Sparsified Adaptive Cross Approximation Algorithm for Accelerated Method of Moments Computations

Abstract

This paper presents a modification of the adaptive cross approximation (ACA) algorithm for accelerated solution of the Method of Moments linear system for electrically large radiation and scattering problems. As with ACA, subblocks of the impedance matrix that represent the interaction between well separated subdomains are substituted by “compressed” approximations allowing for reduced storage and accelerated iterative solution. The modified algorithm approximates the original subblocks with products of sparse matrices, constructed with the aid of the ACA algorithm and of a sub-sampling of the original basis functions belonging to either subdomain. Because of the sampling, an additional error is introduced with respect to ACA, but this error is controllable. Just like ordinary ACA, sparsified ACA is kernel-independent and needs no problem-specific information, except for the topology of the basis functions. As a numerical example, RCS computations of the NASA almond are presented, showing an important gain in efficiency. Furthermore, the numerical experiment reveals a computational complexity close to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> log <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> for sparsified ACA for a target electrical size of up to 50 wavelengths.