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Have a software that solves Helmholtz equation, can I use it for Poisson?

  1. Oct 22, 2014 #1
    I only took one class of PDE and even though I do remember the relationship between Laplace and Poisson I really do not recall Helmholtz at all. Anyways, I am trying to figure out if my software (a software I found online, FISKPACK) that solves Helmholtz equation can be used to solve Poisson equations? I mean, I understand that with Poisson, the function to the right is not necessarily related to the function itself but can we say Helmholtz is a subset of Poisson?
    Any one here can advice about a software that solves Poisson equations? I found FIShPACK and I am trying to understand it enough to use it.
    Thank you
     
  2. jcsd
  3. Oct 22, 2014 #2

    SteamKing

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    According to this website:

    http://people.sc.fsu.edu/~jburkardt/f77_src/fishpack/fishpack.html [Broken]

    FISHPACK can be used to solve Poisson equations, since the parameter lambda can be taken to be equal to zero. Note that these are two-dimensional equations only.
     
    Last edited by a moderator: May 7, 2017
  4. Oct 23, 2014 #3
    Thank you Steamking, my issue is if lambda is zero, wouldn't that reduce to Laplace instead of Poisson?
    Thanks again
     
  5. Oct 23, 2014 #4

    SteamKing

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    The Poisson equation is the same as the Laplace equation, except the RHS is not equal to zero.
     
  6. Oct 24, 2014 #5
    Thank you again SteamKing, I understand that, however if I need to solve a Poisson equation (with non zero RHS) wouldn't making lambda = 0 not be it?
     
  7. Oct 24, 2014 #6

    SteamKing

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    Look at the first page of the link to the FISHPACK routines. They are designed to solve Laplace, Poisson, and Helmholtz type equations.

    As I tried to say, the Laplace equation is ∇2φ = 0 and the Poisson equation is ∇2φ = f(x,y)

    It's the RHS of the equation which determines whether you have a Laplace or a Poisson type equation.
     
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