Ιδρυματικό Αποθετήριο
Πολυτεχνείο Κρήτης
Πολυτεχνείο Κρήτης
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| URI | http://purl.tuc.gr/dl/dias/2370F327-A11D-4367-93AF-9AC4CFF811EA | - |
| Αναγνωριστικό | https://doi.org/10.1016/j.cam.2011.12.011 | - |
| Γλώσσα | en | - |
| Μέγεθος | 14 pages | en |
| Τίτλος | Efficient numerical solution of the generalized Dirichlet–Neumann map for linear elliptic PDEs in regular polygon domains | en |
| Δημιουργός | Saridakis Ioannis | en |
| Δημιουργός | Σαριδακης Ιωαννης | el |
| Δημιουργός | Papadopoulou Eleni | en |
| Δημιουργός | Παπαδοπουλου Ελενη | el |
| Δημιουργός | Sifalakis Anastasios | en |
| Δημιουργός | Σηφαλακης Αναστασιος | el |
| Εκδότης | Elsevier | en |
| Περίληψη | A 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 |
| Τύπος | Peer-Reviewed Journal Publication | en |
| Τύπος | Δημοσίευση σε Περιοδικό με Κριτές | el |
| Άδεια Χρήσης | http://creativecommons.org/licenses/by/4.0/ | en |
| Ημερομηνία | 2015-10-16 | - |
| Ημερομηνία Δημοσίευσης | 2012 | - |
| Θεματική Κατηγορία | Greek mathematics | en |
| Θεματική Κατηγορία | mathematics greek | en |
| Θεματική Κατηγορία | greek mathematics | en |
| Βιβλιογραφική Αναφορά | Y. 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.2011.12.011 | en |
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