Package by.andd3dfx.math.pde.solver

Class AbstractEquationSolver<E extends Equation>

java.lang.Object

by.andd3dfx.math.pde.solver.AbstractEquationSolver<E>

Type Parameters:

E - the type of equation this solver handles

All Implemented Interfaces:

EquationSolver<E>

Direct Known Subclasses:

HyperbolicEquationSolver, ParabolicEquationSolver

public abstract class AbstractEquationSolver<E extends Equation>
extends Object
implements EquationSolver<E>

Abstract base class for partial differential equation solvers. Provides common functionality and utility methods used by specific equation solvers. Implements the core numerical methods and algorithms shared across different types of PDE solvers.

See Also:

• Equation
• EquationSolver

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final record	AbstractEquationSolver.KappaNu	Record class to store boundary condition parameters for the tridiagonal algorithm.

Constructor Summary

Constructors

Constructor	Description
AbstractEquationSolver()

Method Summary

Modifier and Type	Method	Description
protected Area	buildArea(Equation eqn, double h, double tau)	Builds a space-time computational domain for the equation solution.
protected AbstractEquationSolver.KappaNu	calcKappaNu(BorderCondition borderCondition, double h, double time)	Calculates Kappa and Nu parameters for the tridiagonal algorithm based on boundary conditions.
protected Matrix2D	prepare(Equation eqn, Area area)	Initializes the solution matrix with initial conditions.
static double[]	solve3DiagonalEquationsSystem(double[] A, double[] B, double[] C, double[] F, AbstractEquationSolver.KappaNu leftCond, AbstractEquationSolver.KappaNu rightCond)	Solves a tridiagonal system of linear algebraic equations using the Thomas algorithm.

Methods inherited from class java.lang.Object

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

Methods inherited from interface by.andd3dfx.math.pde.solver.EquationSolver

solve

Constructor Details

AbstractEquationSolver

public AbstractEquationSolver()

Method Details

buildArea

protected Area buildArea(Equation eqn,
 double h,
 double tau)

Builds a space-time computational domain for the equation solution. Creates a grid with specified spatial and temporal step sizes.

Parameters:

eqn - the equation to solve

h - spatial step size (must be positive)

tau - temporal step size (must be positive)

Returns:

the computational domain with defined grid points

Throws:

IllegalArgumentException - if parameters h or tau are non-positive

prepare

protected Matrix2D prepare(Equation eqn,
 Area area)

Initializes the solution matrix with initial conditions. Creates a matrix to store the solution and sets the initial values based on the equation's initial condition.

Parameters:

eqn - the equation to solve

area - the computational domain where solution will be found

Returns:

initialized matrix with initial conditions

solve3DiagonalEquationsSystem

public static double[] solve3DiagonalEquationsSystem(double[] A,
 double[] B,
 double[] C,
 double[] F,
 AbstractEquationSolver.KappaNu leftCond,
 AbstractEquationSolver.KappaNu rightCond)

Solves a tridiagonal system of linear algebraic equations using the Thomas algorithm. The system has the form: A[i]*y[i-1] - C[i]*y[i] + B[i]*y[i+1] = -F[i], 0<i<N

The algorithm consists of two phases:

1. Forward phase: computes coefficients Alpha[i] and Beta[i]
2. Backward phase: computes the solution Y[i]

Variable notations follow "Tikhonov, Samarskii - Equations of Mathematical Physics", p.590-592

Parameters:

A - coefficients for y[i-1] terms

B - coefficients for y[i+1] terms

C - coefficients for y[i] terms

F - right-hand side terms

leftCond - left boundary condition parameters

rightCond - right boundary condition parameters

Returns:

solution vector Y[i]

Throws:

IllegalArgumentException - if arrays have different lengths or invalid coefficients

calcKappaNu

protected AbstractEquationSolver.KappaNu calcKappaNu(BorderCondition borderCondition,
 double h,
 double time)

Calculates Kappa and Nu parameters for the tridiagonal algorithm based on boundary conditions. These parameters are used to incorporate different types of boundary conditions into the solution.

Parameters:

borderCondition - the boundary condition to process

h - spatial step size

time - current time point

Returns:

KappaNu record containing calculated parameters

Throws:

IllegalStateException - if an unsupported boundary condition type is encountered