Calderon and Hierarchically Preconditioned Time Domain Integral Equation Solvers

Eric Michielssen
University of Michigan

ABSTRACT:
Marching on in time integral equation solvers provide an appealing avenue
 for analyzing transient electromagnetic interactions with large
 and complex structures. Unfortunately, these solvers often suffer from temporal
 (low-frequency) and spatial (dense-mesh) breakdown phenomena  when applied to
 the analysis of low- to medium-frequency electromagnetic transients on
 geometrically intricate and multiscale structures.  This presentation
 highlights the recent development of two quasi-analytical preconditioners
 that address these breakdown phenomena by leveraging hierarchical basis
 functions and time domain Calderon identities, respectively. The proposed
 solvers are shown to robustly and seamlessly apply to important
 engineering problems that span multiple temporal and spatial scales.