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The method of fundamental solutions for scattering and radiation problems
Engineering Analysis with Boundary Elements, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fairweather, G. +5 more
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Fundamentals of Discrete Solution Methods
1992Wave propagation is an inherent feature of the solutions to the Euler equations. The first part of this chapter surveys the basic theory of wave propagation encountered in hyperbolic differential equations including the concept of haracteristics,1 discontinuities, and weak solutions.2 Boundary conditions and how they affect stability are also discussed.
Albrecht Eberle +2 more
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The Method of Fundamental Solutions for the Solution of Nonlinear Plane Potential Problems
IMA Journal of Numerical Analysis, 1989Neben die Randelement-Methode (BEM) zur Lösung elliptischer Randwertprobleme ist in neuerer Zeit die Methode der Fundamental- Lösungen (MFS) getreten, die sich besonders eignet, wenn die Laplace- Gleichung mit nichtlinearen gemischten Randbedingungen zu lösen ist.
Karageorghis, Andreas +3 more
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Galerkin Formulations of the Method of Fundamental Solutions
Advances in Applied Mathematics and Mechanics, 2013In 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 over the boundary of the domain under consideration.
Berger, J. R. +3 more
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The Method of Fundamental Solutions: A Weighted Least-Squares Approach
BIT Numerical Mathematics, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Smyrlis, Yiorgos-Sokratis +1 more
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Reducing the ill conditioning in the method of fundamental solutions
Advances in Computational Mathematics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Virtual special issue: Trefftz Methods and Method of Fundamental Solutions
Engineering Analysis with Boundary Elements, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anita Uscilowska +2 more
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The Method of Fundamental Solutions in Three-Dimensional Elastostatics
2002We consider the application of the Method of Fundamental Solutions (MFS) to isotropic elastostatics problems in three-space dimensions. The displacements are approximated by linear combinations of the fundamental solutions of the Cauchy-Navier equations of elasticity, which are expressed in terms of sources placed outside the domain of the problem ...
Andreas Poullikkas +2 more
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Methods of Fundamental Solutions in Poroelasticity
2015Although single- and double-layer potentials can be used to reduce the dimension of a problem, this comes at the prize of having to deal with integrals over the boundary of a domain. Moreover, these boundary integrals are singular. In order to remove the singularity, we use an approach by Runge which shifts integration towards the boundary of a larger ...
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The Method of Fundamental Solutions for Optical Fluorescence Tomography
Numerical Mathematics: Theory, Methods and ApplicationsIn this paper, the method of fundamental solutions (MFS) is first developed for solving direct problems in bi-layer materials in the biomedical field of optical fluorescence. The governing system of second-order linear partial differential equations (PDEs) for the emission and excitation fluences is transformed into a single fourth-order PDE with ...
Karageorghis, A., Lesnic, D.
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