Browsing by Author "Fairweather, G."
Now showing items 1-18 of 18
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Article
The Almansi method of fundamental solutions for solving biharmonic problems
Karageorghis, Andreas; Fairweather, G. (1988)A new fundamental solutions method for the numerical solution of two‐dimensional biharmonic problems is described. In this method, which is based on the Almansi representation of a biharmonic function in the plane, the ...
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Article
Compact optimal quadratic spline collocation methods for the Helmholtz equation
Fairweather, G.; Karageorghis, Andreas; Maack, J. (2011)Quadratic spline collocation methods are formulated for the numerical solution of the Helmholtz equation in the unit square subject to non-homogeneous Dirichlet, Neumann and mixed boundary conditions, and also periodic ...
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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
The method of fundamental solutions for axisymmetric acoustic scattering and radiation problems
Karageorghis, Andreas; Fairweather, G. (1998)The method of fundamental solutions (MFS) is applied to acoustic scattering and radiation for axisymmetric bodies and boundary conditions. The fundamental solution of the governing equation and its normal derivative, which ...
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Article
Method of Fundamental Solutions for axisymmetric elasticity problems
Karageorghis, Andreas; Fairweather, G. (2000)We investigate the use of the Method of Fundamental Solutions (MFS) for the approximate solution of certain problems of three-dimensional elastostatics in isotropic materials. Specifically, we consider problems in which ...
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Article
The method of fundamental solutions for axisymmetric potential problems
Karageorghis, Andreas; Fairweather, G. (1999)In this paper, we investigate the application of the Method of Fundamental Solutions (MFS) to two classes of axisymmetric potential problems. In the first, the boundary conditions as well as the domain of the problem, are ...
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Article
The method of fundamental solutions for elliptic boundary value problems
Fairweather, G.; Karageorghis, Andreas (1998)The aim of this paper is to describe the development of the method of fundamental solutions (MFS) and related methods over the last three decades. Several applications of MFS-type methods are presented. Techniques by which ...
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Article
The method of fundamental solutions for scattering and radiation problems
Fairweather, G.; Karageorghis, Andreas; Martin, P. A. (2003)The development of the method of fundamental solutions (MFS) and related methods for the numerical solution of scattering and radiation problems in fluids and solids is described and reviewed. A brief review of the ...
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Article
The method of fundamental solutions for the numerical solution of the biharmonic equation
Karageorghis, Andreas; Fairweather, G. (1987)The method of fundamental solutions (MFS) is a relatively new technique for the numerical solution of certain elliptic boundary value problems. It falls in the class of methods generally called boundary methods, and, like ...
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Article
The method of fundamental solutions for the solution of nonlinear plane potential problems
Karageorghis, Andreas; Fairweather, G. (1989)The method of fundamental solutions is described for the solution of elliptic boundary value problems governed by Laplace's equation in the plane subject to nonlinear radiation-type boundary conditions. The effectiveness ...
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Conference Object
The method of fundamental solutions in geometric design with potential fields
Tankelevich, R.; Fairweather, G.; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis (Association for Computing Machinery, Inc, 2005)
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Article
Optimal superconvergent one step nodal cubic spline collocation methods
Bialecki, B.; Fairweather, G.; Karageorghis, Andreas (2006)We formulate new optimal (fourth) order one step nodal cubic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the respective ...
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Article
Optimal superconvergent one step quadratic spline collocation methods
Bialecki, B.; Fairweather, G.; Karageorghis, Andreas; Nguyen, Q. N. (2008)We formulate new optimal quadratic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the collocation equations can be solved ...
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Article
Potential field based geometric modelling using the method of fundamental solutions
Tankelevich, R.; Fairweather, G.; Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis (2006)We propose a new geometric modelling method based on the so-called potential field (PF) modelling technique. The harmonic problem associated with this technique is solved numerically using the method of fundamental solutions ...
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Article
The simple layer potential method of fundamental solutions for certain biharmonic problems
Karageorghis, Andreas; Fairweather, G. (1989)A novel formulation of the method of fundamental solutions for the numerical solution of plane biharmonic problems, based on the simple layer potential representation of Fichera, is presented. The applicability and accuracy ...
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Article
Three-dimensional image reconstruction using the PF/MFS technique
Tankelevich, R.; Fairweather, G.; Karageorghis, Andreas (2009)We propose a geometric modeling method in R3 based on the so-called potential field (PF) modeling technique. The method is a new technique for surface reconstruction from a data set of scattered points taken on a surface. ...