A multigrid-balancing preconditioner of domain decomposition methods for magnetic field problems

Abstract

A balancing domain decomposition (BDD) method is applied to magnetic field problems with a mixed variational formulation as a preconditioner of iterative domain decomposition methods (DDMs). The BDD method enables us to keep the number of iterations of the DDM even if the number of subdomains increases. However, in case of magnetic field problems with mixed variational formulation, the BDD method causes higher computational costs. In order to settle this difficulty, a kind of multigrid method is introduced into the BDD procedure.