tlm-certified-bounds: certified transmission-line-matrix bounds for elliptic and eddy-current field problems

Abstract

Reference implementation accompanying the paper A Certified Transmission-Line-Matrix Method for Elliptic Field Problems, and Why the Certificate Fails on Approximated Geometry. The code realises a Prager-Synge complementary pair with the two dual TLM diffusion networks, so that a passive scattering solver returns a guaranteed two-sided bound on a quantity of interest, and it reproduces every number and figure of the paper: two- and three-dimensional validation, the effectivity index, the contrast and geometry sweeps, the non-circular benchmark against a dual discrete-geometric solver, the geometric-error experiments, and the certified pad-to-substrate capacitance extraction on a package model. All source files are released under the MIT licence. Release 1.1 adds eddy_current/: guaranteed two-sided bounds on the impedance of an eddy-current coil (inductance, resistance and mutual impedances) for any approximate field, from a Raviart-Thomas equilibrated flux, with the certification of every period of a passive TLM time march, accompanying the paper Guaranteed Two-Sided Bounds on Eddy-Current Coil Impedance for Any Approximate Field, With a Passive TLM Solver and Application to Nondestructive Testing and Induction Tomography.