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

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Max
Max 2013-12-30
评论： Max 2014-1-27
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!

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Bill Greene
Bill Greene 2013-12-30
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
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Bill Greene
Bill Greene 2013-12-31
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
Max 2014-1-27
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

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