H-LU-Based Fast Finite Element Direct Solver for 3D Scattering Problems

Abstract

The nested dissection (ND) H-LU-based fast finite element (FE) direct solver is studied for scattering by large 3D inhomogeneous objects. The mechanism of this fast FE direct solver is elucidated in reducing computational complexity from practical engineering point of view. The special characteristics of the admissibility condition in FEM are demonstrated comparing with those in the moment method. A weaker admissibility condition in FEM is proposed for higher efficiency than the conventional admissibility condition. The difference of numerical performance of this fast FE direct solver is in detail presented in reducing computational complexity for electrodynamic and quasi-static problems. Numerical experiments show that the H-LU has O(NlogN) memory complexity and O(Nlog2N) CPU time complexity for a quasi-static problem, but has a larger and irregular complexity for an electrodynamic problem. A large realistic scattering problem is calculated, showing the capability of our proposed ND based H-LU direct FEM solver.