Browsing by Subject "Laplace equation"
Now showing items 119 of 19

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 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
Galerkin formulations of themethod of fundamental solutions
(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 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
The method of fundamental solutions for elliptic problems in circular domains with mixed boundary conditions
(2015)We apply the method of fundamental solutions (MFS) for the solution of harmonic and biharmonic problems in circular domains subject to mixed boundary conditions. In contrast to the cases when boundary conditions of the ...

Article
The method of fundamental solutions for stationary heat conduction problems in rotationally symmetric domains
(2006)We propose an efficient boundary collocation method for the solution of certain two and threedimensional problems of steadystate heat conduction in Isotropie bimaterials. In particular, in two dimensions we consider the ...

Article
The MFS for numerical boundary identification in twodimensional harmonic problems
(2011)In this study, we briefly review the applications of the method of fundamental solutions to inverse problems over the last decade. Subsequently, we consider the inverse geometric problem of identifying an unknown part of ...

Article
The MFS for the solution of harmonic boundary value problems with nonharmonic boundary conditions
(2013)We investigate applications of the method of fundamental solutions (MFS) for the numerical solution of twodimensional boundary value problems in complex geometries, governed by the Laplace equation and subject to Dirichlet ...

Article
Mortar spectral element discretization of the Laplace and Darcy equations with discontinuous coefficients
(2007)This paper deals with the mortar spectral element discretization of two equivalent problems, the Laplace equation and the Darcy system, in a domain which corresponds to a nonhomogeneous anisotropic medium. The numerical ...

Article
On choosing the location of the sources in the MFS
(2016)The satisfactory location for the sources outside the closure of the domain of the problem under consideration remains one of the major issues in the application of the method of fundamental solutions (MFS). In this work ...

Conference Object
Performance of GMRES for the MFS
(2009)In this work we present some preliminary numerical results regarding the performance of the Generalized Minimal Residual (GMRES) method when it is applied to the solution of the linear systems arising from the discretization ...

Article
The singular function boundary integral method for 3D Laplacian problems with a boundary straight edge singularity
(2012)Threedimensional Laplace problems with a boundary straightedge singularity caused by two intersecting flat planes are considered. The solution in the neighbourhood of the straight edge can be expressed as an asymptotic ...

Article
The singular function boundary integral method for an elastic plane stress wedge beam problem with a point boundary singularity
(2014)The singular function boundary integral method (SFBIM) is applied for the numerical solution of a 2D Laplace model problem of a perfectly elastic wedge beam under plane stress conditions. The beam has a point boundary ...

Article
A singular function boundary integral method for laplacian problems with boundary singularities
(2006)A singular function boundary integral method for Laplacian problems with boundary singularities is analyzed. In this method, the solution is approximated by the truncated asymptotic expansion for the solution near the ...

Article
A singular function boundary integral method for the laplace equation
(1996)The authors present a new singular function boundary integral method for the numerical solution of problems with singularities which is based on approximation of the solution by the leading terms of the local asymptotic ...

Article
The solution of Laplacian problems over Lshaped domains with a singular function boundary integral method
(2002)The singular function boundary integral method is applied for the solution of a Laplace equation problem over an Lshaped domain. The solution is approximated by the leading terms of the local asymptotic solution expansion, ...

Article
Solving Laplacian problems with boundary singularities: A comparison of a singular function boundary integral method with the p/hp version of the finite element method
(2005)We solve a Laplacian problem over an Lshaped domain using a singular function boundary integral method as well as the p/hp finite element method. In the former method, the solution is approximated by the leading terms of ...

Article
Threedimensional image reconstruction using the PF/MFS technique
(2009)We propose a geometric modeling method in R3 based on the socalled 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. ...

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 ...