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THE LOCALIZED METHOD OF FUNDAMENTAL SOLUTIONS FOR PLANAR GROUNDWATER FLOW PROBLEMS

Juraj Mužík

First published: 2023-10-01https://doi.org/10.5593/sgem2023/1.1/s02.34View metrics

Abstract

The method of fundamental solutions is a meshless method that belongs to the Trefftz class of numerical methods. The method needs only the boundary to be defined using the set of boundary collocation nodes; it is mathematically effortless to program. One of the imperfections in the context of MFS is the fictitious boundary without any rigorous definition. The other fact that MFS suffers from is the nature of the characteristic matrix that is non-symmetric and fully populated. This issue is overcome by adopting the localization strategy, which adds internal nodes into the model but results in a sparse linear system that can be solved efficiently. Moreover, the advantages possed by MFS are preserved. This article presents the application of the localized method of fundamental solutions for the simulation of planar 2D steady-state groundwater flow problems. Numerical results are compared with those obtained by the boundary element method and analytical solutions. The localized method of fundamental solutions showed its high potential in dealing with ongoing planar groundwater flow problems.

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Publication details

Title
THE LOCALIZED METHOD OF FUNDAMENTAL SOLUTIONS FOR PLANAR GROUNDWATER FLOW PROBLEMS
Authors
Juraj Mužík
Proceedings
SGEM International Multidisciplinary Scientific GeoConference- EXPO Proceedings; 23rd International Multidisciplinary Scientific GeoConference Proceedings SGEM2023, Science and Technologies in Geology, Exploration And Mining, Vol 23, Issue 1.1
Publisher
STEF92 Technology
Year
2023
Pages
285-292
SWS Citekey
Muzik20232285292
ISSN
1314-2704
ISBN
978-619-7603-56-9
Language
en
Publication type
Conference Paper
Proceedings contents
Open official contents
Keywords
fundamental solutiongroundwaterTrefftz methods
References5

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    View DOICrossrefGoogle ScholarWeb of ScienceScopusOpenCitations
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