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

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.