Fast Direct Error-Controllable Solution of Integral Equations via H,-matrix accelerated Locally Corrected Nyström Method

Abstract

Computational framework for error-controlled fast direct solution of large-scale scattering problems is demonstrated. The approach is based on higher-order Locally Corrected Nystrom (LCN) discretization of the Electric and Magnetic Field Integral Equations (EFIE and MFIE) accelerated with hierarchical matrices. The latter enable $O(N\log N)$ solutions for matrices featuring quasi-constant ranks in their compressed blocks and make solutions largely insensitive to poor conditioning of the matrix equations typically resulting from LCN discretization of EFIE and MFIE.