A numerical study of iterative substructuring method for finite element analysis of high frequency electromagnetic fields

Abstract

This paper describes iterative methods for the high frequency electromagnetic analysis using the finite element method of Maxwell equations including displacement current. The conjugate orthogonal conjugate gradient method has been widely used to solve a complex symmetric system. However, the conventional method suffers from oscillating convergence histories in large-scale analysis. In this paper, to solve large-scale complex symmetric systems arising from the formulation of the E method, an iterative substructuring method like the minimal residual method is presented, and the performance of the convergence of the method is evaluated by numerical results. As the result, the proposed method shows a stable convergence behavior and a fast convergence rate compared to other iterative methods.

Parallel Finite Element Approach for large Thermal Problems Applied to Glass Bending Furnace

“…Many methods and algorithms of iterative sub-structuring methods are proposed in literature [1]- [9]. These methods and algorithms all have a common logical ladder and are similar in handling a large problem numerically.…”

Microwave analysis based on parallel finite element method

“…In the present study, we use the domain decomposition method (DDM) as a parallel calculation method for large-scale analysis [10]. In the domain decomposition method, the analysis domain is first divided into several subdomains.…”

“…The iterative domain decomposition method applied to the parallel electromagnetic field analysis code is developed in the present study, and parallel computation is realized by multiple computers using the hierarchical domain decomposition method [5,10]. In the hierarchical domain decomposition method, the analysis domain is first divided into several domains called Parts, which are further divided into subdomains, so that the domain decomposed data has a hierarchical structure.…”

A COMINRES‐QLP method for solving complex symmetric linear systems

“…COMINRES‐QLP is distinct in that unnecessary iterations are reduced for well‐contitioned problems, while high accuracy solutions can be expected for ill‐conditioned problems; thus, two well‐conditioned problems and one ill‐conditioned problem were used in verification. Specifically, the well‐posed problems were two kinds of complex symmetric matrices selected from SuiteSparse Matrix Collection 20 ; the ill‐posed problem was coefficient matrix TEAM29_1 MHz 12 generated through high frequency electromagnetic field FEM analysis of TEAM Workshop Problem 29 model with a dielectric phantom at 1 MHz. All test matrices are described in Table 3.…”

“…The second type pertains to methods aimed at complex symmetrical problems using matrix symmetry. Examples are conjugate orthogonal conjugate gradient (COCG) method, 9 conjugate A‐orthogonal conjugate residual (COCR) method, 10 QMR_SYM (symmetric version of QMR), 11 MINRES_like_CS method, 12 CSYM method, 13 and CS‐MINRES‐QLP method 14 . These methods are basically extensions of CG, CR, MINRES, and SYMMLQ for real symmetric systems, and their computational cost is of the same order as that of the respective original methods, except for CS‐MINRES‐QLP.…”