Browsing by Author "Karageorghis, Andreas"
Now showing items 41-60 of 170
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Article
Kansa-RBF algorithms for elliptic problems in axisymmetric domains
Karageorghis, Andreas; Chen, C. S.; Liu, X. -Y (2016)We employ a Kansa-radial basis function method for the numerical solution of elliptic boundary value problems in three-dimensional axisymmetric domains. We consider problems governed by the Poisson equation, the inhomogeneous ...
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Article
Kansa-RBF algorithms for elliptic problems in regular polygonal domains
Karageorghis, Andreas; Jankowska, Malgorzata A.; Chen, C. S. (2018)We propose matrix decomposition algorithms for the efficient solution of the linear systems arising from Kansa radial basis function discretizations of elliptic boundary value problems in regular polygonal domains. These ...
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Conference Object
A Kansa-RBF method for Poisson problems in annular domains
Karageorghis, Andreas; Chen, C. S. (WITPress, 2014)We employ a Kansa-radial basis function (RBF) method for Poisson boundary value problems in annular domains. This discretization leads, for any choice of RBF, to linear system matrices possessing block circulant structures. ...
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Article
The Laplace equation with discontinuous boundary data: Convergence of the spectral element discretization
Bernardi, C.; Karageorghis, Andreas (1997)We prove an existence result for the Laplace equation in a disk with discontinuous Dirichlet boundary conditions: 0 on part of the boundary and 1 on its complement. The problem is discretized by the mortar spectral element ...
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Article
Legendre Gauss spectral collocation for the Helmholtz equation on a rectangle
Bialecki, B.; Karageorghis, Andreas (2004)A spectral collocation method with collocation at the Legendre Gauss points is discussed for solving the Helmholtz equation -Δu+κ(x,y)u=f(x,y) on a rectangle with the solution u subject to inhomogeneous Robin boundary ...
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Article
A legendre spectral collocation method for the biharmonic Dirichlet problem
Bialecki, B.; Karageorghis, Andreas (2000)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 ...
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Article
A Legendre spectral Galerkin method for the biharmonic Dirichlet problem
Bialecki, B.; Karageorghis, Andreas (2001)A Legendre spectral Galerkin 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 ...
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Article
A Legendre spectral quadrature Galerkin method for the Cauchy-Navier equations of elasticity with variable coefficients
Bialecki, Bernard; Karageorghis, Andreas (2018)We solve the Dirichlet and mixed Dirichlet-Neumann boundary value problems for the variable coefficient Cauchy-Navier equations of elasticity in a square using a Legendre spectral Galerkin method. The resulting linear ...
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Article
A Legendre spectral quadrature Galerkin method for the Cauchy-Navier equations of elasticity with variable coefficients
Bialecki, B.; Karageorghis, Andreas (2017)We solve the Dirichlet and mixed Dirichlet-Neumann boundary value problems for the variable coefficient Cauchy-Navier equations of elasticity in a square using a Legendre spectral Galerkin method. The resulting linear ...
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Article
A linear least-squares MFS for certain elliptic problems
Smyrlis, Yiorgos-Sokratis; Karageorghis, Andreas (2004)The Method of Fundamental Solutions (MFS) is a boundary-type meshless method for the solution of certain elliptic boundary value problems. In this work, we propose an efficient algorithm for the linear least-squares version ...
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Article
Local RBF Algorithms for Elliptic Boundary Value Problems in Annular Domains
Chen, C. S.; Karageorghis, Andreas (2019)A local radial basis function method (LRBF) is applied for the solution of boundary value problems in annular domains governed by the Poisson equation, the inhomogeneous biharmonic equation and the inhomogeneous Cauchy-Navier ...
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Article
Matrix decomposition algorithms for elliptic boundary value problems: A survey
Bialecki, B.; Fairweather, G.; Karageorghis, Andreas (2011)We provide an overview of matrix decomposition algorithms (MDAs) for the solution of systems of linear equations arising when various discretization techniques are applied in the numerical solution of certain separable ...
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Article
Matrix decomposition algorithms for modified spline collocation for Helmholtz problems
Bialecki, B.; Fairweather, G.; Karageorghis, Andreas (2003)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 ...
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Article
A matrix decomposition MFS algorithm for axisymmetric biharmonic problems
Fairweather, G.; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis (2005)We consider the approximate solution of axisymmetric biharmonic problems using a boundary-type meshless method, the Method of Fundamental Solutions (MFS) with fixed singularities and boundary collocation. For such problems, ...
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Article
A matrix decomposition MFS algorithm for axisymmetric potential problems
Smyrlis, Yiorgos-Sokratis; Karageorghis, Andreas (2004)The method of fundamental solutions is a boundary-type meshless method for the solution of certain elliptic boundary value problems. By exploiting the structure of the matrices appearing when this method is applied to ...
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Article
A matrix decomposition MFS algorithm for biharmonic problems in annular domains
Tsangaris, T.; Smyrlis, Yiorgos-Sokratis; Karageorghis, Andreas (2004)The Method of Fundamental Solutions (MFS) is a boundary-type method for the solution of certain elliptic boundary value problems. In this work, we develop an efficient matrix decomposition MFS algorithm for the solution ...
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Article
A matrix decomposition MFS algorithm for certain linear elasticity problems
Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis; Tsangaris, T. (2006)We propose an efficient matrix decomposition Method of Fundamental Solutions algorithm for the solution of certain two-dimensional linear elasticity problems. In particular, we consider the solution of the Cauchy-Navier ...
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Article
A matrix decomposition MFS algorithm for problems in hollow axisymmetric domains
Tsangaris, Th; Smyrlis, Yiorgos-Sokratis; Karageorghis, Andreas (2006)In this work we apply the Method of Fundamental Solutions (MFS) with fixed singularities and boundary collocation to certain axisymmetric harmonic and biharmonic problems. By exploiting the block circulant structure of the ...
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Conference Object
Matrix decomposition MFS algorithms
Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis (2006)We describe the application of the Method of Fundamental Solutions (MFS) to elliptic boundary value problems in rotationally symmetric problems. In particular, we show how efficient matrix decomposition MFS algorithms can ...
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Article
Matrix decomposition MFS algorithms for elasticity and thermo-elasticity problems in axisymmetric domains
Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis (2007)In this work, we propose an efficient matrix decomposition algorithm for the Method of Fundamental Solutions when applied to three-dimensional boundary value problems governed by elliptic systems of partial differential ...