H-Matrix Accelerated Direct Matrix Solver using Chebyshev-based Nystrom Boundary Integral Equation Method

Abstract

This work introduces a fast direct computational framework based on the high-order Chebyshev Nystrom Boundary Integral Equation (CBIE) method accelerated by hierarchical matrices (H-matrix). The recently introduced CBIE offers substantially faster matrix fill than the popular Locally Corrected Nystrom (LCN) approach. Combination of the methods results in a first-in-class fast direct computational framework which is error-controllable, fast, and insensitive to poor conditioning of the pertinent matrix equations. Matrix fill, factorization, and solution times are reported for a metallic sphere, and more complicated examples such as scattering from a curvilinear NURBS-based airplane CAD model and a spiral antenna are presented to demonstrate the solver's versatility.