论文标题
在GSOR上，双鞍问题的广义连续过度递延方法
On GSOR, the Generalized Successive Overrelaxation Method for Double Saddle-Point Problems
论文作者
论文摘要
我们考虑了一种广义连续的超递延方法（GSOR）方法，用于解决一类三个块的鞍点问题。基于真实立方多项式的所有根的必要条件，使模量小于1，我们在合理的假设下得出收敛结果。我们还分析了从GSOR诱导的一类块下三角预处理，并为预处理的矩阵得出了明确和锋利的光谱边界。我们报告了有关液晶总监模型和耦合Stokes-Darcy流的测试问题的数值实验，证明了GSOR的有用性。
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.
