On GSOR, the Generalized Successive Overrelaxation Method for Double Saddle-Point Problems
arxiv(2022)
摘要
We consider the generalized successive overrelaxation (GSOR) method for
solving a class of block three-by-three saddle-point problems. Based on the
necessary and sufficient conditions for all roots of a real cubic polynomial to
have modulus less than one, we derive convergence results under reasonable
assumptions. We also analyze a class of block lower triangular preconditioners
induced from GSOR and derive explicit and sharp spectral bounds for the
preconditioned matrices. We report numerical experiments on test problems from
the liquid crystal director model and the coupled Stokes-Darcy flow,
demonstrating the usefulness of GSOR.
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