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

In summary, the conversation discusses using a software called FISHPACK to solve Poisson equations, but there is confusion about whether the software can also be used for Helmholtz equations. The experts clarify that FISHPACK can solve both types of equations, with the only difference being the parameter lambda. The conversation also mentions that FISHPACK is only designed for two-dimensional equations.
  • #1
Amani_lama112
3
0
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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  • #2
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.
 
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  • #3
Thank you Steamking, my issue is if lambda is zero, wouldn't that reduce to Laplace instead of Poisson?
Thanks again
 
  • #4
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.
 
  • #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?
 
  • #6
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.
 

1. Can a software that solves Helmholtz equation also be used for Poisson equation?

Yes, a software that solves Helmholtz equation can also be used for Poisson equation because both equations are partial differential equations that are closely related and have similar solution methods.

2. Are there any differences between solving Helmholtz and Poisson equations?

While both equations have similar solution methods, there are some key differences. Helmholtz equation involves a complex-valued parameter and has a non-zero right-hand side, while Poisson equation has a real-valued parameter and may have a zero or non-zero right-hand side.

3. Can I use the same numerical methods to solve both equations?

Yes, many numerical methods used for solving Helmholtz equation can also be applied to Poisson equation. However, some methods may be more efficient or accurate for one equation compared to the other, so it is important to consider the specific problem at hand when choosing a method.

4. Will the same software be able to handle both equations or do I need separate software for each?

It depends on the capabilities of the software. Some software may be designed to handle both Helmholtz and Poisson equations, while others may only be able to solve one or the other. It is important to check the features and specifications of the software to determine if it can handle both equations.

5. Are there any limitations to using a software for both Helmholtz and Poisson equations?

There may be some limitations, depending on the specific software and equations. For example, some software may only be able to handle certain boundary conditions or may have limitations on the size or complexity of the problem. It is important to thoroughly test and validate the software for the specific problem before relying on it for a solution.

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