SOFA API  f384085d
Open source framework for multi-physics simuation
sofa::component::odesolver::backward::EulerImplicitSolver Class Reference

#include <EulerImplicitSolver.h>

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

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
 
Data< SReal > f_rayleighMass
 
Data< SReal > f_velocityDamping
 
Data< boolf_firstOrder
 
Data< boolf_solveConstraint
 
Data< SReal > d_rayleighStiffness
 Rayleigh damping coefficient related to stiffness, > 0. More...
 
Data< SReal > d_rayleighMass
 Rayleigh damping coefficient related to mass, > 0. More...
 
Data< SReal > d_velocityDamping
 Velocity decay coefficient (no decay if null) More...
 
Data< boold_firstOrder
 Use backward Euler scheme for first order ode system. More...
 
Data< boold_trapezoidalScheme
 Optional: use the trapezoidal scheme instead of the implicit Euler scheme and get second order accuracy in time. More...
 
Data< boold_solveConstraint
 Apply ConstraintSolver (requires a ConstraintSolver in the same node as this solver, disabled by by default for now) More...
 
Data< boold_threadSafeVisitor
 If true, do not use realloc and free visitors in fwdInteractionForceField. More...
 
- Public Attributes inherited from sofa::core::objectmodel::BaseObject
Data< boolf_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< boolf_printLog
 if true, emits extra messages at runtime. More...
 
Data< sofa::core::objectmodel::TagSetf_tags
 list of the subsets the objet belongs to More...
 
Data< sofa::type::BoundingBoxf_bbox
 this object bounding box More...
 
Data< sofa::core::objectmodel::ComponentStated_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_DOUBLELINKl_context
 
LinkSlaves l_slaves
 
SingleLink< BaseObject, BaseObject, BaseLink::FLAG_DOUBLELINKl_master
 
- Protected Attributes inherited from sofa::core::objectmodel::Base
std::map< std::string, sofa::core::DataTrackerCallbackm_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...
 
- Protected Attributes inherited from sofa::core::behavior::LinearSolverAccessor
SingleLink< LinearSolverAccessor, LinearSolver, BaseLink::FLAG_STRONGLINKl_linearSolver
 

Public Member Functions

 SOFA_CLASS2 (EulerImplicitSolver, sofa::core::behavior::OdeSolver, sofa::core::behavior::LinearSolverAccessor)
 
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)
 
BasefindLinkDestClass (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 BaseContextgetContext () const
 
BaseContextgetContext ()
 
const BaseObjectgetMaster () const
 
BaseObjectgetMaster ()
 
const VecSlavesgetSlaves () const
 
BaseObjectgetSlave (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 BaseClassgetClass () 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::TagSetgetTags () 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=" ")
 
BaseDatafindData (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...
 
BaseLinkfindLink (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 VecDatagetDataFields () const
 Accessor to the vector containing all the fields of this object. More...
 
const MapDatagetDataAliases () const
 Accessor to the map containing all the aliases of this object. More...
 
const VecLinkgetLinks () const
 Accessor to the vector containing all the fields of this object. More...
 
const MapLinkgetLinkAliases () 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)
 
- Public Member Functions inherited from sofa::core::behavior::LinearSolverAccessor
void init () override
 Initialization method called at graph creation and modification, during top-down traversal. More...
 

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...
 
- Protected Member Functions inherited from sofa::core::behavior::LinearSolverAccessor
 LinearSolverAccessor (LinearSolver *linearSolver=nullptr)
 

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

Attribute details

◆ d_firstOrder

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

Use backward Euler scheme for first order ode system.

◆ d_rayleighMass

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

Rayleigh damping coefficient related to mass, > 0.

◆ d_rayleighStiffness

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

Rayleigh damping coefficient related to stiffness, > 0.

◆ d_solveConstraint

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

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

◆ 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.

◆ d_velocityDamping

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

Velocity decay coefficient (no decay if null)

◆ f_firstOrder

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

◆ f_rayleighMass

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

◆ f_rayleighStiffness

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

◆ f_solveConstraint

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

◆ f_velocityDamping

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

◆ 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 ( void  )
overridevirtual

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

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

◆ SOFA_CLASS2()

sofa::component::odesolver::backward::EulerImplicitSolver::SOFA_CLASS2 ( EulerImplicitSolver  ,
sofa::core::behavior::OdeSolver  ,
sofa::core::behavior::LinearSolverAccessor   
)

◆ 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.