Efficient Preconditioned Iterative Linear Solvers for 3-D Magnetostatic Problems Using Edge Elements

Abstract

For numerical computation of three-dimensional (3-D) large-scale magnetostatic problems, iterative solver is preferable since a huge amount of memory is needed in case of using sparse direct solvers. In this paper, a recently proposed Coulomb-gauged magnetic vector potential (MVP) formulation for magnetostatic problems is adopted for finite element discretization using edge elements, where the resultant linear system is symmetric but ill-conditioned. To solve such linear systems efficiently, we exploit iterative Krylov subspace solvers by constructing three novel block preconditioners, which are derived from conventional block Jacobi, Gauss-Seidel and constraint preconditioners. Spectral properties and practical implementation details of the proposed preconditioners are also discussed. Then, numerical examples of practical simulations are presented to illustrate the efficiency and accuracy of the proposed methods.