Improved Convergence in Eddy-Current Analysis by Singular Value Decomposition of Subdomain Problem

Abstract

The purpose of this study is to improve the convergence of the iterative domain decomposition method for the Interface Problem in time-harmonic eddy-current analysis. The solver applied is the $A$-$\phi$ method, which consists of the magnetic vector potential $A$ and an unknown function of the electric scalar potential $\phi$. However, it is known that the convergence of the iterative domain decomposition method deteriorates for the interface problem in analyses with large-scale numerical models. In addition, the equation obtained by the $A$-$\phi$ method is a singular linear equations. In general, iterative methods are applied to solve this equation, however it is difficult to achieve high-precision because of the truncation error. In this research, to solve this problem, a direct method using a generalized inverse matrix based on a singular value decomposition method is introduced to solve the subdomain problems. Although this increases the computational cost, high-precision arithmetic becomes possible. Here, we investigate the improvement in the convergence of the interface problem by comparing our proposed method with previous method, when applied to the standard time-harmonic eddy-current problem.