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

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Discussion Overview

The discussion revolves around the applicability of a software tool, FISKPACK, designed to solve the Helmholtz equation, for solving Poisson equations. Participants explore the relationships between these equations and the implications of certain parameters within the software.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether FISKPACK, which solves the Helmholtz equation, can also be used for Poisson equations, noting the difference in the right-hand side (RHS) of the equations.
  • Another participant suggests that FISKPACK can solve Poisson equations by setting the parameter lambda to zero, but this raises questions about whether this reduces the equation to Laplace instead of Poisson.
  • There is a clarification that the Poisson equation differs from the Laplace equation primarily due to the non-zero RHS.
  • Participants express uncertainty about the implications of setting lambda to zero and its effect on the type of equation being solved.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether setting lambda to zero in FISKPACK allows for the solution of Poisson equations, as there is confusion about the relationship between the equations involved.

Contextual Notes

There is an ongoing discussion about the definitions and relationships between Laplace, Poisson, and Helmholtz equations, particularly regarding the role of the RHS and the parameter lambda in the software.

Amani_lama112
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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
 
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Amani_lama112 said:
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

According to this website:

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

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:
Thank you Steamking, my issue is if lambda is zero, wouldn't that reduce to Laplace instead of Poisson?
Thanks again
 
Amani_lama112 said:
Thank you Steamking, my issue is if lambda is zero, wouldn't that reduce to Laplace instead of Poisson?
Thanks again

The Poisson equation is the same as the Laplace equation, except the RHS is not equal to zero.
 
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?
 
Amani_lama112 said:
Thank you Steamking, my issue is if lambda is zero, wouldn't that reduce to Laplace instead of Poisson?
Thanks again

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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