A Local Positive (Semi)Definite Shift-Splitting Preconditioner for Saddle Point Problems with Applications to Time-Harmonic Eddy Current Models

Abstract

A local positive (semi)definite shift-splitting preconditioner for non-Hermitian saddle point problems arising in finite element discretisations of hybrid formulations of time-harmonic eddy current models is constructed. The convergence of the corresponding iteration methods is proved and the spectral properties of the associated preconditioned saddle point matrices are studied. Numerical experiments show the efficiency of the proposed preconditioner for Krylov subspace methods.