{"title":"High‐order multigrid strategies for hybrid high‐order discretizations of elliptic equations","authors":"D. D. Pietro, P. Matalon, Paul Mycek, U. Rüde","doi":"10.1002/nla.2456","DOIUrl":null,"url":null,"abstract":"This study compares various multigrid strategies for the fast solution of elliptic equations discretized by the hybrid high‐order method. Combinations of h$$ h $$ ‐, p$$ p $$ ‐, and hp$$ hp $$ ‐coarsening strategies are considered, combined with diverse intergrid transfer operators. Comparisons are made experimentally on 2D and 3D test cases, with structured and unstructured meshes, and with nested and non‐nested hierarchies. Advantages and drawbacks of each strategy are discussed for each case to establish simplified guidelines for the optimization of the time to solution.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":" ","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Linear Algebra with Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/nla.2456","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This study compares various multigrid strategies for the fast solution of elliptic equations discretized by the hybrid high‐order method. Combinations of h$$ h $$ ‐, p$$ p $$ ‐, and hp$$ hp $$ ‐coarsening strategies are considered, combined with diverse intergrid transfer operators. Comparisons are made experimentally on 2D and 3D test cases, with structured and unstructured meshes, and with nested and non‐nested hierarchies. Advantages and drawbacks of each strategy are discussed for each case to establish simplified guidelines for the optimization of the time to solution.
本文比较了用混合高阶方法离散椭圆方程的各种多网格快速求解策略。考虑了h $$ h $$‐，p $$ p $$‐和hp $$ hp $$‐粗化策略的组合，并结合了不同的电网间转移算子。对二维和三维测试用例、结构化和非结构化网格、嵌套和非嵌套层次结构进行了实验比较。针对每种情况，讨论了每种策略的优缺点，以建立优化求解时间的简化准则。
期刊介绍：
Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review.
Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects.
Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.
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