Demo Gallery: Finite Element Solver
This is a finite-element solver built from scratch in Python for PDEs and structural mechanics, with applications including stress analysis, heat/wave propagation, buckling, and topology optimization. Includes the full numerical pipeline: geometry and mesh generation, element formulation and assembly, sparse linear/eigenvalue solvers, error estimation and adaptive refinement, and convergence validation. Every demo below comes with the code that produced it.
16 of 16 rendered, by examples/cli.py gallery, on every push to main.
Meshing & solving PDEs
Solids & structures
linear_elastic
A cantilever under a tip load in 2D and 3D, with four stress invariants of the 2D solve.
elasticity_models
One clamped block stretched by a linear solve, by energy minimisation, and by two finite-strain material laws; then the same stretch walked up from zero, so the force-stretch curve separates the laws quantitatively.
stress_concentration
A plate with a hole, from outline to the stress concentration at its rim, against Kirsch and Howland.
pressurized_cylinder
A thick-walled cylinder pressurized past first yield: the plastic front marches outward through the wall, tracked against Hill's classical solution.
bracket
The stress at an L-bracket's inner corner, sharp and filleted, as the mesh refines into it.
buckling
Buckling loads and modes of a slender column, checked against Euler's column formula.
modalanimated
Natural frequencies and modes of a steel tuning fork meshed from its outline, against beam theory; then the fork struck and ringing down.
topology_optimizationanimated
SIMP topology optimization of a beam to half its material, compared with the solid beam.
Accuracy & performance
