dc.contributor.author | Bialecki, B. | en |
dc.contributor.author | Fairweather, G. | en |
dc.contributor.author | Karageorghis, Andreas | en |
dc.creator | Bialecki, B. | en |
dc.creator | Fairweather, G. | en |
dc.creator | Karageorghis, Andreas | en |
dc.date.accessioned | 2019-12-02T10:34:00Z | |
dc.date.available | 2019-12-02T10:34:00Z | |
dc.date.issued | 2003 | |
dc.identifier.issn | 1064-8275 | |
dc.identifier.uri | http://gnosis.library.ucy.ac.cy/handle/7/56525 | |
dc.description.abstract | We consider the solution of various boundary value problems for the Helmholtz equation in the unit square using a nodal cubic spline collocation method and modifications of it which produce optimal (fourth-) order approximations. For the solution of the collocation equations, we formulate matrix decomposition algorithms, fast direct methods which employ fast Fourier transforms and require O(N2 log N) operations on an N × N uniform partition of the unit square. A computational study confirms the published analysis for the Dirichlet problem and indicates that similar results hold for Neumann, mixed, and periodic boundary conditions. The numerical results also exhibit superconvergence phenomena not reported in earlier studies. | en |
dc.source | SIAM Journal on Scientific Computing | en |
dc.source.uri | https://www.scopus.com/inward/record.uri?eid=2-s2.0-0142009981&doi=10.1137%2fS106482750139964X&partnerID=40&md5=739fc6193f41f77cbaa748efe69db1c7 | |
dc.subject | Algorithms | en |
dc.subject | Approximation theory | en |
dc.subject | Matrix algebra | en |
dc.subject | Convergence of numerical methods | en |
dc.subject | Convergence rates | en |
dc.subject | Polynomials | en |
dc.subject | Boundary value problems | en |
dc.subject | Boundary conditions | en |
dc.subject | Fourier transforms | en |
dc.subject | Piecewise linear techniques | en |
dc.subject | Fast Fourier transforms | en |
dc.subject | Matrix decomposition algorithms | en |
dc.subject | Superconvergence | en |
dc.subject | Helmholtz equation | en |
dc.subject | Helmholtz problems | en |
dc.subject | Modified spline collocation | en |
dc.subject | Spline collocation | en |
dc.subject | Superconvergences | en |
dc.subject | Tensor product | en |
dc.subject | Tensor products | en |
dc.title | Matrix decomposition algorithms for modified spline collocation for Helmholtz problems | en |
dc.type | info:eu-repo/semantics/article | |
dc.identifier.doi | 10.1137/S106482750139964X | |
dc.description.volume | 24 | |
dc.description.issue | 5 | |
dc.description.startingpage | 1733 | |
dc.description.endingpage | 1753 | |
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 | <p>Cited By :9</p> | en |
dc.source.abbreviation | Siam J.Sci.Comput. | en |
dc.contributor.orcid | Karageorghis, Andreas [0000-0002-8399-6880] | |
dc.gnosis.orcid | 0000-0002-8399-6880 | |