Browsing Τμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics by Subject "Elliptic boundary value problems"

Article

Applicability and applications of the method of fundamental solutions

Smyrlis, Yiorgos-Sokratis (2009)

In the present work, we investigate the applicability of the method of fundamental solutions for the solution of boundary value problems of elliptic partial differential equations and elliptic systems. More specifically, ...

Article

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 ...

Article

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 ...

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 ...

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 ...

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 ...

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 ...

Article

A matrix decomposition RBF algorithm: Approximation of functions and their derivatives

Karageorghis, Andreas; Chen, C. S.; Smyrlis, Yiorgos-Sokratis (2007)

We propose an efficient algorithm for the approximation of functions and their derivatives using radial basis functions (RBFs). The interpolation points are placed on concentric circles and the resulting matrix has a block ...

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 ...

Article

The Method of Fundamental Solutions for Stokes Flows with a Free Surface

Poullikkas, A.; Karageorghis, Andreas; Georgiou, Georgios C.; Ascough, J. (1998)

We investigate the use of the Method of Fundamental Solutions (MFS) for solving Stokes flow problems with a free surface. We apply the method to the creeping planar Newtonian extrudate-swell problem and study the effect ...

Article

The method of fundamental solutions: A weighted least-squares approach

Smyrlis, Yiorgos-Sokratis (2006)

We investigate the Method of Fundamental Solutions (MFS) for the solution of certain elliptic boundary value problems. In particular, we study the case in which the number of collocation points exceeds the number of ...

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 ...

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 ...

Article

A practical algorithm for determining the optimal pseudo-boundary in the method of fundamental solutions

Karageorghis, Andreas (2009)

One of the main difficulties in the application of the method of funda- mental solutions (MFS) is the determination of the position of the pseudo-boundary on which are placed the singularities in terms of which the ...

Article

Some aspects of the Method of Fundamental Solutions for certain harmonic problems

Smyrlis, Yiorgos-Sokratis; Karageorghis, Andreas (2001)

The Method of Fundamental Solutions (MFS) is a boundary-type method for the solution of certain elliptic boundary value problems. The basic ideas of the MFS were introduced by Kupradze and Alexidze and its modern form was ...

Article

The under-determined version of the MFS: Taking more sources than collocation points

Smyrlis, Yiorgos-Sokratis; Karageorghis, Andreas (2010)

In this study we investigate the approximation of the solutions of certain elliptic boundary value problems by the Method of Fundamental Solutions (MFS). In particular, we study the case in which the number of singularities ...