A deflated iterative solver for magnetostatic finite element models with large differences in permeability

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Abstract
The presence of materials with a relative large difference in permeability has a harmful influence on the convergence of Krylov subspace iterative solvers. Some slow converging components are not cured by preconditioning and correspond to eigenvectors reflecting the domains with relatively low permeable material. Approximations for those eigenvectors are determined using physical knowledge of the problem. The iterative solution process is split up in a small problem counting for the separated eigenmodes and a full-size problem out of which the slow converging modes are removed. This deflated preconditioned solver is faster converging compared to more common approaches, such as the incomplete Cholesky conjugate gradient method.