Sparse Matrix Factorization Using Overlapped Localizing LOGOS Modes on a Shifted Grid

Different types of local global solution (LOGOS) modes have been proposed to develop fast direct solvers for electromagnetic wave problems. While radiating LOGOS modes are suitable for high frequency problems, this paper focuses on the localizing LOGOS modes, which are suitable for low-to-mid frequency problems. Factorizations relying on non-overlapped, localizing LOGOS (NL-LOGOS) modes are provably error controllable, but fail to provide acceptable asymptotic computational efficiencies. Factorizations using overlapped, localizing LOGOS (OL-LOGOS) modes provide improved asymptotic computational performance, but have been observed to suffer from significant overhead and, in some cases, poorer error control. This paper describes a new procedure for obtaining the OL-LOGOS modes. It is observed that the asymptotic efficiency is similar to previously reported OL-LOGOS schemes while providing stable error control for standard problem formulations. The overhead associated with computing the OL-LOGOS modes is also reduced significantly.