Meshless Method Lab (day 26)¶

Meshless or mesh-based: measure where each wins on your problem. Live at https://meshless.pinneapple.org. Source: apps/meshless_lab.

Smooth Poisson problem on an L-shape: RBF-FD most accurate, FEM best conditioned, Kansa cheapest to 1e-3

Describe a Poisson, Helmholtz or heat problem with a manufactured solution (or a source and boundary value), pick a domain (preset, polygon with holes, uploaded point cloud) and node spacings. Kansa, RBF-FD, finite differences on an embedded grid, linear finite elements and a PINN solve it on the same nodes; the lab reports error, cost, condition number, noise amplification and observed order, and names the winner of each criterion from the numbers.

The re-entrant corner singularity: every method drops to order ≈ 4/3

Heat on a plate with a hole: time-stepped Kansa is unstable, RBF-FD reaches 5e-7

Limits¶

2-D scalar linear problems with Dirichlet conditions; no linear elasticity or Neumann conditions yet; R-OAMS is not in the library. See the app README.

Monetization: runs, problem size and reports.