Description

Implementation of the HHT implicit integrator for II order systems.

This timestepper allows use of an adaptive time-step, as well as optional use of a modified Newton scheme for the solution of the resulting nonlinear problem.

The Newton iteration solves for the accelerations and Lagrange multipliers at the end of the step. At each iteration, it evaluates the following quantities:

R: the dynamics residual (generalized forces, inertial forces, and constraint reactions);
C: the constraint violation, at the position level. For constraints imposed at the velocity level, C is the velocity violation multiplied by (beta/gamma)*h;
Ds: the acceleration update, measured in the WRMS norm with weights 1/(reltol*|a| + abstolS), with a the accelerations at the beginning of the step;
Dl: the Lagrange multiplier update, measured in the WRMS norm with weights 1/(reltol*|l| + abstolL), with l the multipliers at the beginning of the step.

Newton is declared converged if either of the following tests passes:

residual test: |R| < abstolS and |C| < abstolS (2-norms);
update test: |Ds|_WRMS < 1 and |Dl|_WRMS < 1.

The state tolerance abstolS therefore applies to all state-related quantities, while the multiplier tolerance abstolL applies only to the multiplier update. Both tests are limited by round-off: |C| cannot drop below about eps*|q| (with eps the machine precision and q the generalized coordinates), |R| cannot drop below about k*eps*|q| for a force with stiffness k, and the acceleration update cannot drop below about eps*|q|/(beta*h^2). The last limit grows quickly as the step size decreases; with very small steps, abstolS (or reltol) must stay above it for the update test to pass.

When Newton fails to converge, the integrator reports the norms and tolerances of both tests at the last iteration (in the exception message, or in the verbose output if the terminated step is accepted).

#include <ChTimestepperHHT.h>

Inheritance diagram for chrono::ChTimestepperHHT:

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Collaboration diagram for chrono::ChTimestepperHHT:

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Public Member Functions
	ChTimestepperHHT (ChIntegrableIIorder *intgr=nullptr)

virtual ChTimestepper::Type	GetType () const override
	Return type of the integration method.

virtual ChIntegrable *	GetIntegrable () const override
	Return the associated integrable object.

void	SetAlpha (double val)
	Set the numerical damping parameter (in the [-1/3, 0] range). More...

double	GetAlpha ()
	Return the current value of the method parameter alpha.

virtual void	ArchiveOut (ChArchiveOut &archive) override
	Method to allow serialization of transient data to archives.

virtual void	ArchiveIn (ChArchiveIn &archive) override
	Method to allow de-serialization of transient data from archives.

Public Member Functions inherited from chrono::ChTimestepperIIorder
virtual ChState &	GetStatePos ()
	Access the state, position part, at current time.

virtual ChStateDelta &	GetStateVel ()
	Access the state, speed part, at current time.

virtual ChStateDelta &	GetStateAcc ()
	Access the acceleration, at current time.

virtual void	SetIntegrable (ChIntegrableIIorder *intgr)
	Set the integrable object.

ChIntegrableIIorder *	GetIntegrableIIorder () const
	Get the integrable object.

Public Member Functions inherited from chrono::ChTimestepperImplicit
void	SetMaxIters (int iters)
	Set the max number of Newton iterations.

void	SetRelTolerance (double rel_tol)
	Set the relative tolerance. More...

void	SetAbsTolerances (double abs_tolS, double abs_tolL)
	Set the absolute tolerances for states and Lagrange multipliers. More...

void	SetAbsTolerances (double abs_tol)
	Set the same absolute tolerance for states and Lagrange multipliers. More...

void	SetJacobianUpdateMethod (JacobianUpdate method)
	Set the strategy for Jacobian update (default: EVERY_STEP).

double	GetMaxIters () const
	Get the max number of iterations using the Newton Raphson procedure.

JacobianUpdate	GetJacobianUpdateMethod () const
	Get the current Jacobian update strategy.

unsigned int	GetNumStepIterations () const
	Return the number of Newton iterations over the last step.

unsigned int	GetNumStepSetupCalls () const
	Return the number of calls to the solver's Setup function made during the last step.

unsigned int	GetNumStepSolveCalls () const
	Return the number of calls to the solver's Solve function made over the last step.

double	GetEstimatedConvergenceRate () const
	Get the last estimated convergence rate for the internal Newton solver. More...

unsigned int	GetNumIterations () const
	Return the cumulative number of Newton iterations.

unsigned int	GetNumSetupCalls () const
	Return the cumulative number of calls to the solver's Setup function.

unsigned int	GetNumSolveCalls () const
	Return the cumulative number of calls to the solver's Solve function.

void	AcceptTerminatedStep (bool accept)
	Accept step after a non-converged Newton solve (default: true). More...

unsigned int	GetNumTerminated () const
	Return the number of terminated Newton solves. More...

void	SetStepControl (bool enable)
	Turn on/off the internal step size control. More...

void	SetMinStepSize (double step)
	Set the minimum step size. More...

void	SetMaxItersSuccess (int iters)
	Set the maximum allowable number of iterations for counting a step towards a stepsize increase. More...

void	SetRequiredSuccessfulSteps (int num_steps)
	Set the minimum number of (internal) steps that use at most maxiters_success before considering a stepsize increase. More...

void	SetStepIncreaseFactor (double factor)
	Set the multiplicative factor for a stepsize increase (must be larger than 1). More...

void	SetStepDecreaseFactor (double factor)
	Set the multiplicative factor for a stepsize decrease (must be smaller than 1). More...

virtual void	Advance (double dt) override final
	Perform an integration step. More...

virtual void	SaveInternalState (ChCheckpointWriter &writer) const override
	Save the step size control state (internal step size and number of successive successful steps).

virtual void	LoadInternalState (ChCheckpointReader &reader) override
	Load the step size control state.

Public Member Functions inherited from chrono::ChTimestepper
virtual ChVectorDynamic &	GetLagrangeMultipliers ()
	Access the Lagrange multipliers, if any.

virtual double	GetTime () const
	Get the current time.

virtual void	SetTime (double mt)
	Set the current time.

void	SetVerbose (bool verb)
	Turn on/off logging of messages.

std::string	GetTypeAsString () const
	Return this integrator's type as a string.

Additional Inherited Members
Public Types inherited from chrono::ChTimestepperImplicit
enum	JacobianUpdate { JacobianUpdate::EVERY_ITERATION, JacobianUpdate::EVERY_STEP, JacobianUpdate::NEVER, JacobianUpdate::AUTOMATIC }
	Newton Jacobian update strategies. More...

Public Types inherited from chrono::ChTimestepper
enum	Type { EULER_EXPLICIT_I, EULER_EXPLICIT_II, EULER_SEMI_IMPLICIT, RUNGE_KUTTA, HEUN, LEAPFROG, EULER_IMPLICIT, EULER_IMPLICIT_LINEARIZED, EULER_IMPLICIT_PROJECTED, TRAPEZOIDAL, TRAPEZOIDAL_LINEARIZED, NEWMARK, HHT, CUSTOM }
	Methods for time integration.

Static Public Member Functions inherited from chrono::ChTimestepperImplicit
static std::string	GetJacobianUpdateMethodAsString (JacobianUpdate jacobian_update)
	Return Jacobian update method as a string.

Static Public Member Functions inherited from chrono::ChTimestepper
static std::string	GetTypeAsString (Type type)
	Return the provided integrator type as a string.

Protected Member Functions inherited from chrono::ChTimestepperIIorder
	ChTimestepperIIorder (ChIntegrableIIorder *intgr=nullptr)

Protected Member Functions inherited from chrono::ChTimestepperImplicit
virtual void	OnAdvance (double dt)
	Implementation of integrator-specific time advance. More...

bool	CheckConvergence (int iteration)
	Check convergence of Newton process. More...

std::string	GetConvergenceReport () const
	Return a description of the last convergence check (norms, tolerances, and failed tests).

std::string	GetResidualTestReport () const
	Return a description of the residual test at the last convergence check.

void	ProcessTerminatedSolve (const std::string &report)
	Handle a Newton solve that did not converge within the maximum number of iterations. More...

void	CalcErrorWeights (const ChVectorDynamic<> &x, double rtol, double atol, ChVectorDynamic<> &ewt)
	Calculate error weights based on the given state and tolerances.

Protected Member Functions inherited from chrono::ChTimestepper
	ChTimestepper (ChIntegrable *intgr=nullptr)

Protected Attributes inherited from chrono::ChTimestepperIIorder
ChIntegrableIIorder *	integrable

ChState	X

ChStateDelta	V

ChStateDelta	A

Protected Attributes inherited from chrono::ChTimestepperImplicit
JacobianUpdate	jacobian_update_method
	Jacobian update strategy.

bool	call_setup
	should the solver's Setup function be called?

bool	call_analyze
	should the solver's Setup analyze phase be called?

bool	jacobian_is_current
	was the Jacobian evaluated at current Newton iteration?

unsigned int	max_iters
	maximum number of iterations

double	reltol
	relative tolerance

double	abstolS
	absolute tolerance (states)

double	abstolL
	absolute tolerance (Lagrange multipliers)

unsigned int	num_step_iters
	number of iterations during last step

unsigned int	num_step_setups
	number of calls to the solver Setup() function during last step

unsigned int	num_step_solves
	number of calls to the solver Solve() function during last step

unsigned int	num_iters
	current cumulative number of Newton iterations

unsigned int	num_setups
	current cumulative number of Setup() calls

unsigned int	num_solves
	current cumulative number of Solve() calls

unsigned int	num_terminated
	number of terminated NEwton iterations

double	convergence_rate
	estimated Newton rate of convergence

ChStateDelta	Ds
	state update

ChVectorDynamic	Dl
	Lagrange multiplier update.

ChVectorDynamic	R
	residual of nonlinear system (dynamics portion)

ChVectorDynamic	Qc
	residual of nonlinear system (constraints portion)

double	Qc_scale
	factor converting the constraint residual Qc to a position-level constraint violation

double	R_nrm
	norm of the dynamics residual at the last convergence check

double	C_nrm
	norm of the position-level constraint violation at the last convergence check

double	Ds_nrm
	WRMS norm of the state update at the last convergence check.

double	Dl_nrm
	WRMS norm of the Lagrange multiplier update at the last convergence check.

std::array< double, 3 >	Ds_nrm_hist
	last 3 update norms

std::array< double, 3 >	Dl_nrm_hist
	last 3 update norms

ChVectorDynamic	ewtS
	vector of error weights (states)

ChVectorDynamic	ewtL
	vector of error weights (Lagrange multipliers)

bool	accept_terminated
	accept or reject steps after a non-converged Newton solve

bool	step_control
	step size control enabled?

unsigned int	maxiters_success
	maximum number of NR iterations to declare a step successful

unsigned int	req_successful_steps
	required number of successive successful steps for a stepsize increase

double	step_increase_factor
	factor used in increasing stepsize (>1)

double	step_decrease_factor
	factor used in decreasing stepsize (<1)

double	h_min
	minimum allowable stepsize

double	h
	internal stepsize

unsigned int	num_successful_steps
	number of successful steps

Protected Attributes inherited from chrono::ChTimestepper
bool	verbose

double	T

ChVectorDynamic	L

bool	Qc_do_clamp

double	Qc_clamping

Member Function Documentation

◆ SetAlpha()

void chrono::ChTimestepperHHT::SetAlpha ( double val )

Set the numerical damping parameter (in the [-1/3, 0] range).

The closer to -1/3, the more damping. The closer to 0, the less damping (for 0, it is the trapezoidal method). The method coefficients gamma and beta are set automatically, based on alpha. Default: -0.2.

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

/builds/uwsbel/chrono/src/chrono/timestepper/ChTimestepperHHT.h
/builds/uwsbel/chrono/src/chrono/timestepper/ChTimestepperHHT.cpp

Description

Public Member Functions

Additional Inherited Members

Member Function Documentation

◆ SetAlpha()