Proposed for presentation at the 3rd Pan American Congress on Computational Mechanics (PANACM) 2021 held November 9-12, 2021 in Online, Brazil最新文献

{"title":"The Schwarz alternating method for multi-scale coupling and contact in solid mechanics.","authors":"A. Mota, I. Tezaur, Jonathan Hoy","doi":"10.2172/1891604","DOIUrl":"https://doi.org/10.2172/1891604","url":null,"abstract":"Multi-scale methods are essential for the understanding and prediction of behavior of engineering systems when a small-scale event will eventually determine the performance of the entire system. In this talk, we will discuss a novel recently-proposed [1,2] approach that enables concurrent multi-scale coupling in finite deformation quasistatic and dynamic solid mechanics by leveraging the domain-decomposition-based Schwarz alternating method. The approach is based on the simple idea that if the solution to a partial differential equation is known in two or more regularly shaped domains comprising a more complex domain, these local solutions can be used to iteratively build a solution for the more complex domain. The proposed methodology has a number of advantages over competing multiscale coupling methods, most notably its concurrent nature, its ability to couple non-conformal meshes with different element topologies and different time integrators with different time steps for dynamic problems all without introducing non-physical artifacts into the solution, and its non-intrusive implementation into existing codes. In the first part of the talk, we will describe the formulation and theoretical properties of the Schwarz alternating method as a means for concurrent multiscale coupling in quasistatic and dynamic solid mechanics. We will show several large-scale numerical examples demonstrating the method’s numerical properties and convergence based on its implementation in two massively-parallel HPC codes: Albany/LCM and Sierra/Solid Mechanics. In the second part of the talk, we will describe some more recent work in extending the Schwarz alternating method to multi-scale contact mechanics problems. Unlike the original formulation of the method for multi-scale coupling, which relies on an overlapping domain decomposition with Dirichlet transmission conditions, the contact formulation requires a non-overlapping domain decomposition with Dirichlet-Neumann or Robin-Robin transmission conditions. After describing our Schwarz contact formulation, we will demonstrate on several collision problems that","PeriodicalId":277702,"journal":{"name":"Proposed for presentation at the 3rd Pan American Congress on Computational Mechanics (PANACM) 2021 held November 9-12, 2021 in Online, Brazil","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130074455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}