Fast analysis of three-dimensional electromagnetic problems using dual-primal finite-element tearing and interconnecting method combined with ℋ-matrix technique

As a powerful variant of the dual-primal finite-element tearing and interconnecting (FETI-DP) method in electromagnetics (EM), the FETI-DPEM method shows excellent convergence properties and numerical scalability. A key factor affecting the performance of the FETI-DPEM is the direct solution of sub-domain FE systems. An efficient direct solver based on hierarchical (ℋ-) matrix technique is proposed to solve the sub-domain FE systems. ℋ-matrix formatted lower-upper (LU) decomposition with subsequent forward and backward substitution (FBS) can significantly reduce the computational costs of the direct solution with sufficient accuracy. The nested dissection technique is employed to further accelerate the ℋ-LU decomposition and the ℋ-FBS. Numerical examples demonstrate that the proposed method is very robust for the three-dimensional EM simulation.