Class PoissonEquation2D

  • All Implemented Interfaces:
    PDE

    public class PoissonEquation2D
    extends Object
    implements PDE
    Poisson's equation is an elliptic PDE that takes the following general form. \[ \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = f(x, y) \] with Dirichlet boundary conditions: \[ u(0, y) = g(0, y) \\ u(a, y) = g(a, y) \\ u(x, 0) = g(x, 0) \\ u(x, b) = g(x, b) \] assuming that the domain of the independent variables is a rectangular region in the x-y plane.

    Note that LaPlace's equation emerges as a special case when \(f(x, y) = 0\).

    See Also:
    Wikipedia: Poisson's equation
    • Constructor Detail

      • PoissonEquation2D

        public PoissonEquation2D​(double a,
                                 double b,
                                 BivariateRealFunction f,
                                 BivariateRealFunction g)
        Constructs a Poisson's equation problem.
        Parameters:
        a - the region of interest (0, a)
        b - the region of interest (0, b)
        f - the forcing term in the equation f(x, y)
        g - the Dirichlet boundary condition g(x, y)
    • Method Detail

      • a

        public double a()
        Gets the width (x-axis) of the rectangular region.
        Returns:
        the x size of the region
      • b

        public double b()
        Gets the height (y-axis) of the rectangular region.
        Returns:
        the y size of the region
      • f

        public double f​(double x,
                        double y)
        The forcing term.
        Parameters:
        x - the first independent variable
        y - the second independent variable
        Returns:
        f(x, y), the forcing function
      • g

        public double g​(double x,
                        double y)
        The boundary value function. These are Dirichlet (or first-type) boundary conditions.
        Parameters:
        x - the first independent variable
        y - the second independent variable
        Returns:
        g(x, y), the boundary condition