{"title":"Efficient and Parallel Solution of High-Order Continuous Time Galerkin for Dissipative and Wave Propagation Problems","authors":"Zhiming Chen, Yong Liu","doi":"10.1137/23m1572787","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Scientific Computing, Volume 46, Issue 3, Page A2073-A2100, June 2024. <br/> Abstract. We propose efficient and parallel algorithms for the implementation of the high-order continuous time Galerkin method for dissipative and wave propagation problems. By using Legendre polynomials as shape functions, we obtain a special structure of the stiffness matrix that allows us to extend the diagonal Padé approximation to solve ordinary differential equations with source terms. The unconditional stability, [math] error estimates, and [math] superconvergence at the nodes of the continuous time Galerkin method are proved. Numerical examples confirm our theoretical results.","PeriodicalId":49526,"journal":{"name":"SIAM Journal on Scientific Computing","volume":"26 1","pages":""},"PeriodicalIF":3.0000,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Scientific Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1572787","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Scientific Computing, Volume 46, Issue 3, Page A2073-A2100, June 2024. Abstract. We propose efficient and parallel algorithms for the implementation of the high-order continuous time Galerkin method for dissipative and wave propagation problems. By using Legendre polynomials as shape functions, we obtain a special structure of the stiffness matrix that allows us to extend the diagonal Padé approximation to solve ordinary differential equations with source terms. The unconditional stability, [math] error estimates, and [math] superconvergence at the nodes of the continuous time Galerkin method are proved. Numerical examples confirm our theoretical results.
期刊介绍：
The purpose of SIAM Journal on Scientific Computing (SISC) is to advance computational methods for solving scientific and engineering problems.
SISC papers are classified into three categories:
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