Browsing by Author "Karageorghis, Andreas"
Now showing items 21-40 of 170
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Conference Object
Determination of shape parameter in RBF approximation
Karageorghis, Andreas; Tryfonos, Pinelopi (WIT Press, 2019)We apply a radial basis function (RBF) collocation method for the approximation of functions in two dimensions. The solution is approximated by a linear combination of radial basis functions. The issue of determining the ...
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Direct methods for spectral approximations in nonconforming domain decompositions
Karageorghis, Andreas; Paprzycki, M. (1998)The application of a conforming spectral collocation method to certain nonconforming domain decompositions leads to global matrices which have a particular block structure. We study the performance of various direct linear ...
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Efficient algorithms for approximating particular solutions of elliptic equations using Chebyshev polynomials
Karageorghis, Andreas; Kyza, I. (2007)In this paper, we propose efficient algorithms for approximating particular solutions of second and fourth order elliptic equations. The approximation of the particular solution by a truncated series of Chebyshev polynomials ...
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An efficient direct method for fully conforming spectral collocation schemes
Karageorghis, Andreas; Paprzycki, M. (1996)An efficient direct method is presented for the solution of the linear systems arising in the solution of second and fourth order problems by certain multidomain spectral collocation schemes. In it, the block structure of ...
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Efficient implementation of the MFS: The three scenarios
Smyrlis, Yiorgos-Sokratis; Karageorghis, Andreas (2009)In this study we investigate the approximation of the solutions of harmonic problems subject to Dirichlet boundary conditions by the Method of Fundamental Solutions (MFS). In particular, we study the application of the MFS ...
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Efficient Kansa-type MFS algorithm for elliptic problems
Karageorghis, Andreas (2010)In this study we propose an efficient Kansa-type method of fundamental solutions (MFS-K) for the numerical solution of certain problems in circular geometries. In particular, we consider problems governed by the inhomogeneous ...
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Efficient MFS algorithms for inhomogeneous polyharmonic problems
Karageorghis, Andreas (2011)In this work we develop an efficient algorithm for the application of the method of fundamental solutions to inhomogeneous polyharmonic problems, that is problems governed by equations of the form Δ ℓ u=f, ℓ ε ℕ, in circular ...
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Efficient MFS algorithms for problems in thermoelasticity
Karageorghis, Andreas; Marin, L. (2013)We propose efficient fast Fourier transform (FFT)-based algorithms using the method of fundamental solutions (MFS) for the numerical solution of certain problems in planar thermoelasticity. In particular, we consider ...
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Efficient MFS algorithms in regular polygonal domains
Karageorghis, Andreas (2009)In this work, we apply the Method of Fundamental Solutions (MFS) to harmonic and biharmonic problems in regular polygonal domains. The matrices resulting from the MFS discretization possess a block circulant structure. ...
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Efficient Trefftz collocation algorithms for elliptic problems in circular domains
Karageorghis, Andreas (2013)We consider the numerical solution of certain elliptic boundary value problems in disks and annuli using the Trefftz collocation method. In particular we examine boundary value problems for the Laplace, Helmholtz, modified ...
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Finite Difference Schemes for the Cauchy–Navier Equations of Elasticity with Variable Coefficients
Bialecki, B.; Karageorghis, Andreas (2015)We solve the variable coefficient Cauchy–Navier equations of elasticity in the unit square, for Dirichlet and Dirichlet-Neumann boundary conditions, using second order finite difference schemes. The resulting linear systems ...
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A fully bayesian approach to shape estimation of objects from tomography data using MFS forward solutions
Aykroyd, R. G.; Lesnic, D.; Karageorghis, Andreas (2015)It is possible to characterise the aim of many practical inverse geometric problems as one of identifying the shape of an object within some domain of interest using non-intrusive measurements collected on the boundary of ...
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Article
A fully conforming spectral collocation scheme for second- and fourth-order problems
Karageorghis, Andreas (1995)A spectral element scheme is presented for the solution of second- and fourth-order problems in two and three space dimensions. This scheme is based on a collocation formulation and, for a certain class of problems, results ...
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Galerkin formulations of themethod of fundamental solutions
Berger, J. R.; Karageorghis, Andreas (2013)In this paper,we introduce two Galerkin formulations of the Method of Fundamental Solutions (MFS). In contrast to the collocation formulation of the MFS, the proposed Galerkin formulations involve the evaluation of integrals ...
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High performance solution of linear systems arising from conforming spectral approximations for non-conforming domain decompositions
Paprzycki, M.; Karageorghis, Andreas (1997)We apply a conforming spectral collocation technique to nonconforming domain decompositions. The resulting global matrices have a particular block structure. We study the performance of various direct methods of solution ...
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High performance solution of partial differential equations discretized using a chebyshev spectral collocation method
Cyphers, C.; Paprzycki, M.; Karageorghis, Andreas (1996)When a Chebyshev spectral collocation method is applied to a flow problem in a rectangularly decomposable domain it leads to the solution of a structured linear system. Since the linear system is solved at each step of a ...
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Identification and reconstruction of a small leak zone in a pipe by a spectral element method
Belhachmi, Z.; Karageorghis, Andreas; Taous, K. (2006)This paper deals with the identification of a zone permitting fluid to leak out of a drain. Using the analogy with crack identification by boundary measurements, we give uniqueness and stability results and we propose an ...
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Improved Kansa RBF method for the solution of nonlinear boundary value problems
Jankowska, Malgorzata A.; Karageorghis, Andreas; Chen, C. S. (2018)We apply the Kansa–radial basis function (RBF) collocation method to two-dimensional nonlinear boundary value problems. In it, the solution is approximated by a linear combination of RBFs and the governing equation and ...
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Kansa RBF method for nonlinear problems
Jankowska, Małgorzata; Karageorghis, Andreas; Chen, CS (2018)We apply the Kansa–radial basis function (RBF) collocation method to two– dimensional nonlinear boundary value problems. The system of nonlinear equations resulting from the Kansa–RBF discretization is solved by directly ...
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A Kansa-Radial Basis Function Method for Elliptic Boundary Value Problems in Annular Domains
Liu, X. -Y; Karageorghis, Andreas; Chen, C. S. (2015)We employ a Kansa-radial basis function (RBF) method for the numerical solution of elliptic boundary value problems in annular domains. This discretization leads, with an appropriate selection of collocation points and for ...