On the Coarse Matrix Solver of Preconditioners for Magnetostatic Domain Decomposition Analysis

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 (NN) 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 DIAGonal scaling (BDD-DIAG) preconditioner. Specially, the coarse matrix solver is changed to an iterative solver for the first time.