A Relation of Preconditioners in Domain Decomposition Method for Magnetostatic Problems.

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]