An algebraic domain decomposition algorithm for the vector finite‐element analysis of 3D electromagnetic field problems

Abstract

This Letter, proposes an algebraic domain decomposition algorithm (ADDA) to solve large sparse linear systems derived from the vector finite‐element method (FEM) for 3D electromagnetic field problems. The proposed method segments the problem into several smaller pieces, solves each subproblem by direct methods, and then reassembles the subproblem solutions together to get the global result. Block LU factorization and multifrontal method are applied to solve each subproblem for the generation of the reduced system, and iterative methods are applied to solve the reduced system. It is shown that if combined with ADDA, biconjugate gradient method (BCG) converges more rapidly than the conjugate gradient method (CG), and both of them are faster than the conventional CG method. The simulation results demonstrate that the proposed algorithm can efficiently solve large and sparse linear equations arising from the finite‐element method for the electromagnetic problems involving complex media such as perfectly matched layers (PMLs), which often make the linear equation ill‐conditioned. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 414–417, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10480

Parallel realization of algebraic domain decomposition for the vector finite element analysis of 3D time-harmonic EM field problems

“…In this scheme, the iteration number is determined by the order of the linear equations of the reduced system, but not influenced by the condition number of the linear equations in sub-domains. This algorithm combines the advantages of both iterative and direct methods [6,7], and is very suitable for parallel realization. In this paper, the whole problem is first divided into several sub-problems, then the main process sends data to interrelated processes and the multifrontal method is employed for solving intermediate equations associated with each sub-problem, after that, slaver processes send results with MPI to the main process to get global results.…”

Application of algebraic domain decomposition combined with Krylov subspace iterative methods to solve 3D vector finite element equations

“…Of the Krylov iterative methods, the conjugate gradient (CGN applied to normal equations), BCG, and GMRES methods are most popular and suitable for solving nondefinite systems. For comparison, we choose these three methods in our investigation to solve the reduced interface system and compare their efficiency when applied to our problems [18,19]. The intermediate equations associated with each subproblem can be solved with a suitable solver according to their characteristics.…”