Package pulse.problem.schemes.solvers

Class ExplicitLinearisedSolver

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.ExplicitScheme

pulse.problem.schemes.solvers.ExplicitLinearisedSolver

All Implemented Interfaces:

Serializable, Solver<ClassicalProblem>, Descriptive, Reflexive

public class ExplicitLinearisedSolver
extends ExplicitScheme
implements Solver<ClassicalProblem>

Performs a fully-dimensionless calculation for the LinearisedProblem.

Relies on using the heat equation to calculate the value of the grid-function at the next timestep. Fills 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 explicit scheme uses a standard 4-point template on a one-dimensional grid that utilises the following grid-function values on each step: $$Θ(x_i,t_m), Θ(x_i,t_m+1), Θ(x_i-1,t_m), Θ(x_i+1,t_m). Hence, the calculation of the grid-function at the timestep $$m+1 can be done explicitly. The derivative in the boundary conditions is approximated using a simple forward difference.

The explicit scheme is stable only if $$τ ≤ h² and has an order of approximation of $$O(τ + h). Note that this scheme is only used for validating more complex schemes and does not give accurate results due to the lower order of approximation. When calculations using this scheme are performed, the gridDensity is chosen to be at least 80, which ensures that the error is not too high (typically a 1.5E-2 relative error).

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
ExplicitLinearisedSolver()
ExplicitLinearisedSolver(NumericProperty N, NumericProperty timeFactor)
ExplicitLinearisedSolver(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.
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.
void	timeStep(int m)

Methods inherited from class pulse.problem.schemes.ExplicitScheme

explicitSolution, phi, 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

Constructor Detail

ExplicitLinearisedSolver

public ExplicitLinearisedSolver()

ExplicitLinearisedSolver

public ExplicitLinearisedSolver(NumericProperty N,
                                NumericProperty timeFactor)

ExplicitLinearisedSolver

public ExplicitLinearisedSolver(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 DifferenceScheme

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<ClassicalProblem>

Parameters:

problem - - an accepted instance of T

Throws:

SolverException

timeStep

public void timeStep(int m)

Specified by:

timeStep in class DifferenceScheme

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.