#include <EulerImplicitSolver.h>

Inheritance diagram for sofa::component::odesolver::backward::EulerImplicitSolver:

[legend]

Detailed Description

Semi-implicit time integrator using backward Euler scheme for first and second degree ODEs. (default: second)

2nd Order ***

This is based on [Baraff and Witkin, Large Steps in Cloth Simulation, SIGGRAPH 1998] The integration scheme is based on the following equations:

$x_{t+h} = x_t + h v_{t+h}$ $v_{t+h} = v_t + h a_{t+h}$

The unknown is $v_{t+h} - v_t = dv$

Newton's law is $ M dv = h f(t+h) $ $ M dv = h ( f(t) + K dx + (B - r_M M + r_K K) (v+dv) )$ $ M dv = h ( f(t) + K h (v+dv) + (B - r_M M + r_K K) (v+dv) )$

$ M $ is the mass matrix. $ K = df/dx $ is the stiffness implemented (or not) by the force fields. $ B = df/dv $ is the damping implemented (or not) by the force fields. An additional, uniform Rayleigh damping $- r_M M + r_K K$ is imposed by the solver.

This corresponds to the following equation system:

$ ( (1+h r_M) M - h B - h(h + r_K) K ) dv = h ( f(t) + (h+r_K) K v + B v - r_M M v )$

Moreover, the projective constraints filter out the forbidden motions. This is equivalent with multiplying vectors with a projection matrix $P$ . Finally, the equation system set by this ode solver is:

$ P ( (1+h r_M) M - h B - h(h + r_K) K ) P dv = P h ( f(t) + (h + r_K) K v + B v - r_M M v )$

1st Order ***

This integration scheme is based on the following equation:

$x_{t+h} = x_t + h v_{t+h}$

Applied to this mechanical system:

$M v_t = f_{ext}$

$M v_{t+h} = f_{ext_{t+h}}$ $= f_{ext_{t}} + h (df_{ext}/dt)_{t+h}$ $= f_{ext_{t}} + h (df_{ext}/dx)_{t+h} v_{t+h}$ $= f_{ext_{t}} - h K v_{t+h}$

$( M + h K ) v_{t+h} = f_{ext}$

Trapezoidal Rule ***

The trapezoidal scheme is based on

$v_{t+h} = h/2 ( f(t+h) + f(t) )$

With this and the same techniques as for the implicit Euler scheme we receive for *** 2nd Order *** equations

$ P ( (1+h/2 r_M) M - h/2 B - h/2 (h + r_K) K ) P dv = P h/2 ( 2 f(t) + (h + r_K) K v + B v - r_M M v )$

and for *** 1st Order ***

$( M + h/2 K ) v_{t+h} = f_{ext}$

Public Attributes
Data< SReal >	f_rayleighStiffness
	Rayleigh damping coefficient related to stiffness, > 0. More...

Data< SReal >	f_rayleighMass
	Rayleigh damping coefficient related to mass, > 0. More...

Data< SReal >	f_velocityDamping
	Velocity decay coefficient (no decay if null) More...

Data< bool >	f_firstOrder
	Use backward Euler scheme for first order ode system. More...

Data< bool >	d_trapezoidalScheme
	Optional: use the trapezoidal scheme instead of the implicit Euler scheme and get second order accuracy in time. More...

Data< bool >	f_solveConstraint
	Apply ConstraintSolver (requires a ConstraintSolver in the same node as this solver, disabled by by default for now) More...

Data< bool >	d_threadSafeVisitor
	If true, do not use realloc and free visitors in fwdInteractionForceField. More...

Public Attributes inherited from sofa::core::objectmodel::BaseObject
Data< bool >	f_listening
	if true, handle the events, otherwise ignore the events More...

Public Attributes inherited from sofa::core::objectmodel::Base
std::vector< lifecycle::DeprecatedData * >	m_oldAttributes

Data< int >	d_messageLogCount

Data< std::string >	name
	Name of the object. More...

Data< bool >	f_printLog
	if true, emits extra messages at runtime. More...

Data< sofa::core::objectmodel::TagSet >	f_tags
	list of the subsets the objet belongs to More...

Data< sofa::type::BoundingBox >	f_bbox
	this object bounding box More...

Data< sofa::core::objectmodel::ComponentState >	d_componentState
	the object state More...

std::string	m_definitionSourceFileName {""}

int	m_definitionSourceFilePos {-1}

std::string	m_instanciationSourceFileName {""}

int	m_instanciationSourceFilePos {-1}

Protected Attributes
core::behavior::MultiVecDeriv	x
	the solution vector is stored for warm-start More...

Protected Attributes inherited from sofa::core::objectmodel::BaseObject
SingleLink< BaseObject, BaseContext, BaseLink::FLAG_DOUBLELINK >	l_context

LinkSlaves	l_slaves

SingleLink< BaseObject, BaseObject, BaseLink::FLAG_DOUBLELINK >	l_master

Protected Attributes inherited from sofa::core::objectmodel::Base
std::map< std::string, sofa::core::DataTrackerCallback >	m_internalEngine

VecData	m_vecData
	List of fields (Data instances) More...

MapData	m_aliasData
	name -> Data multi-map (includes names and aliases) More...

VecLink	m_vecLink
	List of links. More...

MapLink	m_aliasLink
	name -> Link multi-map (includes names and aliases) More...

Public Member Functions
	SOFA_CLASS (EulerImplicitSolver, sofa::core::behavior::OdeSolver)

void	init () override
	Initialization method called at graph creation and modification, during top-down traversal. More...

void	cleanup () override

void	solve (const core::ExecParams *params, SReal dt, sofa::core::MultiVecCoordId xResult, sofa::core::MultiVecDerivId vResult) override

SReal	getVelocityIntegrationFactor () const override

SReal	getPositionIntegrationFactor () const override

virtual SReal	getPositionIntegrationFactor (SReal dt) const

SReal	getIntegrationFactor (int inputDerivative, int outputDerivative) const override

SReal	getIntegrationFactor (int inputDerivative, int outputDerivative, SReal dt) const

SReal	getSolutionIntegrationFactor (int outputDerivative) const override

SReal	getSolutionIntegrationFactor (int outputDerivative, SReal dt) const

Public Member Functions inherited from sofa::core::behavior::OdeSolver
	SOFA_ABSTRACT_CLASS (OdeSolver, objectmodel::BaseObject)

virtual void	solve (const core::ExecParams *params, SReal dt)

virtual void	computeResidual (const core::ExecParams *, SReal, sofa::core::MultiVecCoordId, sofa::core::MultiVecDerivId)

bool	insertInNode (objectmodel::BaseNode *node) override

bool	removeInNode (objectmodel::BaseNode *node) override

Public Member Functions inherited from sofa::core::objectmodel::BaseObject
	SOFA_CLASS (BaseObject, Base)

virtual void	draw (const core::visual::VisualParams *)
	Render internal data of this object, for debugging purposes. More...

virtual void	computeBBox (const core::ExecParams *, bool=false)

void	setSrc (const std::string &v, std::vector< std::string > *attributeList=nullptr)
	Sets a source Object and parses it to collect dependent Data. More...

void	setSrc (const std::string &v, const BaseObject loader, std::vector< std::string > attributeList=nullptr)

Base *	findLinkDestClass (const BaseClass destType, const std::string &path, const BaseLink link) override

virtual std::string	getPathName () const override
	Return the full path name of this object. More...

SReal	getTime () const
	Current time. More...

const BaseContext *	getContext () const

BaseContext *	getContext ()

const BaseObject *	getMaster () const

BaseObject *	getMaster ()

const VecSlaves &	getSlaves () const

BaseObject *	getSlave (const std::string &name) const

virtual void	addSlave (BaseObject::SPtr s)

virtual void	removeSlave (BaseObject::SPtr s)

virtual void	handleEvent (Event *)
	Handle an event. More...

virtual void	handleTopologyChange ()

virtual void	handleTopologyChange (core::topology::Topology *t)

void	parse (BaseObjectDescription *arg) override
	Parse the given description to assign values to this object's fields and potentially other parameters. More...

virtual void	bwdInit ()
	Initialization method called at graph creation and modification, during bottom-up traversal. More...

virtual void	reinit ()
	Update method called when variables used in precomputation are modified. More...

void	updateInternal ()
	Update method called when variables (used to compute other internal variables) are modified. More...

virtual void	storeResetState ()
	Save the initial state for later uses in reset() More...

virtual void	reset ()
	Reset to initial state. More...

Public Member Functions inherited from sofa::core::objectmodel::Base
virtual const BaseClass *	getClass () const

void	addDeprecatedAttribute (lifecycle::DeprecatedData *attribute)

void	addUpdateCallback (const std::string &name, std::initializer_list< BaseData * > inputs, std::function< sofa::core::objectmodel::ComponentState(const DataTracker &)> function, std::initializer_list< BaseData * > outputs)

void	addOutputsToCallback (const std::string &name, std::initializer_list< BaseData * > outputs)

const std::string &	getName () const
	Accessor to the object name. More...

void	setName (const std::string &n)
	Set the name of this object. More...

void	setName (const std::string &n, int counter)
	Set the name of this object, adding an integer counter. More...

std::string	getTypeName () const
	Get the type name of this object (i.e. class and template types) More...

virtual std::string	getClassName () const
	Get the class name of this object. More...

virtual std::string	getTemplateName () const final
	Get the template type names (if any) used to instantiate this object. More...

std::string	getNameSpaceName () const
	Get the template type names (if any) used to instantiate this object. More...

void	setDefinitionSourceFileName (const std::string &sourceFileName)
	Set the source filename (where the component is implemented) More...

const std::string &	getDefinitionSourceFileName () const
	Get the source filename (where the component is implemented) More...

void	setDefinitionSourceFilePos (const int)
	Set the source location (where the component is implemented) More...

int	getDefinitionSourceFilePos () const
	Get the source location (where the component is implemented) More...

void	setInstanciationSourceFileName (const std::string &sourceFileName)

const std::string &	getInstanciationSourceFileName () const

void	setInstanciationSourceFilePos (const int)

int	getInstanciationSourceFilePos () const

void	addMessage (const sofa::helper::logging::Message &m) const

size_t	countLoggedMessages (sofa::helper::logging::Message::TypeSet t=sofa::helper::logging::Message::AnyTypes) const

const std::deque< sofa::helper::logging::Message > &	getLoggedMessages () const

const std::string	getLoggedMessagesAsString (sofa::helper::logging::Message::TypeSet t=sofa::helper::logging::Message::AnyTypes) const

void	clearLoggedMessages () const

bool	notMuted () const

const sofa::core::objectmodel::TagSet &	getTags () const
	Represents the subsets the object belongs to. More...

bool	hasTag (Tag t) const
	Return true if the object belong to the given subset. More...

void	addTag (Tag t)
	Add a subset qualification to the object. More...

void	removeTag (Tag t)
	Remove a subset qualification to the object. More...

ComponentState	getComponentState () const

bool	isComponentStateValid () const

virtual bool	parseField (const std::string &attribute, const std::string &value)
	Assign one field value (Data or Link) More...

virtual bool	hasField (const std::string &attribute) const
	Check if a given Data field or Link exists. More...

void	parseFields (const std::list< std::string > &str)
	Assign the field values stored in the given list of name + value pairs of strings. More...

virtual void	parseFields (const std::map< std::string, std::string * > &str)
	Assign the field values stored in the given map of name -> value pairs. More...

void	writeDatas (std::map< std::string, std::string * > &str)
	Write the current field values to the given map of name -> value pairs. More...

void	writeDatas (std::ostream &out, const std::string &separator=" ")

BaseData *	findData (const std::string &name) const

std::vector< BaseData * >	findGlobalField (const std::string &name) const
	Find data fields given a name: several can be found as we look into the alias map. More...

BaseLink *	findLink (const std::string &name) const

std::vector< BaseLink * >	findLinks (const std::string &name) const
	Find link fields given a name: several can be found as we look into the alias map. More...

virtual void	updateLinks (bool logErrors=true)
	Update pointers in case the pointed-to objects have appeared. More...

template<class T >
BaseData::BaseInitData	initData (::sofa::core::objectmodel::Data< T > field, const char name, const char *help, ::sofa::core::objectmodel::BaseData::DataFlags dataflags)
	Helper method used to initialize a data field containing a value of type T. More...

template<class T >
BaseData::BaseInitData	initData (Data< T > field, const char name, const char *help, bool isDisplayed=true, bool isReadOnly=false)
	Helper method used to initialize a data field containing a value of type T. More...

template<class T >
Data< T >::InitData	initData (Data< T > field, const T &value, const char name, const char *help, bool isDisplayed=true, bool isReadOnly=false)
	Helper method used to initialize a data field containing a value of type T. More...

void	addData (BaseData *f, const std::string &name)

void	addData (BaseData *f)

void	removeData (BaseData *f)
	Remove a data field. More...

void	addAlias (BaseData field, const char alias)
	Add an alias to a Data. More...

void	addLink (BaseLink *l)
	Add a link. More...

void	addAlias (BaseLink link, const char alias)
	Add an alias to a Link. More...

const VecData &	getDataFields () const
	Accessor to the vector containing all the fields of this object. More...

const MapData &	getDataAliases () const
	Accessor to the map containing all the aliases of this object. More...

const VecLink &	getLinks () const
	Accessor to the vector containing all the fields of this object. More...

const MapLink &	getLinkAliases () const
	Accessor to the map containing all the aliases of this object. More...

virtual bool	findDataLinkDest (BaseData &ptr, const std::string &path, const BaseLink link)

template<class T >
bool	findLinkDest (T &ptr, const std::string &path, const BaseLink link)

Protected Member Functions
	EulerImplicitSolver ()

Protected Member Functions inherited from sofa::core::behavior::OdeSolver
	OdeSolver ()

	~OdeSolver () override

Protected Member Functions inherited from sofa::core::objectmodel::BaseObject
	BaseObject ()

	~BaseObject () override

virtual void	doUpdateInternal ()
	Implementation of the internal update. More...

void	changeContextLink (BaseContext before, BaseContext &after)

void	changeSlavesLink (BaseObject::SPtr ptr, std::size_t, bool add)
	This method insures that slaves objects have master and context links set correctly. More...

void	trackInternalData (const BaseData &data)
	Method called to add the Data to the DataTracker (listing the Data to track) More...

void	cleanTracker ()

bool	hasDataChanged (const BaseData &data)
	Method called to know if a tracked Data has changed. More...

Protected Member Functions inherited from sofa::core::objectmodel::Base
	Base ()

virtual	~Base ()

void	initData0 (BaseData field, BaseData::BaseInitData &res, const char name, const char *help, bool isDisplayed=true, bool isReadOnly=false)
	Helper method used by initData() More...

void	initData0 (BaseData field, BaseData::BaseInitData &res, const char name, const char *help, BaseData::DataFlags dataFlags)
	Helper method used by initData() More...

template<class T >
void	initData0 (Data< T > field, typename Data< T >::InitData &res, const T &value, const char name, const char *help, bool isDisplayed=true, bool isReadOnly=false)
	Helper method used by initData() More...

Additional Inherited Members
Static Public Member Functions inherited from sofa::core::objectmodel::BaseObject
template<class T >
static bool	canCreate (T , BaseContext , BaseObjectDescription *)
	Pre-construction check method called by ObjectFactory. More...

template<class T >
static T::SPtr	create (T , BaseContext context, BaseObjectDescription *arg)
	Construction method called by ObjectFactory. More...

Static Public Member Functions inherited from sofa::core::objectmodel::Base
static const BaseClass *	GetClass ()

template<class T >
static std::string	shortName (const T ptr=nullptr, BaseObjectDescription =nullptr)

Attribute details

◆ d_threadSafeVisitor

Data<bool> sofa::component::odesolver::backward::EulerImplicitSolver::d_threadSafeVisitor

If true, do not use realloc and free visitors in fwdInteractionForceField.

◆ d_trapezoidalScheme

Data<bool> sofa::component::odesolver::backward::EulerImplicitSolver::d_trapezoidalScheme

Optional: use the trapezoidal scheme instead of the implicit Euler scheme and get second order accuracy in time.

◆ f_firstOrder

Data<bool> sofa::component::odesolver::backward::EulerImplicitSolver::f_firstOrder

Use backward Euler scheme for first order ode system.

◆ f_rayleighMass

Data<SReal> sofa::component::odesolver::backward::EulerImplicitSolver::f_rayleighMass

Rayleigh damping coefficient related to mass, > 0.

◆ f_rayleighStiffness

Data<SReal> sofa::component::odesolver::backward::EulerImplicitSolver::f_rayleighStiffness

Rayleigh damping coefficient related to stiffness, > 0.

◆ f_solveConstraint

Data<bool> sofa::component::odesolver::backward::EulerImplicitSolver::f_solveConstraint

Apply ConstraintSolver (requires a ConstraintSolver in the same node as this solver, disabled by by default for now)

◆ f_velocityDamping

Data<SReal> sofa::component::odesolver::backward::EulerImplicitSolver::f_velocityDamping

Velocity decay coefficient (no decay if null)

◆ x

core::behavior::MultiVecDeriv sofa::component::odesolver::backward::EulerImplicitSolver::x

protected

the solution vector is stored for warm-start

Constructor details

◆ EulerImplicitSolver()

sofa::component::odesolver::backward::EulerImplicitSolver::EulerImplicitSolver ( )

protected

Function details

◆ cleanup()

void sofa::component::odesolver::backward::EulerImplicitSolver::cleanup ( )

overridevirtual

Called just before deleting this object Any object in the tree bellow this object that are to be removed will be removed only after this call, so any references this object holds should still be valid.

Reimplemented from sofa::core::objectmodel::BaseObject.

◆ getIntegrationFactor() [1/2]

SReal sofa::component::odesolver::backward::EulerImplicitSolver::getIntegrationFactor	(	int	inputDerivative,
		int	outputDerivative
	)		const

overridevirtual

Given an input derivative order (0 for position, 1 for velocity, 2 for acceleration), how much will it affect the output derivative of the given order.

This method is used to compute the compliance for contact corrections. For example, a backward-Euler dynamic implicit integrator would use: Input: x_t v_t a_{t+dt} x_{t+dt} 1 dt dt^2 v_{t+dt} 0 1 dt

If the linear system is expressed on s = a_{t+dt} dt, then the final factors are: Input: x_t v_t a_t s x_{t+dt} 1 dt 0 dt v_{t+dt} 0 1 0 1 a_{t+dt} 0 0 0 1/dt The last column is returned by the getSolutionIntegrationFactor method.

Reimplemented from sofa::core::behavior::OdeSolver.

◆ getIntegrationFactor() [2/2]

SReal sofa::component::odesolver::backward::EulerImplicitSolver::getIntegrationFactor	(	int	inputDerivative,
		int	outputDerivative,
		SReal	dt
	)		const

◆ getPositionIntegrationFactor() [1/2]

SReal sofa::component::odesolver::backward::EulerImplicitSolver::getPositionIntegrationFactor ( ) const

overridevirtual

Given a displacement as computed by the linear system inversion, how much will it affect the position

This method is used to compute the compliance for contact corrections For Euler methods, it is typically dt².

Reimplemented from sofa::core::behavior::OdeSolver.

◆ getPositionIntegrationFactor() [2/2]

virtual SReal sofa::component::odesolver::backward::EulerImplicitSolver::getPositionIntegrationFactor ( SReal dt ) const

inlinevirtual

◆ getSolutionIntegrationFactor() [1/2]

SReal sofa::component::odesolver::backward::EulerImplicitSolver::getSolutionIntegrationFactor ( int outputDerivative ) const

overridevirtual

Given a solution of the linear system, how much will it affect the output derivative of the given order.

Reimplemented from sofa::core::behavior::OdeSolver.

◆ getSolutionIntegrationFactor() [2/2]

SReal sofa::component::odesolver::backward::EulerImplicitSolver::getSolutionIntegrationFactor	(	int	outputDerivative,
		SReal	dt
	)		const

◆ getVelocityIntegrationFactor()

SReal sofa::component::odesolver::backward::EulerImplicitSolver::getVelocityIntegrationFactor ( ) const

inlineoverridevirtual

Given a displacement as computed by the linear system inversion, how much will it affect the velocity

This method is used to compute the compliance for contact corrections For Euler methods, it is typically dt.

Reimplemented from sofa::core::behavior::OdeSolver.

◆ init()

void sofa::component::odesolver::backward::EulerImplicitSolver::init ( )

overridevirtual

Initialization method called at graph creation and modification, during top-down traversal.

Reimplemented from sofa::core::objectmodel::BaseObject.

◆ SOFA_CLASS()

sofa::component::odesolver::backward::EulerImplicitSolver::SOFA_CLASS	(	EulerImplicitSolver	,
		sofa::core::behavior::OdeSolver
	)

◆ solve()

void sofa::component::odesolver::backward::EulerImplicitSolver::solve	(	const core::ExecParams *	,
		SReal	,
		sofa::core::MultiVecCoordId	,
		sofa::core::MultiVecDerivId
	)

overridevirtual

Main computation method.

Specify and execute all computation for timestep integration, i.e. advancing the state from time t to t+dt, putting the resulting position and velocity in the provided vectors.

Implements sofa::core::behavior::OdeSolver.

Detailed Description

Public Attributes

Protected Attributes

Public Member Functions

Protected Member Functions

Additional Inherited Members

Attribute details

◆ d_threadSafeVisitor

◆ d_trapezoidalScheme

◆ f_firstOrder

◆ f_rayleighMass

◆ f_rayleighStiffness

◆ f_solveConstraint

◆ f_velocityDamping

◆ x

Constructor details

◆ EulerImplicitSolver()

Function details

◆ cleanup()

◆ getIntegrationFactor() [1/2]

◆ getIntegrationFactor() [2/2]

◆ getPositionIntegrationFactor() [1/2]

◆ getPositionIntegrationFactor() [2/2]

◆ getSolutionIntegrationFactor() [1/2]

◆ getSolutionIntegrationFactor() [2/2]

◆ getVelocityIntegrationFactor()

◆ init()

◆ SOFA_CLASS()

◆ solve()