Browsing by Subject "Method of fundamental solutions"

Now showing items 1-20 of 71

    • 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, ...
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      Application of the MFS to inverse obstacle scattering problems 

      Karageorghis, Andreas; Lesnic, D. (2011)
      In this paper, the method of fundamental solutions (MFS) is used to detect the shape, size and location of a scatterer embedded in a host acoustic homogeneous medium from scant measurements of the scattered acoustic pressure ...
    • Article  

      Approximation by solutions of elliptic equations in semilocal spaces 

      Smyrlis, Yiorgos-Sokratis (2009)
      In the present work, we investigate the approximability of solutions of elliptic partial differential equations in a bounded domain Ω by solutions of the same equations in a larger domain. We construct an abstract framework ...
    • Article  

      Conformal mapping for the efficient MFS solution of Dirichlet boundary value problems 

      Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis (2008)
      In this work, we use conformal mapping to transform harmonic Dirichlet problems of Laplace's equation which are defined in simply-connected domains into harmonic Dirichlet problems that are defined in the unit disk. We ...
    • Article  

      Density results with linear combinations of translates of fundamental solutions 

      Smyrlis, Yiorgos-Sokratis (2009)
      In the present work, we investigate the approximability of solutions of elliptic partial differential equations in a bounded domain Ω by linear combinations of translates of fundamental solutions of the underlying partial ...
    • Article  

      Detection of cavities using the method of fundamental solutions 

      Karageorghis, Andreas; Lesnic, D. (2009)
      The determination of the boundary of a cavity, defined here as a perfectly insulated inclusion, within a conducting medium from a single voltage and current flux measurements on the accessible boundary of the medium, can ...
    • 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  

      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 ...
    • Article  

      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 ...
    • Article  

      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. ...
    • Article  

      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 ...
    • Article  

      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 ...
    • 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 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, ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...