Approximate Matrix Factorization Using Overlapped Localizing Functions on a Shifted Tree

摘要

Different types of local global solution (LOGOS) modes have been proposed to develop fast direct solvers for electromagnetic wave problems. While the non-overlapping localizing LOGOS (NL-LOGOS) factorization is provably error controllable, it is more difficult to control the factorization error when using overlapped localizing LOGOS (OL-LOGOS) modes. This paper describes a new procedure for obtaining the OL-LOGOS modes. It is shown, that the new procedure provides higher efficiency than the NL-LOGOS factorization while providing improved error control performance.