrixType &	rD,
		LocalSystemMatrixType &	rM,
		const ProcessInfo &	rCurrentProcessInfo
	)

inlineoverrideprotectedvirtual

It adds the dynamic LHS contribution of the elements.

\[ LHS = \frac{d(-RHS)}{d(u_{n0})} = c_0^2\mathbf{M} + c_0 \mathbf{D} + \mathbf{K} \]

Parameters

rLHS_Contribution	The dynamic contribution for the LHS
rD	The damping matrix
rM	The mass matrix
rCurrentProcessInfo	The current process info instance

Reimplemented from Kratos::ResidualBasedImplicitTimeScheme< TSparseSpace, TDenseSpace >.

Reimplemented in Kratos::ShallowWaterResidualBasedBDFScheme< TSparseSpace, TDenseSpace >.

◆ AddDynamicsToRHS() [1/2]

template<class TSparseSpace , class TDenseSpace >

void Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::AddDynamicsToRHS	(	Condition &	rCondition,
		LocalSystemVectorType &	rRHS_Contribution,
		LocalSystemMatrixType &	rD,
		LocalSystemMatrixType &	rM,
		const ProcessInfo &	rCurrentProcessInfo
	)

inlineoverrideprotectedvirtual

It adds the dynamic RHS contribution of the condition.

\[ RHS = f_{ext} - \ddot{u}_{n0} \mathbf{M} + \dot{u}_{n0} \mathbf{D} + u_{n0} \mathbf{K} \]

Parameters

rCondition	The condition to compute
RHS_Contribution	The dynamic contribution for the RHS
D	The damping matrix
M	The mass matrix
rCurrentProcessInfo	The current process info instance

Reimplemented from Kratos::ResidualBasedImplicitTimeScheme< TSparseSpace, TDenseSpace >.

Reimplemented in Kratos::ShallowWaterResidualBasedBDFScheme< TSparseSpace, TDenseSpace >.

◆ AddDynamicsToRHS() [2/2]

template<class TSparseSpace , class TDenseSpace >

void Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::AddDynamicsToRHS	(	Element &	rElement,
		LocalSystemVectorType &	rRHS_Contribution,
		LocalSystemMatrixType &	rD,
		LocalSystemMatrixType &	rM,
		const ProcessInfo &	rCurrentProcessInfo
	)

inlineoverrideprotectedvirtual

It adds the dynamic RHS contribution of the elements.

\[ \mathbf{b} - \mathbf{M} a - \mathbf{D} v \]

Parameters

rElement	The element to compute
RHS_Contribution	The dynamic contribution for the RHS
D	The damping matrix
M	The mass matrix
rCurrentProcessInfo	The current process info instance

Reimplemented from Kratos::ResidualBasedImplicitTimeScheme< TSparseSpace, TDenseSpace >.

Reimplemented in Kratos::ShallowWaterResidualBasedBDFScheme< TSparseSpace, TDenseSpace >.

◆ Check()

template<class TSparseSpace , class TDenseSpace >

int Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::Check ( const ModelPart & rModelPart ) const

inlineoverridevirtual

This function is designed to be called once to perform all the checks needed on the input provided.

Checks can be "expensive" as the function is designed to catch user's errors.

Parameters

rModelPart The model of the problem to solve

Returns: Zero means all ok

Reimplemented from Kratos::Scheme< TSparseSpace, TDenseSpace >.

◆ Clear()

template<class TSparseSpace , class TDenseSpace >

void Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::Clear ( )

inlineoverridevirtual

Free memory allocated by this class.

Reimplemented from Kratos::Scheme< TSparseSpace, TDenseSpace >.

Reimplemented in Kratos::ShallowWaterResidualBasedBDFScheme< TSparseSpace, TDenseSpace >.

◆ Clone()

template<class TSparseSpace , class TDenseSpace >

BaseTypePointer Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::Clone ( )

inlineoverridevirtual

Clone

Reimplemented from Kratos::Scheme< TSparseSpace, TDenseSpace >.

Reimplemented in Kratos::ShallowWaterResidualBasedBDFScheme< TSparseSpace, TDenseSpace >, and Kratos::FluxCorrectedShallowWaterScheme< TSparseSpace, TDenseSpace >.

◆ GetDefaultParameters()

template<class TSparseSpace , class TDenseSpace >

Parameters Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::GetDefaultParameters ( ) const

inlineoverridevirtual

This method provides the defaults parameters to avoid conflicts between the different constructors.

Returns: The default parameters

Reimplemented from Kratos::Scheme< TSparseSpace, TDenseSpace >.

Reimplemented in Kratos::ShallowWaterResidualBasedBDFScheme< TSparseSpace, TDenseSpace >.

◆ Info()

template<class TSparseSpace , class TDenseSpace >

std::string Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::Info ( ) const

inlineoverridevirtual

Turn back information as a string.

Reimplemented from Kratos::Scheme< TSparseSpace, TDenseSpace >.

Reimplemented in Kratos::ShallowWaterResidualBasedBDFScheme< TSparseSpace, TDenseSpace >, and Kratos::FluxCorrectedShallowWaterScheme< TSparseSpace, TDenseSpace >.

◆ InitializeSolutionStep()

template<class TSparseSpace , class TDenseSpace >

void Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::InitializeSolutionStep	(	ModelPart &	rModelPart,
		TSystemMatrixType &	rA,
		TSystemVectorType &	rDx,
		TSystemVectorType &	rb
	)

inlineoverridevirtual

It initializes time step solution. Only for reasons if the time step solution is restarted.

Parameters

rModelPart	The model of the problem to solve
rA	LHS matrix
rDx	Incremental update of primary variables
rb	RHS Vector

Todo:: I cannot find the formula for the higher orders with variable time step. I tried to deduce by myself but the result was very unstable

Reimplemented from Kratos::Scheme< TSparseSpace, TDenseSpace >.

Reimplemented in Kratos::FluxCorrectedShallowWaterScheme< TSparseSpace, TDenseSpace >.

◆ KRATOS_CLASS_POINTER_DEFINITION()

template<class TSparseSpace , class TDenseSpace >

Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::KRATOS_CLASS_POINTER_DEFINITION ( ResidualBasedBDFScheme< TSparseSpace, TDenseSpace > )

◆ Predict()

template<class TSparseSpace , class TDenseSpace >

void Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::Predict	(	ModelPart &	rModelPart,
		DofsArrayType &	rDofSet,
		TSystemMatrixType &	rA,
		TSystemVectorType &	rDx,
		TSystemVectorType &	rb
	)

inlineoverridevirtual

Performing the prediction of the solution.

It predicts the solution for the current step x = xold + vold * Dt

Parameters

rModelPart	The model of the problem to solve
rDofSet	set of all primary variables
rA	LHS matrix
rDx	Incremental update of primary variables
rb	RHS Vector

Reimplemented from Kratos::Scheme< TSparseSpace, TDenseSpace >.

Reimplemented in Kratos::ShallowWaterResidualBasedBDFScheme< TSparseSpace, TDenseSpace >.

◆ PrintData()

template<class TSparseSpace , class TDenseSpace >

void Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::PrintData ( std::ostream & rOStream ) const

inlineoverridevirtual

Print object's data.

Reimplemented from Kratos::Scheme< TSparseSpace, TDenseSpace >.

◆ PrintInfo()

template<class TSparseSpace , class TDenseSpace >

void Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::PrintInfo ( std::ostream & rOStream ) const

inlineoverridevirtual

Print information about this object.

Reimplemented from Kratos::Scheme< TSparseSpace, TDenseSpace >.

◆ TemplateAddDynamicsToRHS()

template<class TSparseSpace , class TDenseSpace >

template<class TObjectType >

void Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::TemplateAddDynamicsToRHS	(	TObjectType &	rObject,
		LocalSystemVectorType &	rRHS_Contribution,
		LocalSystemMatrixType &	rD,
		LocalSystemMatrixType &	rM,
		const ProcessInfo &	rCurrentProcessInfo
	)

inlineprotected

It adds the dynamic RHS contribution of the objects.

\[ \mathbf{b} - \mathbf{M} a - \mathbf{D} v \]

Parameters

rObject	The object to compute
rRHS_Contribution	The dynamic contribution for the RHS
rD	The damping matrix
rM	The mass matrix
rCurrentProcessInfo	The current process info instance

◆ Update()

template<class TSparseSpace , class TDenseSpace >

void Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::Update	(	ModelPart &	rModelPart,
		DofsArrayType &	rDofSet,
		TSystemMatrixType &	rA,
		TSystemVectorType &	rDx,
		TSystemVectorType &	rb
	)

inlineoverridevirtual

Performing the update of the solution.

Incremental update within newton iteration. It updates the state variables at the end of the time step

\[ u_{n+1}^{k+1}= u_{n+1}^{k}+ \Delta u\]

Parameters

rModelPart	The model of the problem to solve
rDofSet	Set of all primary variables
rA	LHS matrix
rDx	incremental update of primary variables
rb	RHS Vector

Reimplemented from Kratos::Scheme< TSparseSpace, TDenseSpace >.

Reimplemented in Kratos::ShallowWaterResidualBasedBDFScheme< TSparseSpace, TDenseSpace >.

◆ UpdateDerivatives()

template<class TSparseSpace , class TDenseSpace >

void Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::UpdateDerivatives	(	ModelPart &	rModelPart,
		DofsArrayType &	rDofSet,
		TSystemMatrixType &	rA,
		TSystemVectorType &	rDx,
		TSystemVectorType &	rb
	)

inlineprotected

Performing the update of the derivatives.

Parameters

rModelPart	The model of the problem to solve
rDofSet	Set of all primary variables
rA	LHS matrix
rDx	incremental update of primary variables
rb	RHS Vector

◆ UpdateFirstDerivative()

template<class TSparseSpace , class TDenseSpace >

virtual void Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::UpdateFirstDerivative ( NodesArrayType::iterator itNode )

inlineprotectedvirtual

Updating first time derivative (velocity)

Parameters

itNode the node iterator

Reimplemented in Kratos::ResidualBasedBDFDisplacementScheme< TSparseSpace, TDenseSpace >, Kratos::ResidualBasedBDFCustomScheme< TSparseSpace, TDenseSpace >, and Kratos::ShallowWaterResidualBasedBDFScheme< TSparseSpace, TDenseSpace >.

◆ UpdateSecondDerivative()

template<class TSparseSpace , class TDenseSpace >

virtual void Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::UpdateSecondDerivative ( NodesArrayType::iterator itNode )

inlineprotectedvirtual

Updating second time derivative (acceleration)

Parameters

itNode the node iterator

Reimplemented in Kratos::ResidualBasedBDFDisplacementScheme< TSparseSpace, TDenseSpace >, Kratos::ResidualBasedBDFCustomScheme< TSparseSpace, TDenseSpace >, and Kratos::ShallowWaterResidualBasedBDFScheme< TSparseSpace, TDenseSpace >.

Member Data Documentation

◆ mBDF

template<class TSparseSpace , class TDenseSpace >

Vector Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::mBDF

protected

The integration order.

◆ mOrder

template<class TSparseSpace , class TDenseSpace >

const std::size_t Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::mOrder

protected

◆ mpBDFUtility

template<class TSparseSpace , class TDenseSpace >

Kratos::unique_ptr<TimeDiscretization::BDF> Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::mpBDFUtility

protected

The structure containing the derivatives.

◆ mVector

template<class TSparseSpace , class TDenseSpace >

GeneralVectors Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::mVector

protected

The BDF coefficients.

◆ ZeroTolerance

template<class TSparseSpace , class TDenseSpace >

constexpr double Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >::ZeroTolerance = std::numeric_limits<double>::epsilon()

staticconstexpr

Definition of epsilon.

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

/home/runner/work/Documentation/Documentation/master/kratos/solving_strategies/schemes/residual_based_bdf_scheme.h

Classes

Public Member Functions

Protected Member Functions

Protected Attributes

Type Definitions

Additional Inherited Members

Detailed Description

template<class TSparseSpace, class TDenseSpace> class Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >

Member Typedef Documentation

◆ BaseType

◆ BaseTypePointer

◆ DofsArrayType

◆ DofsVectorType

◆ ImplicitBaseType

◆ LocalSystemMatrixType

◆ LocalSystemVectorType

◆ NodesArrayType

◆ TDataType

◆ TSystemMatrixType

◆ TSystemVectorType

Constructor & Destructor Documentation

◆ ResidualBasedBDFScheme() [1/2]

◆ ResidualBasedBDFScheme() [2/2]

◆ ~ResidualBasedBDFScheme()

Member Function Documentation

◆ AddDynamicsToLHS()

◆ AddDynamicsToRHS() [1/2]

◆ AddDynamicsToRHS() [2/2]

◆ Check()

◆ Clear()

◆ Clone()

◆ GetDefaultParameters()

◆ Info()

◆ InitializeSolutionStep()

◆ KRATOS_CLASS_POINTER_DEFINITION()

◆ Predict()

◆ PrintData()

◆ PrintInfo()

◆ TemplateAddDynamicsToRHS()

◆ Update()

◆ UpdateDerivatives()

◆ UpdateFirstDerivative()

◆ UpdateSecondDerivative()

Member Data Documentation

◆ mBDF

◆ mOrder

◆ mpBDFUtility

◆ mVector

◆ ZeroTolerance

template<class TSparseSpace, class TDenseSpace>
class Kratos::ResidualBasedBDFScheme< TSparseSpace, TDenseSpace >