Efficient multigrid solution of elliptic interface problems using viscosity-upwinded local discontinuous Galerkin methods

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-12-31 DOI:10.2140/camcos.2019.14.247

R. Saye

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引用次数: 10

Abstract

Author(s): Saye, RI | Abstract: © 2019 Mathematical Sciences Publishers. With an emphasis on achieving ideal multigrid solver performance, this paper explores the design of local discontinuous Galerkin schemes for multiphase elliptic interface problems. In particular, for cases exhibiting coefficient discontinuities several orders in magnitude, the role of viscosity-weighted numerical fluxes on interfacial mesh faces is examined: findings support a known strategy of harmonic weighting, but also show that further improvements can be made via a stronger kind of biasing, denoted herein as viscosity-upwinded weighting. Applying this strategy, multigrid performance is assessed for a variety of elliptic interface problems in 1D, 2D, and 3D, across 16 orders of viscosity ratio. These include constant-and variable-coefficient problems, multiphase checkerboard patterns, implicitly defined interfaces, and 3D problems with intricate geometry. With the exception of a challenging case involving a lattice of vanishingly small droplets, in all demonstrated examples the condition number of the multigrid V-cycle preconditioned system has unit order magnitude, independent of the mesh size h.

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椭圆界面问题的粘逆风局部不连续伽辽金法多网格解

作者:Saye, RI |摘要:©2019 Mathematical Sciences Publishers。为了达到理想的多网格解算器性能，本文研究了多相椭圆界面问题局部不连续伽辽金格式的设计。特别是，对于显示系数不连续数个数量级的情况，研究了粘度加权数值通量在界面网格面上的作用:研究结果支持已知的谐波加权策略，但也表明可以通过一种更强的偏置来进一步改进，这里表示为粘度逆风加权。应用该策略，在16阶粘度比下，对一维、二维和三维的各种椭圆界面问题进行了多网格性能评估。这些问题包括常系数和变系数问题、多相棋盘模式、隐式定义的接口和复杂几何的3D问题。除了涉及消失的小液滴晶格的具有挑战性的情况外，在所有演示的示例中，多网格v循环预处理系统的条件数具有单位数量级，与网格尺寸h无关。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.