dc.contributor.author Bialecki, B. en dc.contributor.author Karageorghis, Andreas en dc.creator Bialecki, B. en dc.creator Karageorghis, Andreas en dc.date.accessioned 2019-12-02T10:34:01Z dc.date.available 2019-12-02T10:34:01Z dc.date.issued 2007 dc.identifier.uri http://gnosis.library.ucy.ac.cy/handle/7/56532 dc.description.abstract We consider the Dirichlet boundary value problem for Poisson's equation in an L-shaped region or a rectangle with a cross-point. In both cases, we approximate the Dirichlet problem using Legendre spectral collocation, that is, polynomial collocation at the Legendre-Gauss nodes. The L-shaped region is partitioned into three nonoverlapping rectangular subregions with two interfaces and the rectangle with the cross-point is partitioned into four rectangular subregions with four interfaces. In each rectangular subregion, the approximate solution is a polynomial tensor product that satisfies Poisson's equation at the collocation points. The approximate solution is continuous on the entire domain and its normal derivatives are continuous at the collocation points on the interfaces, but continuity of the normal derivatives across the interfaces is not guaranteed. At the cross point, we require continuity of the normal derivative in the vertical direction. The solution of the collocation problem is first reduced to finding the approximate solution on the interfaces. The discrete Steklov-Poincaré operator corresponding to the interfaces is self-adjoint and positive definite with respect to the discrete inner product associated with the collocation points on the interfaces. The approximate solution on the interfaces is computed using the preconditioned conjugate gradient method. A preconditioner is obtained from the discrete Steklov-Poincaré operators corresponding to pairs of the adjacent rectangular subregions. Once the solution of the discrete Steklov- Poincaré equation is obtained, the collocation solution in each rectangular subregion is computed using a matrix decomposition method. The total cost of the algorithm is O(N 3), where the number of unknowns is proportional to N 2. © 2007 Springer Science+Business Media, LLC. en dc.source Journal of Scientific Computing en dc.source.uri https://www.scopus.com/inward/record.uri?eid=2-s2.0-34547372364&doi=10.1007%2fs10915-007-9136-x&partnerID=40&md5=424d87f1ede28b30bd8f2db374522570 dc.subject Problem solving en dc.subject Approximation theory en dc.subject Spectrum analysis en dc.subject Polynomials en dc.subject Dirichlet problems en dc.subject Tensors en dc.subject Poisson equation en dc.subject Domain decomposition methods en dc.subject Poisson's equation en dc.subject Preconditioned conjugate gradient method en dc.subject Dirichlet problem en dc.subject Gradient methods en dc.subject Legendre spectral collocation en dc.subject Legendre spectral collocation problems en dc.subject Nonoverlapping domain decomposition en dc.subject Preconditioned conjugate gradient methods en dc.title A nonoverlapping domain decomposition method for Legendre spectral collocation problems en dc.type info:eu-repo/semantics/article dc.identifier.doi 10.1007/s10915-007-9136-x dc.description.volume 32 dc.description.issue 2 dc.description.startingpage 373 dc.description.endingpage 409 dc.author.faculty Σχολή Θετικών και Εφαρμοσμένων Επιστημών / Faculty of Pure and Applied Sciences dc.author.department Τμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics dc.type.uhtype Article en dc.description.notes

Cited By :5

en dc.source.abbreviation J.Sci.Comput. en dc.contributor.orcid Karageorghis, Andreas [0000-0002-8399-6880] dc.gnosis.orcid 0000-0002-8399-6880
﻿

## Files in this item

FilesSizeFormatView

There are no files associated with this item.