Performing Some Laplace Experiments

So I’m looking at the sparse solver capabilities of python.

Trying a 3d poisson problem (electrostatics of a point charge) in V=0 boundary conditions

\nabla^2 \phi = \delta^3 (x)

 

isosurface

Looks like a sphere. Cool.

Using scikit-image for finding the isosurface (constant potential surface). Ripped right from their examples.

http://scikit-image.org/docs/dev/auto_examples/plot_marching_cubes.html

Note that it needs to be rescaled, since verts is in the integer index format.

Seems to work. Takes a couple seconds to finish on my macbook pro at N=25.

 

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