Package pulse.problem.schemes.solvers

Class MixedLinearisedSolver

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.MixedScheme

pulse.problem.schemes.solvers.MixedLinearisedSolver

All Implemented Interfaces:

Serializable, Solver<ClassicalProblem>, Descriptive, Reflexive

public class MixedLinearisedSolver
extends MixedScheme
implements Solver<ClassicalProblem>

Performs a fully-dimensionless calculation for the LinearisedProblem.

Calls super.solve(Problem), then 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 semi-implicit scheme uses a 6-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), Θ(x_i-1,t_m+1), Θ(x_i+1,t_m+1). The boundary conditions are approximated with a Taylor expansion up to the third term, hence the scheme has an increased order of approximation.

The semi-implicit scheme is unconditionally stable and has an order of approximation of $$O(τ² + h²). Note this scheme is prone to spurious oscillations when either a high spatial resolution or a large timestep are used. It has been noticed that due to the pulse term in the boundary condition, a higher error is introduced into the calculation than for the implicit scheme.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
MixedLinearisedSolver()
MixedLinearisedSolver(NumericProperty N, NumericProperty timeFactor)
MixedLinearisedSolver(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.
double	pulse(int m)
void	solve(ClassicalProblem problem)	Calculates the solution of the t and stores it in the respective HeatingCurve.

Methods inherited from class pulse.problem.schemes.MixedScheme

toString

Methods inherited from class pulse.problem.schemes.ImplicitScheme

getTridiagonalMatrixAlgorithm, leftBoundary, setTridiagonalMatrixAlgorithm, timeStep

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, 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

MixedLinearisedSolver

public MixedLinearisedSolver()

MixedLinearisedSolver

public MixedLinearisedSolver(NumericProperty N,
                             NumericProperty timeFactor)

MixedLinearisedSolver

public MixedLinearisedSolver(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

evalRightBoundary

public double evalRightBoundary(double alphaN,
                                double betaN)

Specified by:

evalRightBoundary in class ImplicitScheme

pulse

public double pulse(int m)

Overrides:

pulse in class DifferenceScheme

firstBeta

public double firstBeta()

Specified by:

firstBeta in class ImplicitScheme

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

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.