# Finite Difference Solution to Poisson's Equation on Irregular Domain

• Morberticus
In summary, the conversation is about finding open source C or Fortran libraries for solving 3D Poisson's equation on an irregular domain. The person is having difficulty finding them and asks for any papers or recipes that could help them write their own. The expert recommends using the FISHPACK library for regular domains, but suggests looking for a finite element or finite volume code for solving in arbitrary regions. They also remind the person that Google can be a useful resource for finding these codes.
Morberticus
Hi,

Are there any open source C or Fortran libraries for solving 3D Poisson'sequation on an irrefular domain? I'm having difficulty finding them.

If not, is there any papers or recipes that would be useful so I could write my own? Speed is not a priority, I just need anything that works.

Thanks

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

The FISHPACK library should give you a good starting point.

Last edited by a moderator:
SteamKing said:
The FISHPACK library should give you a good starting point.

... except it only handles regular domains and grids (in several different coordinate systems).

If you want to solve in a completely arbitrary region, I would look for a finite element or finite volume code. Google is your friend, again.

## 1. What is Poisson's Equation?

Poisson's Equation is a partial differential equation that describes the relationship between a function and its sources in a given domain. It is commonly used in fields such as physics and engineering to model physical systems.

## 2. What is the Finite Difference Method?

The Finite Difference Method is a numerical technique used to approximate solutions to differential equations. It involves replacing the derivatives in the equation with discrete approximations, which can then be solved using matrix methods.

## 3. How is the Finite Difference Method used to solve Poisson's Equation on an Irregular Domain?

In order to solve Poisson's Equation on an irregular domain using the Finite Difference Method, the domain must first be discretized into a grid of points. Then, the discrete approximation of the equation can be solved using matrix methods, taking into account the irregularities of the domain.

## 4. What are the advantages of using the Finite Difference Method to solve Poisson's Equation?

The Finite Difference Method is relatively easy to implement and can handle complex domains and boundary conditions. It also provides a fast and accurate solution to Poisson's Equation compared to other numerical methods.

## 5. What are the limitations of using the Finite Difference Method for solving Poisson's Equation?

The accuracy of the Finite Difference Method can be affected by the size of the grid used and the complexity of the domain. It also may not be suitable for problems with discontinuous solutions or domains with sharp corners.

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