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Efficient numerical solution of the generalized Dirichlet–Neumann map for linear elliptic PDEs in regular polygon domains

Saridakis Ioannis, Papadopoulou Eleni, Sifalakis Anastasios

Απλή Εγγραφή


URIhttp://purl.tuc.gr/dl/dias/2370F327-A11D-4367-93AF-9AC4CFF811EA-
Αναγνωριστικόhttps://doi.org/10.1016/j.cam.2011.12.011-
Γλώσσαen-
Μέγεθος14 pagesen
ΤίτλοςEfficient numerical solution of the generalized Dirichlet–Neumann map for linear elliptic PDEs in regular polygon domains en
ΔημιουργόςSaridakis Ioannisen
ΔημιουργόςΣαριδακης Ιωαννηςel
ΔημιουργόςPapadopoulou Elenien
ΔημιουργόςΠαπαδοπουλου Ελενηel
ΔημιουργόςSifalakis Anastasiosen
ΔημιουργόςΣηφαλακης Αναστασιοςel
ΕκδότηςElsevieren
ΠερίληψηA new and novel approach for analyzing boundary value problems for linear and for integrable nonlinear PDEs was recently introduced. For linear elliptic PDEs, an important aspect of this approach is the characterization of a generalized Dirichlet–Neumann map: given the derivative of the solution along a direction of an arbitrary angle to the boundary, the derivative of the solution perpendicularly to this direction is computed without solving on the interior of the domain. For this computation, a collocation-type numerical method has been recently developed. Here, we study the collocation’s coefficient matrix properties. We prove that, for the Laplace’s equation on regular polygon domains with the same type of boundary conditions on each side, the collocation matrix is block circulant, independently of the choice of basis functions. This leads to the deployment of the FFT for the solution of the associated collocation linear system, yielding significant computational savings. Numerical experiments are included to demonstrate the efficiency of the whole computation.en
ΤύποςPeer-Reviewed Journal Publicationen
ΤύποςΔημοσίευση σε Περιοδικό με Κριτέςel
Άδεια Χρήσηςhttp://creativecommons.org/licenses/by/4.0/en
Ημερομηνία2015-10-16-
Ημερομηνία Δημοσίευσης2012-
Θεματική ΚατηγορίαGreek mathematicsen
Θεματική Κατηγορίαmathematics greeken
Θεματική Κατηγορίαgreek mathematicsen
Βιβλιογραφική ΑναφοράY. G. Saridakis, A. Sifalakis , E. P. Papadopoulou, “Efficient numerical solution of the generalized dirichlet-neumann map for linear elliptic PDEs on regular polygon domains," J. Comp. & Applied Math.,vol. 236 ,no. 9, pp. 2515-2528, 2012. doi:10.1016/j.cam.2011.12.011en

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