A relation of preconditioners for magnetostatic domain decomposition analysis

Abstract

A relation of preconditioners of domain decomposition method is shown for numerical analysis of 3-Dimensional (3D) 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 small number subdomain problems. In this paper, we consider its improvement making use of 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. Finally, nonlinear processing is also tried for the first time.