2014•Keisan Rikigaku Koenkai koen ronbunshu/Keisan Rikigaku Kouenkai kouen rombunshuuOpen access

Application of the BDD Preconditioner to Domain Decomposition Analysis for Magnetostatic Problems

Hiroshi Kanayama, Masao Ogino, Shin-ichiro Sugimoto

Abstract

An iterative domain decomposition method is proposed for numerical analysis of 3-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 preconditioner. Numerical results showed that the method was only effective for smaller problems. In this paper, we consider its improvement with the Balancing Domain Decomposition (BDD) preconditioner.

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Key concepts: Preconditioner, Domain decomposition methods, Conjugate gradient method, Domain (mathematical analysis), Iterative method, Decomposition, Applied mathematics, Decomposition method (queueing theory)