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Direct and iterative solution of the generalized dirichlet–deumann map for elliptic PDEs on square domains

Saridakis Ioannis, Sifalakis Anastasios, Papadopoulou Eleni, Fulton, Ruth, 1887-1948

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URIhttp://purl.tuc.gr/dl/dias/C27ABBA2-F64D-4A17-954B-3BD57289B9EF-
Identifierhttps://doi.org/10.1016/j.cam.2008.07.025-
Languageen-
Extent14 pagesen
TitleDirect and iterative solution of the generalized dirichlet–deumann map for elliptic PDEs on square domains en
CreatorSaridakis Ioannisen
CreatorΣαριδακης Ιωαννηςel
CreatorSifalakis Anastasiosen
CreatorΣηφαλακης Αναστασιοςel
CreatorPapadopoulou Elenien
CreatorΠαπαδοπουλου Ελενηel
CreatorFulton, Ruth, 1887-1948en
PublisherElsevieren
Content SummaryIn this work we derive the structural properties of the Collocation coefficient matrix associated with the Dirichlet–Neumann map for Laplace’s equation on a square domain. The analysis is independent of the choice of basis functions and includes the case involving the same type of boundary conditions on all sides, as well as the case where different boundary conditions are used on each side of the square domain. Taking advantage of said properties, we present efficient implementations of direct factorization and iterative methods, including classical SOR-type and Krylov subspace (Bi-CGSTAB and GMRES) methods appropriately preconditioned, for both Sine and Chebyshev basis functions. Numerical experimentation, to verify our results, is also included.en
Type of ItemPeer-Reviewed Journal Publicationen
Type of ItemΔημοσίευση σε Περιοδικό με Κριτέςel
Licensehttp://creativecommons.org/licenses/by/4.0/en
Date of Item2015-10-16-
Date of Publication2009-
SubjectTransformation, Laplaceen
Subjectlaplace transformationen
Subjecttransformation laplaceen
Bibliographic CitationA. Sifalakis, S.R. Fulton, E. P. Papadopoulou ,Y. G. Saridakis, “Direct and iterative solution of the generalized dirichlet-neumann map for linear elliptic PDEs on square domains," J, Comp. and Applied Math.,vol. 227,no.1 pp. 171-184, 2009. doi:10.1016/j.cam.2008.07.025en

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