{"title":"A variable order wavelet method for the sparse representation of layer potentials in the non-standard form","authors":"J. Tausch","doi":"10.1515/1569395041931473","DOIUrl":null,"url":null,"abstract":"We discuss a variable order wavelet method for boundary integral formulations of elliptic boundary value problems. The wavelet basis functions are transformations of standard nodal basis functions and have a variable number of vanishing moments. For integral equations of the second kind we will show that the non-standard form can be compressed to contain only O(N) non-vanishing entries while retaining the asymptotic converge of the full Galerkin scheme, where N is the number of degrees of freedom in the discretization.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"140 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"23","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"J. Num. Math.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/1569395041931473","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 23
Abstract
We discuss a variable order wavelet method for boundary integral formulations of elliptic boundary value problems. The wavelet basis functions are transformations of standard nodal basis functions and have a variable number of vanishing moments. For integral equations of the second kind we will show that the non-standard form can be compressed to contain only O(N) non-vanishing entries while retaining the asymptotic converge of the full Galerkin scheme, where N is the number of degrees of freedom in the discretization.