W. Hackbusch, Kishore Kumar Naraparaju, J. Schneider
{"title":"On the efficient convolution with the Newton potential","authors":"W. Hackbusch, Kishore Kumar Naraparaju, J. Schneider","doi":"10.1515/jnum.2010.013","DOIUrl":null,"url":null,"abstract":"Abstract The convolution , where ƒ is smooth, except for some local singularities, arises for example in electronic structure calculations. An efficient convolution with the Newton potential in d dimensions has been proposed in [Hackbusch, Numer. Math. 110: 449–489, 2008]. The convolution is approximated on a refined grid and additional approximations are introduced for efficient evaluation. This paper studies the performance of the method and a precise error analysis of the method is discussed.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"74 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"J. Num. Math.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/jnum.2010.013","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
Abstract The convolution , where ƒ is smooth, except for some local singularities, arises for example in electronic structure calculations. An efficient convolution with the Newton potential in d dimensions has been proposed in [Hackbusch, Numer. Math. 110: 449–489, 2008]. The convolution is approximated on a refined grid and additional approximations are introduced for efficient evaluation. This paper studies the performance of the method and a precise error analysis of the method is discussed.
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