Package pulse.problem.schemes.solvers

Class ImplicitLinearisedSolver<T extends ClassicalProblem>

java.lang.Object

pulse.util.UpwardsNavigable

pulse.util.Group

pulse.util.Accessible

pulse.util.PropertyHolder

pulse.problem.schemes.DifferenceScheme

pulse.problem.schemes.OneDimensionalScheme

pulse.problem.schemes.ImplicitScheme

pulse.problem.schemes.solvers.ImplicitLinearisedSolver<T>

Type Parameters:

T - a subclass of ClassicalProblem

All Implemented Interfaces:

Serializable, Solver<T>, Descriptive, Reflexive

public class ImplicitLinearisedSolver<T extends ClassicalProblem>
extends ImplicitScheme
implements Solver<T>

Performs a fully-dimensionless calculation for the LinearisedProblem.

Initiates constants for calculations and uses a sweep method to evaluate the solution for each subsequent timestep, filling the grid completely at each specified spatial point. The heating curve is updated with the rear-side temperature $$Θ(x_N,t_i) (here $$N is the grid density) at the end of timeLimit intervals, which comprise of timeLimit/tau time steps. The HeatingCurve is scaled (re-normalised) by a factor of maxTemp/maxVal, where maxVal is the absolute maximum of the calculated solution (with respect to time), and maxTemp is the maximumTemperature NumericProperty of problem.

The fully implicit scheme uses a standard 4-point template on a one-dimensional grid that utilises the following grid-function values on each step: $$Θ(x_i,t_m), Θ(x_i,t_m+1), Θ(x_i-1,t_m+1), Θ(x_i+1,t_m+1). Because no explicit formula can be used for calculating the grid-function at timestep $$m+1, a sweep method is implemented instead. The boundary conditions are approximated with a Taylor expansion up to the third term, hence the scheme has an increased order of approximation.

The fully implicit scheme is unconditionally stable and has an order of approximation of at least $$O(τ + h²) for both the heat equation and the boundary conditions.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected double	_2HTAU
protected double	Bi1HTAU
protected double	HH
protected double	tau

Constructor Summary

Constructors

Constructor	Description
ImplicitLinearisedSolver()
ImplicitLinearisedSolver(NumericProperty N, NumericProperty timeFactor)
ImplicitLinearisedSolver(NumericProperty N, NumericProperty timeFactor, NumericProperty timeLimit)

Method Summary

Modifier and Type	Method	Description
DifferenceScheme	copy()	Creates a DifferenceScheme, which is an exact copy of this object.
Class<? extends Problem>[]	domain()	Retrieves all problem statements that can be solved with this implementation of the difference scheme.
double	evalRightBoundary(double alphaN, double betaN)
double	firstBeta()
void	prepare(Problem problem)	Contains preparatory steps to ensure smooth running of the solver.This includes creating a DiscretePulseobject and adjusting the grid of this scheme to match the DiscretePulsecreated for this problem Finally, a heating curve is cleared from the previously calculated values.
void	solve(ClassicalProblem problem)	Calculates the solution of the t and stores it in the respective HeatingCurve.

Methods inherited from class pulse.problem.schemes.ImplicitScheme

getTridiagonalMatrixAlgorithm, leftBoundary, setTridiagonalMatrixAlgorithm, timeStep, toString

Methods inherited from class pulse.problem.schemes.OneDimensionalScheme

clearArrays, finaliseStep, getCurrentSolution, getPreviousSolution, setSolutionAt, signal

Methods inherited from class pulse.problem.schemes.DifferenceScheme

areDetailsHidden, copyFrom, getCurrentPulseValue, getDiscretePulse, getGrid, getTimeInterval, getTimeLimit, initFrom, listedKeywords, normalOperation, prepareStep, pulse, runTimeSequence, runTimeSequence, scaleSolution, set, setDetailsHidden, setGrid, setTimeInterval, setTimeLimit

Methods inherited from class pulse.util.PropertyHolder

addListener, data, describe, firePropertyChanged, getDescriptor, getListeners, getPrefix, ignoreSiblings, initListeners, isListedNumericType, isListedParameter, listedTypes, numericData, parameterListChanged, removeListeners, setPrefix, updateProperties, updateProperty

Methods inherited from class pulse.util.Accessible

accessibleChildren, genericProperties, genericProperty, numericProperties, numericProperty, property, update, update

Methods inherited from class pulse.util.Group

access, children, contents, getSimpleName, subgroups

Methods inherited from class pulse.util.UpwardsNavigable

addHierarchyListener, getHierarchyListeners, getParent, identify, removeHierarchyListener, removeHierarchyListeners, setParent, specificAncestor, tellParent

Methods inherited from class java.lang.Object

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

Field Detail

Bi1HTAU

protected double Bi1HTAU

tau

protected double tau

HH

protected double HH

_2HTAU

protected double _2HTAU

Constructor Detail

ImplicitLinearisedSolver

public ImplicitLinearisedSolver()

ImplicitLinearisedSolver

public ImplicitLinearisedSolver(NumericProperty N,
                                NumericProperty timeFactor)

ImplicitLinearisedSolver

public ImplicitLinearisedSolver(NumericProperty N,
                                NumericProperty timeFactor,
                                NumericProperty timeLimit)

Method Detail

prepare

public void prepare(Problem problem)
             throws SolverException

Description copied from class: DifferenceScheme

Contains preparatory steps to ensure smooth running of the solver.This includes creating a DiscretePulseobject and adjusting the grid of this scheme to match the DiscretePulsecreated for this problem Finally, a heating curve is cleared from the previously calculated values.

All subclasses of DifferenceScheme should override and explicitly call this superclass method where appropriate.

Overrides:

prepare in class ImplicitScheme

Parameters:

problem - the heat problem to be solved

Throws:

SolverException

solve

public void solve(ClassicalProblem problem)
           throws SolverException

Description copied from interface: Solver

Calculates the solution of the t and stores it in the respective HeatingCurve.

Specified by:

solve in interface Solver<T extends ClassicalProblem>

Parameters:

problem - - an accepted instance of T

Throws:

SolverException

firstBeta

public double firstBeta()

Specified by:

firstBeta in class ImplicitScheme

evalRightBoundary

public double evalRightBoundary(double alphaN,
                                double betaN)

Specified by:

evalRightBoundary in class ImplicitScheme

copy

public DifferenceScheme copy()

Description copied from class: DifferenceScheme

Creates a DifferenceScheme, which is an exact copy of this object.

Specified by:

copy in class DifferenceScheme

Returns:

an exact copy of this DifferenceScheme.

domain

public Class<? extends Problem>[] domain()

Description copied from class: DifferenceScheme

Retrieves all problem statements that can be solved with this implementation of the difference scheme.

Specified by:

domain in class DifferenceScheme

Returns:

an array containing subclasses of the Problem class which can be used as input for this difference scheme.