Deep dives on the finite-element method, multiphysics, validation, and what it takes to make simulation something an agent can simply call.

The moving heat source behind welding and 3D-printed metal: a travelling melt pool with a comet tail of heat. Solved on physicsbase's transient field engine and checked against Rosenthal's classic solution.
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The eXtended Finite Element Method on physicsbase: a crack that cuts straight through elements, no remeshing. K₁ recovered from the energy release rate — within 1.5% of the handbook.

Two physics in a loop: the single-edge-notched fracture benchmark, coupling physicsbase's structural and field solvers to watch a crack propagate on its own.

The classic SIMP topology-optimization method on the engine — an FE solve wrapped in an optimization loop. The iconic optimized cantilever, with the complete code.
How a single scalar-field solver does heat conduction, mass diffusion, potential flow, and transport — and why they're all the same equation wearing different labels.
Every element and analysis is checked against a closed-form answer — the test suite is the spec. A tour of the 59 validations that keep the engine honest.