Euler Implicit ode solver. More...

Inheritance diagram for SurgSim::Math::OdeSolverEulerImplicit:

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

virtual void	solve (double dt, const OdeState &currentState, OdeState *newState) override
	Solves the equation. More...

Public Member Functions inherited from SurgSim::Math::OdeSolver
	OdeSolver (OdeEquation *equation)
	Constructor. More...

virtual	~OdeSolver ()
	Virtual destructor. More...

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

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

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

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

const Matrix &	getCompliance () const
	Queries the current compliance matrix. More...

Additional Inherited Members
Protected Member Functions inherited from SurgSim::Math::OdeSolver
void	allocate (size_t size)
	Allocates the system and compliance matrices. More...

Protected Attributes inherited from SurgSim::Math::OdeSolver
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) More...

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

Matrix	m_systemMatrix
	System matrix (can be M, K, combination of MDK depending on the solver) 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. More...

Matrix	m_compliance
	Compliance matrix which is the inverse of the system matrix. More...

Detailed Description

Euler Implicit ode solver.

Note: 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 = (x v)^t:; y' = ( x' ) = ( dx/dt ) = ( v ); ( v' ) = ( dv/dt ) = ( M(x, v)^{-1}.f(x, v) ); y' = f(t, y); Euler Implicit is also called backward Euler as it solves this integral using a backward evaluation:; y' = (y(t) - y(t-dt)) / dt; which leads to the integration scheme:; { x(t+dt) = x(t) + dt.v(t+dt); { v(t+dt) = v(t) + dt.a(t+dt)