| Автор | Bialecki, Bernard |
| Автор | Karageorghis, Andreas |
| Дата выпуска | 2000 |
| dc.description | A Legendre spectral collocation method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which are linear combinations of Legendre polynomials. A Schur complement approach is used to reduce the resulting linear system to one involving the approximation of the Laplacian of the solution on the two vertical sides of the square. The Schur complement system is solved by a preconditioned conjugate gradient method. The total cost of the algorithm is O(N <sup>3</sup>). Numerical results demonstrate the spectral convergence of the method. |
| Формат | application.pdf |
| Издатель | EDP Sciences |
| Копирайт | © EDP Sciences, SMAI, 2000 |
| Тема | Biharmonic Dirichlet problem |
| Тема | spectral collocation |
| Тема | Schur complement |
| Тема | preconditioned conjugate gradient method. |
| Название | A Legendre Spectral Collocation Method for the Biharmonic Dirichlet Problem |
| Тип | research-article |
| DOI | 10.1051/m2an:2000160 |
| Electronic ISSN | 1290-3841 |
| Print ISSN | 0764-583X |
| Журнал | ESAIM: Mathematical Modelling and Numerical Analysis |
| Том | 34 |
| Первая страница | 637 |
| Последняя страница | 662 |
| Аффилиация | Bialecki Bernard; Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado 80401, U.S.A. (bbialeck@mines.edu) |
| Аффилиация | Karageorghis Andreas; Department of Mathematics and Statistics, University of Cyprus, P.O. Box 537, 1678 Nicosia, Cyprus. |
| Выпуск | 3 |
