The dimensional splitting iteration methods for solving saddle point problems arising from time-harmonic eddy current models

Abstract

A dimensional splitting iteration method is proposed for solving the saddle point problems arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current models, which is by making use of the special positive semidefinite splittings of the saddle point matrix. It is proved that the proposed iteration method is unconditionally convergent for both cases of simple topology and general topology. Numerical results show that the corresponding preconditioner is superior to the existing preconditioners, when those preconditioners are used to accelerate the convergence rate of Krylov subspace methods.