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2d Laplace equation in a 1/4 plane

  1. Oct 17, 2008 #1
    I wish to approximate the Laplace PDE in a 1/4 plane by truncation of the domain in (x,y) variables:

    U_xx + U_yy = 0

    Now the PDE is approximated in a box [0, xMax] X [0, yMax] and I can solve it using finite differences.

    But the problems are:

    1. How to choose xMAx, yMax appropriately
    2. What boundary conditions (if any) at xMax, yMax

  2. jcsd
  3. Oct 26, 2008 #2
    Another option I am using is to transform the 1/4 plane domain in which Laplace PDE is defined into a unit square, for example using the transformation:

    z1 = tanh(x)
    z2 = tanh(y)

    We then get a convection-diffusion PDE in z1 and z2.

    Does anyone know of any sources to this approach?

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