3D Poisson equation with point source using pdetoolbox

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Arseny Sidelnickow
Arseny Sidelnickow 2022-3-12
编辑： Torsten 2022-3-12
Hello! I'm trying to solve a 3D Poisson equation with a point source using pdetoolbox, but I'm having the problem that the mesh "doesn't feel" the Dirac delta function, hence I get a null solution. The lack of RAM does not allow me to make the mesh smaller. For 2D, I found an interesting "adaptmesh" command. Is there any equivalent of this command for 3D? If not, what can be done to make the mesh "feel" the Dirac delta function?
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Torsten
Torsten 2022-3-12
编辑：Torsten 2022-3-12
You can't do anything.
In numerical simulations, a source must be a volume source, and since a point has no volume, the source cannot be represented adequately. The effect of the source will depend on the volume of the cell(s) in which you define the source.

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回答（1 个）

William Rose
William Rose 2022-3-12
@Arseny Sidelnickow,
I would replace the dirac delta function in your numerical simulation with a finite valued function over a finite (not infinitely small) area, so that the total flux out of the source is conserved, of course.

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