On the $\mathcal{H}$ -LU-Based Fast Finite Element Direct Solver for 3-D Scattering Problems

The nested dissection (ND) H-LU-based fast unite element (FE) direct solver is studied for scattering by large 3-D inhomogeneous objects. The special characteristics of the admissibility condition in FE method (FEM) are demonstrated comparing with those in the moment method. A weaker admissibility condition in FEM is proposed for higher efficiency than the conventional one. A better reduction scheme is presented for electrodynamic scattering problem. Numerical experiments show that our developed ND H-LU-based FE direct solver has O(NlogN) memory complexity and O(Nlog
²
N) CPU time complexity for a quasi-static problem, but a larger and irregular complexity for an electrodynamic problem. It has been compared with other most advanced direct sparse solvers and proved to have a better performance. A large realistic scattering problem with more than 10 million unknowns is calculated, showing the capability of our proposed ND-based l·t-LU direct FEM solver.