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

DOI10.1016/j.apnum.2009.05.001zbMath1196.65187OpenAlexW1998198994MaRDI QIDQ972297

Andreas Karageorghis, Yiorgos-Sokratis Smyrlis

Publication date: 25 May 2010

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2009.05.001

zbMATH Keywords

algorithmDirichlet problemnumerical experimentsvariational methodscollocationelliptic boundary value problemscirculant matricesLaplace's equationunder-determined linear systemsmethod of fundamental solutions (MFS)

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items (8)

The method of fundamental solutions for Helmholtz-type equations in composite materials ⋮ A comparative study on applying the method of fundamental solutions to the backward heat conduction problem ⋮ A modification of the method of fundamental solutions for solving 2D problems with concave and complicated domains ⋮ The under-determined version of the MFS: taking more sources than collocation points ⋮ Applicability and applications of the method of fundamental solutions ⋮ The adaptive algorithm for the selection of sources of the method of fundamental solutions ⋮ Efficient implementation of the MFS: The three scenarios ⋮ Mathematical foundation of the MFS for certain elliptic systems in linear elasticity

Cites Work

• Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution
• The under-determined version of the MFS: taking more sources than collocation points
• Efficient implementation of the MFS: The three scenarios
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• The method of fundamental solutions for elliptic boundary value problems
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• Some aspects of the method of fundamental solutions for certain harmonic problems
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• On the Theory of Kernels of Schwartz
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• Numerical analysis of the MFS for certain harmonic problems
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