Preconditioning of the Interface Problem in Magnetostatic Domain Decomposition Analysis

Towards Multi-part Processing

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). 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 a variant of balancing domain decomposition preconditioner (BDD-DIAG). Specially, we consider the dealing without explicit construction of Schur complement matrix towards multi-part processing.