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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...
Matrix factorization and inversion methods based on overlapped localizing local global solution (OL-LOGOS) modes have been shown to have approximately O(N log N) or better complexity for low frequency electromagnetic problems. This efficiency of the OL-LOGOS factorization method makes it a good candidate for developing reduced order models (ROMs) for specific analysis and design tasks. This paper...
Overlapped, localizing local-global solution (OL-LOGOS) modes have been proposed to develop fast direct solvers for low frequency electromagnetic wave problems. The efficiencies of the resulting OL-LOGOS factorization algorithms have been demonstrated for the matrix equations associated with dense three-dimensional integral equations and sparse two-dimensional partial differential equations. In both...
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