How we test a physics engine.

A finite-element engine that gives an agent the wrong number is worse than no engine at all — the agent will trust it. So in physicsbase the test suite isn't an afterthought. It's the specification.

Most software tests check that code does what the author intended. Physics tests have a harder job: they check that the code agrees with the universe. The beautiful thing about mechanics is that for a great many problems, the universe's answer is written down in closed form — a clean formula from a textbook. A cantilever's tip deflects by \(PL^3/3EI\). A column buckles at \(\pi^2 EI/L^2\). A restrained bar heated by \(\Delta T\) carries \(-E\alpha\,\Delta T\). If the engine disagrees with the formula, the engine is wrong. Full stop.

The test is the spec

Every element and every analysis in physicsbase ships with at least one test that builds a problem whose answer is known exactly, solves it, and asserts equality to tolerance. Nothing is trusted because it "looks right." Here's a real one — Euler buckling of a pinned column:

def test_buckling_pinned():
    m, p = _column("pinned")                 # pin-ended steel column
    res = buckling(m, num_modes=1)
    expected = math.pi**2 * p["E"] * p["I"] / p["L"]**2   # Euler's Pcr
    assert res.critical_loads[0] == pytest.approx(expected, rel=1e-2)

No golden files, no "close enough by eye." The engine's returned critical load must match Euler's formula to within 1%, or the build fails.

The 53

As of this writing the suite is 53 checks, all green, spanning the whole engine:

The uniform-strain patch test deserves a special mention, because it's the cleanest idea in the whole file. Impose a displacement field corresponding to a constant strain on an element's nodes, ask the element what stress it reports, and check it equals the exact \(\mathbf{D}\!:\!\boldsymbol{\varepsilon}\). If an element passes the patch test, its strain-displacement matrix is correct — the single most important property a new element can have. Every solid element in physicsbase passes it.