| Issue |
ESAIM: M2AN
Volume 34, Number 3, May/june 2000
|
|
|---|---|---|
| Page(s) | 637 - 662 | |
| DOI | https://doi.org/10.1051/m2an:2000160 | |
| Published online | 15 April 2002 | |
A Legendre Spectral Collocation Method for the Biharmonic Dirichlet Problem
1
Department of Mathematical and Computer Sciences,
Colorado School of Mines, Golden, Colorado 80401, U.S.A. (bbialeck@mines.edu)
2
Department of Mathematics and Statistics,
University of Cyprus, P.O. Box 537, 1678 Nicosia, Cyprus.
Received:
17
March
1999
Revised:
23
November
1999
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(N3). Numerical results demonstrate the spectral convergence of the method.
Mathematics Subject Classification: 65N35 / 65N22
Key words: Biharmonic Dirichlet problem / spectral collocation / Schur complement / preconditioned conjugate gradient method.
© EDP Sciences, SMAI, 2000
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.