integrators
Class SemiExplicitAPCIntegrator

java.lang.Object
  integrators.Integrator
      integrators.SemiExplicitAPCIntegrator

public class SemiExplicitAPCIntegrator

extends Integrator

The SemiExplicitAPCIntegrator implements a custom-modified fourth-order Adams-Bashforth-Moulton predictor-corrector method, with a special way of writing the corrector formula that, dependent on the parameters of the underlying equations, allows the fixed-point iteration to converge for larger values of the partial derivatives of the system than would be possible for the straight Adams method. In a nutshell, all those terms of the derivative at y(t+h) that happen to be linear in y sub i are moved to the left hand side of the formula; then the formula is re- solved for y(t+h) to yield a partially-explicit formula. The advantage of this is that the coefficients of terms linear in y sub i now appear in the denominator of the right hand side, thus improving the likelihood that fixed-point iteration will converge for a large time step. In practice, this Integrator is typically able to take much larger time steps than the straight Adams method (even as implemented in AdamsIntegrator where convergence is assisted with a mild trick). On the other hand, if the coefficients of linear terms are not large, the Cash-Karp integration method generally takes larger time steps (although this method remains competetive because it uses fewer derivative evaluations). Like the AdamsIntegrator, this Integrator uses fourth-order Runge-Kutta steps to start off the integration or to restart it internally. See the documentation for the AdamsIntegrator for a description of the basic Adams-Bashforth-Moulton method.

Nested Class Summary

Nested classes inherited from class integrators.Integrator

Integrator.NVmatrix, Integrator.NVvector

Constructor Summary

SemiExplicitAPCIntegrator()

Method Summary

protected void	getFhatAndDfdyi(NodeValues[] fhat_vals, NodeValues[] dfdyi_vals)
void	init(Model model) Any object planning to use an Integrator of any kind MUST call its init(Model) method, which (among other things) is generally used to allocate storage arrays for the intermediates in an integration method.
float	IntegrateOneStep() Integrates across a single time step.
void	reset() Should be called after the Integrator has crossed an entire interval.

Methods inherited from class integrators.Integrator

copyNVarray, getCurrentValues, getDerivatives, getErrorEstimate, isType, setDefaultStepSize, setErrorTolerance, setFinalValues, setIntegrationValues, setStepSize

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SemiExplicitAPCIntegrator

public SemiExplicitAPCIntegrator()

Method Detail

init

public void init(Model model)

Description copied from class: Integrator

Any object planning to use an Integrator of any kind MUST call its init(Model) method, which (among other things) is generally used to allocate storage arrays for the intermediates in an integration method. This method does NOT do any numerics so does not depend on the state of the model, but it DOES need to be called after the model has been properly populated with Cells and Nodes, and needs to be called again if these change.

Overrides:

init in class Integrator

reset

public void reset()

Description copied from class: Integrator

Should be called after the Integrator has crossed an entire interval. The base class does nothing; typical subclasses will override Integrator.reset() to reset the time step size to the default value. This method is NOT used to reallocate storage; that requires a call to init().

Overrides:

reset in class Integrator

IntegrateOneStep

public float IntegrateOneStep()

Description copied from class: Integrator

Integrates across a single time step. Return value is the size of the timestep, which may differ from that specified by the calling method if the Integrator subclass adapts the step size to match error requirements.

Overrides:

IntegrateOneStep in class Integrator

getFhatAndDfdyi

protected void getFhatAndDfdyi(NodeValues[] fhat_vals,
                               NodeValues[] dfdyi_vals)