If you have any questions, please contact q8ye@ucsd.edu

STEP 1: Generation

Generate Proper Point Cloud

1. Initialize Point Cloud

pic Domain: the gray area
Extended domain: the whole area
Interior point: points that are inside the domain
Boundary point: points that are outside the domain
Voxel: small blocks that divide the extended domain

STEP 2: Assembly

Matrix Assembly: Assign Matrix A to the Proper Point Cloud

STEP 3: Solving

Solve Equation Using Assembled Matrix

Reindex the interior points, we get a low bandwidth matrix represents the nonzero relations between interior points
Then the only remaining thing is to solve a sparse linear system

Numerical Results

Here we only put the results of the continuous coefficient matrices, because these are the most essential results.

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2d tests

3d tests