{"title":"耗散和波传播问题的高阶连续时间 Galerkin 高效并行解法","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":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":3,\"journal\":{\"name\":\"ACS Applied Electronic Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2024-06-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Electronic Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1572787\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Electronic Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1572787","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Efficient and Parallel Solution of High-Order Continuous Time Galerkin for Dissipative and Wave Propagation Problems
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.
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