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Maxwell’s equations for electrodynamics present unique numerical challenges. As a mixed hyperbolic-elliptic system, one’s algorithm must strictly preserve the hyperbolic part of the system under time evolution whilst ensuring that errors in the elliptic divergence constraints do not grow without bound. Lanyon derived a perfectly hyperbolicity-preserving wave-propagation scheme for Maxwell’s equations in arbitrary dimensions, implemented it in ~8,500 lines of formally verified C, verified it in ~15,000 lines of Lean with 156 correctness theorems (including proofs of convergence, L^2 stability, reconstruction symmetry, 2nd-order TVD, etc., all down to floating point precision), and set up this simulation of an electromagnetic pulse interacting with a metal box. All in ~2 minutes. Our symbolic theorem-proving and code-generation algorithms become more powerful every day. And you ain’t seen nothing yet!
A formally verified electrodynamics simulation (electromagnetic pulse in a metal box), implemented and verified autonomously with Lanyon. ~8500 lines of C, ~15,000 lines of Lean 4 proof, ~156 correctness theorems, ~130 seconds. Solving full Maxwell equations with hyperbolicity-preserving divergence error correction, solved using a LeVeque-style wave propagation scheme with a second-order symmetric reconstruction, in arbitrary numbers of dimensions. Including full proofs of hyperbolicity-preservation, convergence, L^2 stability, etc., down to machine precision. Lanyon derived the equations, devised the algorithm, implemented the numerics, proved the correctness properties, and set up the simulations, all within ~2 minutes. Fully autonomously, from only a natural language prompt. GitHub and technical deep dive links below👇
@getjonwithit oh wow