{"title":"Caveats of three direct linear solvers for finite element analyses","authors":"Dorival M. Pedroso","doi":"10.1002/nme.7545","DOIUrl":null,"url":null,"abstract":"<p>The solution of large linear systems of equations with sparse matrices is a critical component of finite element analyses. Three linear solvers are investigated here: MUMPS, UMFPACK, and Intel DSS (PARDISO). Often, these solvers are employed as “black boxes.” However, some caveats in their implementation must be observed. For instance, the solvers may yield incorrect results or perform extremely poorly in a multithread environment. These issues are demonstrated, and suggestions to fix them are provided. Some performance benchmarks are also presented with a focus on the multithreaded behavior.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":null,"pages":null},"PeriodicalIF":2.7000,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7545","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Numerical Methods in Engineering","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/nme.7545","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The solution of large linear systems of equations with sparse matrices is a critical component of finite element analyses. Three linear solvers are investigated here: MUMPS, UMFPACK, and Intel DSS (PARDISO). Often, these solvers are employed as “black boxes.” However, some caveats in their implementation must be observed. For instance, the solvers may yield incorrect results or perform extremely poorly in a multithread environment. These issues are demonstrated, and suggestions to fix them are provided. Some performance benchmarks are also presented with a focus on the multithreaded behavior.
期刊介绍：
The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems.
The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.
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