Base class for all solvers of ode equation of order 2 of the form \(M(x(t), v(t)).a(t) = f(t, x(t), v(t))\). More...

#include <OdeSolver.h>

Inheritance diagram for SurgSim::Math::OdeSolver:

Public Member Functions
	OdeSolver (OdeEquation *equation)
	Constructor. More...

virtual	~OdeSolver ()
	Virtual destructor.

const std::string	getName () const
	Gets the solver's name. More...

void	setLinearSolver (std::shared_ptr< LinearSparseSolveAndInverse > linearSolver)
	Sets the specialized linear solver to use with this Ode solver. More...

std::shared_ptr< LinearSparseSolveAndInverse >	getLinearSolver () const
	Gets the specialized linear solver used with this Ode solver. More...

virtual void	solve (double dt, const OdeState &currentState, OdeState *newState, bool computeCompliance=true)=0
	Solves the equation. More...

void	computeMatrices (double dt, const OdeState &state, bool computeCompliance=true)
	Computes the system and compliance matrices for a given state. More...

const SparseMatrix &	getSystemMatrix () const
	Queries the current system matrix. More...

const Matrix &	getComplianceMatrix () const

Protected Member Functions
virtual void	assembleLinearSystem (double dt, const OdeState &state, const OdeState &newState, bool computeRHS=true)=0
	Assemble the linear system (A.x=b) to be solved for the state and new states (useful for certain ode solver). More...

void	computeComplianceMatrixFromSystemMatrix (const OdeState &state)
	Helper method computing the compliance matrix from the system matrix and setting the boundary conditions. More...

Protected Attributes
std::string	m_name
	Name for this solver. More...

OdeEquation &	m_equation
	The ode equation (API providing the necessary evaluation methods and the initial state)

std::shared_ptr< LinearSparseSolveAndInverse >	m_linearSolver
	The specialized linear solver to use when solving the ode equation.

SparseMatrix	m_systemMatrix
	Linear system matrix (can be M, K, combination of MDK depending on the solver), including boundary conditions. More...

Vector	m_solution
	Linear system solution and rhs vectors (including boundary conditions)

Vector	m_rhs

Matrix	m_complianceMatrix
	Compliance matrix which is the inverse of the system matrix, including boundary conditions.

Detailed Description

Base class for all solvers of ode equation of order 2 of the form \(M(x(t), v(t)).a(t) = f(t, x(t), v(t))\).

This ode equation is solved as an ode of order 1 by defining the state vector \(y = \left(\begin{array}{c}x\\v\end{array}\right)\):

\[ y' = \left(\begin{array}{c} x' \\ v' \end{array}\right) = \left(\begin{array}{c} v \\ M(x, v)^{-1}.f(t, x, v) \end{array}\right) \]

Note: To allow the use of explicit and implicit solver, we need to be able to evaluate:; \(M(x(t), v(t))\); \(f(t, x(t), v(t))\) but also; \(K = -\frac{\partial f}{\partial x}(x(t), v(t))\); \(D = -\frac{\partial f}{\partial v}(x(t), v(t))\); Models wanting the use of implicit solvers will need to compute these Jacobian matrices.; Matrices all have dense storage, but a specialized linear solver can be set per solver.

Constructor & Destructor Documentation

§ OdeSolver()

SurgSim::Math::OdeSolver::OdeSolver ( OdeEquation * equation )

explicit

Constructor.

Parameters

equation The ode equation to be solved

Member Function Documentation

§ assembleLinearSystem()

virtual void SurgSim::Math::OdeSolver::assembleLinearSystem	(	double	dt,
		const OdeState &	state,
		const OdeState &	newState,
		bool	computeRHS = `true`
	)

protectedpure virtual

Assemble the linear system (A.x=b) to be solved for the state and new states (useful for certain ode solver).

Parameters

dt	The time step used in the system
state,newState	The state and newState to be used to evaluate the system
computeRHS	True to compute the RHS vector, False otherwise

Note: The method should fill up the LHS matrix in m_systemMatrix and the RHS vector in m_b (if requested); The method should take care of the boundary conditions properly on both the matrix and the vector.; The method should prepare the linear solver m_linearSolver to be used with the m_systemMatrix

Implemented in SurgSim::Math::OdeSolverEulerExplicit, SurgSim::Math::OdeSolverRungeKutta4, SurgSim::Math::OdeSolverEulerExplicitModified, SurgSim::Math::MockOdeSolver, SurgSim::Math::OdeSolverEulerImplicit, and SurgSim::Math::OdeSolverStatic.

§ computeComplianceMatrixFromSystemMatrix()

void SurgSim::Math::OdeSolver::computeComplianceMatrixFromSystemMatrix ( const OdeState & state )

protected

Helper method computing the compliance matrix from the system matrix and setting the boundary conditions.

Parameters

state The state describing the boundary conditions

Note: The full system is not re-evaluated from the state, the current m_systemMatrix is directly used.; This method supposes that the linear solver has been updated with the current m_systemMatrix.

§ computeMatrices()

void SurgSim::Math::OdeSolver::computeMatrices	(	double	dt,
		const OdeState &	state,
		bool	computeCompliance = `true`
	)

Computes the system and compliance matrices for a given state.

Parameters

dt	The time step
state	The state to compute the system and compliance matrices for
computeCompliance	True to explicitly compute the compliance matrix, False otherwise

Compute the system matrix (and discard the RHS calculation)

Compute the compliance matrix

§ getComplianceMatrix()

const Matrix & SurgSim::Math::OdeSolver::getComplianceMatrix ( ) const

Returns: The latest compliance matrix computed (either by calling solve or computeMatrices)

§ getLinearSolver()

std::shared_ptr< LinearSparseSolveAndInverse > SurgSim::Math::OdeSolver::getLinearSolver ( ) const

Gets the specialized linear solver used with this Ode solver.

Returns: The linear solver used when solving the ode equation

§ getName()

const std::string SurgSim::Math::OdeSolver::getName ( ) const

Gets the solver's name.

Returns: The solver name

§ getSystemMatrix()

const SparseMatrix & SurgSim::Math::OdeSolver::getSystemMatrix ( ) const

Queries the current system matrix.

Returns: The latest system matrix calculated

§ setLinearSolver()

void SurgSim::Math::OdeSolver::setLinearSolver ( std::shared_ptr< LinearSparseSolveAndInverse > linearSolver )

Sets the specialized linear solver to use with this Ode solver.

Parameters

linearSolver the linear solver to use when solving the ode equation

§ solve()

virtual void SurgSim::Math::OdeSolver::solve	(	double	dt,
		const OdeState &	currentState,
		OdeState *	newState,
		bool	computeCompliance = `true`
	)

pure virtual

Solves the equation.

Parameters

	dt	The time step
	currentState	State at time t
[out]	newState	State at time t+dt
	computeCompliance	True to explicitly compute the compliance matrix, False otherwise

Implemented in SurgSim::Math::OdeSolverEulerExplicit, SurgSim::Math::OdeSolverRungeKutta4, SurgSim::Math::OdeSolverEulerExplicitModified, SurgSim::Math::MockOdeSolver, SurgSim::Math::OdeSolverEulerImplicit, SurgSim::Math::OdeSolverLinearEulerImplicit, SurgSim::Math::OdeSolverStatic, SurgSim::Math::OdeSolverLinearEulerExplicit, SurgSim::Math::OdeSolverLinearEulerExplicitModified, SurgSim::Math::OdeSolverLinearRungeKutta4, and SurgSim::Math::OdeSolverLinearStatic.

Member Data Documentation

§ m_name

std::string SurgSim::Math::OdeSolver::m_name

protected

Name for this solver.

Note: MUST be set by the derived classes

§ m_systemMatrix

SparseMatrix SurgSim::Math::OdeSolver::m_systemMatrix

protected

Linear system matrix (can be M, K, combination of MDK depending on the solver), including boundary conditions.

Note: A static solver will have K for system matrix; A dynamic explicit solver will have M for system matrix; A dynamic implicit solver will have a combination of M, D and K for system matrix

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

SurgSim/Math/OdeSolver.h
SurgSim/Math/OdeSolver.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

§ OdeSolver()

Member Function Documentation

§ assembleLinearSystem()

§ computeComplianceMatrixFromSystemMatrix()

§ computeMatrices()

§ getComplianceMatrix()

§ getLinearSolver()

§ getName()

§ getSystemMatrix()

§ setLinearSolver()

§ solve()

Member Data Documentation

§ m_name

§ m_systemMatrix