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An iterative domain decomposition method is proposed for numerical analysis of three-dimensional (3D) linear magnetostatic problems taking the magnetic vector potential as an unknown function. The iterative domain decomposition method is combined with the preconditioned conjugate gradient (PCG) procedure and the hierarchical domain decomposition method (HDDM) which is adopted in parallel computing. Our previously employed preconditioner was the Neumann–Neumann (NN) preconditioner. Numerical results showed that the method was only effective for problems with a small number of subdomains. In this paper, we show its improvement with the balancing domain decomposition diagonal scaling (BDD-DIAG) preconditioner and show the asymptotic equivalence between BDD-DIAG and the simplified diagonal scaling (diag) preconditioner, which is derived from the following numerical evidences. [ABSTRACT FROM AUTHOR]

This paper describes a large-scale 3D magnetostatic analysis using the Domain Decomposition Method (DDM). To improve the convergence of an interface problem of DDM, DDM based on the Conjugate Residual (CR) method or the MINimal RESidual (MINRES) method is proposed. The CR or MINRES method improves convergence rate and shows stable convergence behavior in solving the interface problem, compared with the Conjugate Gradient (CG) method, and reduces the computation time for a large-scale problem with 100 million degrees of freedom. [ABSTRACT FROM AUTHOR]

Effectiveness of the A-Φ method in a parallel computing with an iterative domain decomposition method is considered. Convergence of interface problems is faster with the electric scalar potential than without it. A simple model is considered as a numerical example. [ABSTRACT FROM AUTHOR]