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Robust isogeometric preconditioners for the Stokes system based on the Fast Diagonalization method

机译:基于快速对角化方法的Stokes系统鲁棒等几何预处理器

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In this paper we propose a new class of preconditioners for the isogeometric discretization of the Stokes system. Their application involves the solution of a Sylvester-like equation, which can be done efficiently thanks to the Fast Diagonalization method. These preconditioners are robust with respect to both the spline degree and mesh size. By incorporating information on the geometry parametrization and equation coefficients, we maintain efficiency on non-trivial computational domains and for variable kinematic viscosity. In our numerical tests we compare to a standard approach, showing that the overall iterative solver based on our preconditioners is significantly faster. (C) 2018 Elsevier B.V. All rights reserved.
机译:在本文中,我们为Stokes系统的等几何离散化提出了一类新的预处理器。它们的应用涉及一个类似于Sylvester方程的解决方案,这要归功于快速对角化方法。这些预处理器在样条度和网格大小方面都非常强大。通过合并有关几何参数化和方程系数的信息,我们在非平凡的计算域和可变运动粘度上保持了效率。在我们的数值测试中,我们与标准方法进行了比较,结果表明,基于预处理器的整体迭代求解器的速度明显更快。 (C)2018 Elsevier B.V.保留所有权利。

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