Multilevel compressed block decomposition–based finite‐element domain decomposition method for the fast analysis of finite periodic structures

Abstract

An efficient finite‐element domain decomposition method based on the multilevel compressed block decomposition (MLCBD) algorithm is presented. The dual‐primal finite element tearing and interconnecting (FETI‐DP) method is first introduced to generate a nonoverlapping domain decomposition method with good convergence properties. A second‐order transmission condition is adopted to further accelerate the convergence rate of the FETI‐DP. With the MLCBD algorithm, the computational complexity for the direct solution of FETI‐DP subdomain equations can be reduced to be almost logarithmic linear. The accuracy of the MLCBD algorithm is highly adjustable according to practical requirements. Exploiting the repetitiveness of finite periodic structures, the proposed method can significantly reduce the computational costs. Numerical examples demonstrate the effectiveness of the proposed method for the electromagnetic simulation of finite periodic structures.