Low Rank Direct Finite Element Solvers

A low-rank direct domain decomposition method (LR-D
³
M) is proposed. The proposed method couples the memory efficient direct domain decomposition method with single-level rank-revealing numerical linear algebra algorithms to produce a scalable direct solver suitable for the finite element (FEM) analysis of Maxwell's equations in the frequency domain. Through numerical experiments, the method was found to be error controllable with low memory footprint and approximate
$O(N^{1.5})$
factorization complexity in both memory and time for 3D problems of increasing electrical size up to 6.2 million unknowns.