Updatable reduced order models for the finite element method

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 discusses how to build a reduced order model using the OL-LOGOS factorization for the finite element method (FEM). It is also shown that the resulting ROM can be rapidly updated when local changes are made to the underlying geometry. In some cases, the ROM update can be performed at a cost which scales as o(N).