Help with Poisson equation in irregular mesh

[tucuman87]

Hi all,

I've written a program that solves the Poisson equation in
an irregular mesh, using a finite volume discretization.

the method works well, and the solution is very good at a
distance of 2-3 mesh sizes off of the source.

The problem is that I need to know what is the contribution
of the nodes to their neighbors- a place too close to have an
accurate solution (i.e. m/r)-

my question is, how could this be calculated? or- is there
a method to impose the influence to be m/r?

Thanks in advance,
Ariel.

 

[jvicens]

Dear Ariel,

Thank you for sharing your work on solving the Poisson equation using a finite volume discretization. It is great to hear that the method is working well and producing accurate solutions.

To address your question about calculating the contribution of nodes to their neighbors, there are a few possible approaches. One option is to use a more refined mesh near the source to improve the accuracy of the solution in that region. This can help capture the influence of nearby nodes more accurately. Another option is to use a higher order discretization method, such as a higher order finite volume scheme or a finite element method, which can also improve the accuracy of the solution near the source.

Additionally, you could consider using a different type of discretization method altogether, such as a spectral method or a boundary element method, which may better capture the influence of nodes on their neighbors. It may also be helpful to analyze the convergence properties of your current method and see if there are any modifications that can be made to improve the accuracy in the region of interest.

In terms of imposing the influence to be m/r, this can be achieved by adjusting the boundary conditions or the source term in your Poisson equation. You may also want to consider using a different coordinate system that better accounts for the influence of nodes on their neighbors.

Overall, I would recommend exploring these different options and considering the specific requirements of your problem to determine the best approach for calculating the contribution of nodes to their neighbors. I hope this helps and I wish you success in your research.