{"title":"二阶有限元求解椭圆型问题的区域分解算法的块循环预条件","authors":"B. Kiss, G. Molnárka","doi":"10.1016/0956-0521(95)00039-9","DOIUrl":null,"url":null,"abstract":"<div><p>A preconditioned conjugate gradient domain decomposition method was given Refs 1 and 2 for the solution of a system of linear equations arising in the finite element method applied to the elliptic Dirichlet, Neumann and mixed boundary value problems. We have proved that the construction can be generalized<sup>2</sup> for higher order finite element method. Here we give a construction and theoretical investigation of preconditioners for second order finite elements. A method and the the results of calculation is given. The presented numerical experiments show that this preconditioner works well.</p></div>","PeriodicalId":100325,"journal":{"name":"Computing Systems in Engineering","volume":"6 4","pages":"Pages 369-376"},"PeriodicalIF":0.0000,"publicationDate":"1995-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0956-0521(95)00039-9","citationCount":"1","resultStr":"{\"title\":\"A block-circulant preconditioner for domain decomposition algorithm for the solution of the elliptic problems by second order finite elements\",\"authors\":\"B. Kiss, G. Molnárka\",\"doi\":\"10.1016/0956-0521(95)00039-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A preconditioned conjugate gradient domain decomposition method was given Refs 1 and 2 for the solution of a system of linear equations arising in the finite element method applied to the elliptic Dirichlet, Neumann and mixed boundary value problems. We have proved that the construction can be generalized<sup>2</sup> for higher order finite element method. Here we give a construction and theoretical investigation of preconditioners for second order finite elements. A method and the the results of calculation is given. The presented numerical experiments show that this preconditioner works well.</p></div>\",\"PeriodicalId\":100325,\"journal\":{\"name\":\"Computing Systems in Engineering\",\"volume\":\"6 4\",\"pages\":\"Pages 369-376\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1995-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0956-0521(95)00039-9\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computing Systems in Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0956052195000399\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computing Systems in Engineering","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0956052195000399","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A block-circulant preconditioner for domain decomposition algorithm for the solution of the elliptic problems by second order finite elements
A preconditioned conjugate gradient domain decomposition method was given Refs 1 and 2 for the solution of a system of linear equations arising in the finite element method applied to the elliptic Dirichlet, Neumann and mixed boundary value problems. We have proved that the construction can be generalized2 for higher order finite element method. Here we give a construction and theoretical investigation of preconditioners for second order finite elements. A method and the the results of calculation is given. The presented numerical experiments show that this preconditioner works well.
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