steppers Package Documentation

This page contains the steppers Package documentation.

The steppers Package

fipy.steppers.L1error(var, matrix, RHSvector)

Parameters :

• var: The CellVariable in question.
• matrix: (ignored)
• RHSvector: (ignored)

Returns :

where is the -norm of .

fipy.steppers.L2error(var, matrix, RHSvector)

Parameters :

• var: The CellVariable in question.
• matrix: (ignored)
• RHSvector: (ignored)

Returns :

where is the -norm of .

fipy.steppers.LINFerror(var, matrix, RHSvector)

Parameters :

• var: The CellVariable in question.
• matrix: (ignored)
• RHSvector: (ignored)

Returns :

where is the -norm of .

fipy.steppers.error(var, matrix, RHSvector, norm)

Parameters :

• var: The CellVariable in question.
• matrix: (ignored)
• RHSvector: (ignored)
• norm: A function that will normalize its array argument and return a single number

Returns :

where is the normalization of provided by norm().

fipy.steppers.residual(var, matrix, RHSvector)

Determines the residual for the current solution matrix and variable.

Parameters :

• var: The CellVariable in question, prior to solution.
• matrix: The coefficient matrix at this step/sweep
• RHSvector: The

Returns :

where is the -norm of .

fipy.steppers.sweepMonotonic(fn, *args, **kwargs)

Repeatedly calls fn(*args, **kwargs)() until the residual returned by fn() is no longer decreasing.

Parameters :

• fn: The function to call
• args: The unnamed function argument list
• kwargs: The named function argument dict

Returns :

the final residual

The pidStepper Module

class fipy.steppers.pidStepper.PIDStepper(vardata=(), proportional=0.075, integral=0.175, derivative=0.01)

Bases: fipy.steppers.stepper.Stepper

Adaptive stepper using a PID controller, based on:

@article{PIDpaper,
   author =  {A. M. P. Valli and G. F. Carey and A. L. G. A. Coutinho},
   title =   {Control strategies for timestep selection in finite element
              simulation of incompressible flows and coupled
              reaction-convection-diffusion processes},
   journal = {Int. J. Numer. Meth. Fluids},
   volume =  47,
   year =    2005,
   pages =   {201-231},
}

The pseudoRKQSStepper Module

class fipy.steppers.pseudoRKQSStepper.PseudoRKQSStepper(vardata=(), safety=0.9, pgrow=-0.2, pshrink=-0.25, errcon=0.000189)

Bases: fipy.steppers.stepper.Stepper

Adaptive stepper based on the rkqs (Runge-Kutta “quality-controlled” stepper) algorithm of numerixal Recipes in C: 2nd Edition, Section 16.2.

Not really appropriate, since we’re not doing Runge-Kutta steps in the first place, but works OK.

The stepper Module

class fipy.steppers.stepper.Stepper(vardata=())

static failFn(vardata, dt, *args, **kwargs)

step(dt, dtTry=None, dtMin=None, dtPrev=None, sweepFn=None, successFn=None, failFn=None, *args, **kwargs)

static successFn(vardata, dt, dtPrev, elapsed, *args, **kwargs)

static sweepFn(vardata, dt, *args, **kwargs)