多物理场问题的有理逼近预条件

IF 1.9 4区数学 Q1 MATHEMATICS

Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-09-23 DOI:10.48550/arXiv.2209.11659

Ana Budiša, Xiaozhe Hu, M. Kuchta, Kent-A Mardal, L. Zikatanov

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引用次数: 5

摘要

我们考虑了一类描述通过接口相互作用的多物理场现象的数学模型。在这样的接口上，域的迹线(近似地)位于两个分数阶微分算子的加权和的范围内。我们使用一个有理函数近似来为这些运算符设定前提条件。我们首先证明了由分数指数加权和给出的普通函数近似的鲁棒性。此外，我们提出了更现实的例子，利用所提出的预处理技术在达西和斯托克斯方程之间的界面耦合。

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Rational approximation preconditioners for multiphysics problems

We consider a class of mathematical models describing multiphysics phenomena interacting through interfaces. On such interfaces, the traces of the fields lie (approximately) in the range of a weighted sum of two fractional differential operators. We use a rational function approximation to precondition such operators. We first demonstrate the robustness of the approximation for ordinary functions given by weighted sums of fractional exponents. Additionally, we present more realistic examples utilizing the proposed preconditioning techniques in interface coupling between Darcy and Stokes equations.

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来源期刊

Numerical Mathematics-Theory Methods and Applications 数学-数学

CiteScore

2.80

自引率

7.70%

发文量

审稿时长

>12 weeks

期刊介绍： Numerical Mathematics: Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction, analysis and application of numerical methods for solving scientific and engineering problems. Important research and expository papers devoted to the numerical solution of mathematical equations arising in all areas of science and technology are expected. The journal originates from the journal Numerical Mathematics: A Journal of Chinese Universities (English Edition). NM-TMA is a refereed international journal sponsored by Nanjing University and the Ministry of Education of China. As an international journal, NM-TMA is published in a timely fashion in printed and electronic forms.