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Institutional Repository [SANDBOX]
Technical University of Crete
Technical University of Crete
EN
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| URI: | http://purl.tuc.gr/dl/dias/C27ABBA2-F64D-4A17-954B-3BD57289B9EF | ||
| Year | 2009 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
| License |
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| Bibliographic Citation | A. 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.2008.07.025 https://doi.org/10.1016/j.cam.2008.07.025 | ||
| Appears in Collections |
In 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.
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