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Specify meshes and boundaries in NDSolveValue?

Robert Curl, Rice University
Posted 6 years ago

I am trying to solve Laplace's equations in two-dimensions in order obtain the voltage field with specified regions and boundaries. One of the regions in the problem is a half-disk. I wish to specify a voltage on the boundary of that half-disk. I do not think that I know what my problem is, but I suspect that the boundary I am generating for that half-disk is wrong.

Ultimately NDSolveValue appears to work, but does not give a plausible answer. This problem does not require much code. It would be very helpful if someone could examine it and let me know what I am doing wrong.

Attachments:
NDSolve issue.nb
POSTED BY: Robert Curl
2 Replies
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The second element in DirichletCondition should be a predicate, not a region. Something like this:

phil = NDSolveValue[{Laplacian[v[x, y], {x, y}] == 0, 
       {DirichletCondition[v[x, y] == 0., Element[{x, y}, boundary1]], 
         DirichletCondition[v[x, y] == 3000.,  Element[{x, y}, boundary2]], 
         DirichletCondition[v[x, y] == 0.,  Element[{x, y}, boundary3]]}}, 
       v,   Element[{x, y}, \[CapitalOmega]elMesh]]
POSTED BY: Gianluca Gorni

It will need some refinement, but I WORKS! THANK YOU!
POSTED BY: Robert Curl
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