Abstract
In this paper, an alternating positive semidefinite splitting (APSS) preconditioner is proposed for solving double saddle point problems. The corresponding APSS iteration method is proved to be convergent unconditionally. Moreover, to further improve its efficiency, a relaxed variant is established for the APSS preconditioner, which results in better spectral distribution and numerical performance. Numerical experiments with liquid crystal director models demonstrate the effectiveness of the APSS preconditioner and its relaxed variant when compared with other preconditioners. Comparison between the related numerical results shows that the proposed preconditioners are comparable with (though not really better than) the best existing preconditioners.
Published Version
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