A linear complexity direct finite element solver for large-scale 3-D electromagnetic analysis

A direct finite-element solver of linear complexity is developed to analyze general 3-D electromagnetic problems where conductors and dielectrics can be arbitrarily shaped, inhomogeneous, and lossy. Numerical experiments have demonstrated its superior performance over state-of-the-art direct finite-element solvers as well as an iterative finite-element solver. A linear complexity in both CPU time and memory consumption has been theoretically proved and numerically verified with controlled accuracy. The finite-element matrix of an electrodynamic problem having over 5.64 million unknowns is factorized in less than 2.5 hours on a single core running at 2.8 GHz.