A numerical method for the solution of wave scattering by fractal screens

Mikael Slevinsky (Manitoba)

Fractals have surprising analytical properties when considered as screens or apertures in wave scattering problems. An optimal numerical method abstracts the self-similarity of a pre-fractal screen and assembles boundary integral operators hierarchically. In this setting, a recursive block operator factorization exploits the bounded off-diagonal numerical rank of the integral operators. This hierarchical solver involves a pre-computation independent of the incident wave. Once an integral operator is factored, the solution for multiple incident waves exhibits even lower complexity, and may even be simulated live.