Why use triangular mesh when solving poisson equation in pde toolbox?

Hello guys. I have this question when I am trying to solve poisson equation in matlab. Why use triangular mesh when solving poisson equation in pde toolbox? e.g. poisolv And how do I convert my data in rectangular mesh to triangular mesh? Because I only found the reverse, which is tri2grid(). The problem I have now is that I do not have a closed expression for the function on the right hand side. What I have is numerical, i.e. a matrix in rectangular mesh. How could I modify the fast poisson solver to satisfy my needs? Thanks!

Answer 1

[Bill Greene]

Hi,

Because your domain is rectangular, you can use the poimesh function to generate a "regular" triangular mesh on that domain-- i.e. one that looks like your rectangular mesh except each cell has a diagonal across it.

Since your f-coefficient is defined from numerical data, you will need to write a MATLAB function to define f. That is described on this page:

http://www.mathworks.com/help/pde/ug/scalar-coefficients-in-function-form.html

That page also describes how to use the pdeintrp to interpolate your numerical data from the nodes (i.e. your rectangular grid) to the centroids of the triangular elements where f must be defined.

Bill

[Max]

Hi Bill,

Thank you very much for the response! I think I am getting to understand the idea, but may I avoid defining a fixed function from the beginning? Because the right hand side is not fixed, but is gotten from measurement.

Thanks!

[Bill Greene]

You can certainly define your f-coefficient matrix and then pass that to poisolv, if you like. Or you can create a function that poisolv will call. That is described on the documentation page I listed above. For this particular example, I think one approach will work as well as the other.

Bill

[Max]

Hi Bill,

I ended up using the assempde function because the equation that i was trying to solve was exactly that form. Your answer helped a lot.

Now I am trying to define my own Dirichlet boundary condition based, again, on numerical data. The function assempde only accepts boundary condition matrix or boundary condition file, but I am confused how to customize it. Do you know how i can customize that? Thank you!

Max