Fast Multilevel Computation of Low-Rank Representation of ${\mathcal{ H}}$ -Matrix Blocks

A physics-based algorithm for accelerating the computation of method of moments matrix blocks' low-rank approximation is presented. The algorithm relies on efficient sampling of phase- and amplitude-compensated interactions using nonuniform grids. Rank-revealing analysis is applied, in a multilevel fashion, to matrices of reduced column and row dimensions that describe subdomains' interactions with these coarse grids, rather than to the original matrix blocks. As a result, significant savings are achieved, especially for the inherently more compressible dynamic quasi-planar and quasi-static cases. The algorithm's reduced storage and computation time requirements are estimated analytically and verified numerically for representative examples.