A Balancing Domain Decomposition Method for Magnetostatic Problems with a Multigrid Strategy

A balancing domain decomposition (BDD) method is considered as a preconditioner of the iterative domain decomposition method (DDM) for magnetostatic problems. The BDD method enables us to keep convergence properties of the iterative DDM even if the number of subdomains increases. However, in case of magnetostatic problems, the dimension of the coarse problem required in the BDD procedure depends on the number of nodal points of the discretization based on the finite element method. This fact causes that computational costs increase as computational models become larger. Therefore, to reduce the computational costs, a kind of multigrid strategy is introduced into the BDD procedure.