Browsing by Subject "Circulant matrices"
Now showing items 113 of 13

Article
Conformal mapping for the efficient MFS solution of Dirichlet boundary value problems
(2008)In this work, we use conformal mapping to transform harmonic Dirichlet problems of Laplace's equation which are defined in simplyconnected domains into harmonic Dirichlet problems that are defined in the unit disk. We ...

Article
Efficient implementation of the MFS: The three scenarios
(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 Kansatype MFS algorithm for elliptic problems
(2010)In this study we propose an efficient Kansatype method of fundamental solutions (MFSK) 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
(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 in regular polygonal domains
(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 matrix decomposition MFS algorithm for biharmonic problems in annular domains
(2004)The Method of Fundamental Solutions (MFS) is a boundarytype 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
(2006)We propose an efficient matrix decomposition Method of Fundamental Solutions algorithm for the solution of certain twodimensional linear elasticity problems. In particular, we consider the solution of the CauchyNavier ...

Article
A matrix decomposition MFS algorithm for problems in hollow axisymmetric domains
(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 ...

Article
Matrix decomposition MFS algorithms for elasticity and thermoelasticity problems in axisymmetric domains
(2007)In this work, we propose an efficient matrix decomposition algorithm for the Method of Fundamental Solutions when applied to threedimensional boundary value problems governed by elliptic systems of partial differential ...

Article
A matrix decomposition RBF algorithm: Approximation of functions and their derivatives
(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: A weighted leastsquares approach
(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
Some aspects of the Method of Fundamental Solutions for certain harmonic problems
(2001)The Method of Fundamental Solutions (MFS) is a boundarytype 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 underdetermined version of the MFS: Taking more sources than collocation points
(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 ...