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Title: THE LOCALIZED METHOD OF FUNDAMENTAL SOLUTIONS FOR PLANAR GROUNDWATER FLOW PROBLEMS
THE LOCALIZED METHOD OF FUNDAMENTAL SOLUTIONS FOR PLANAR GROUNDWATER FLOW PROBLEMS

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Juraj Muzik
10.5593/sgem2023/1.1/s02.34
10.5593/sgem2023/1.1
1314-2704
978-619-7603-56-9
English
23
1
•    Prof. DSc. Oleksandr Trofymchuk, UKRAINE 
•    Prof. Dr. hab. oec. Baiba Rivza, LATVIA
Hydrogeology, Engineering Geology and Geotechnics
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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[4] Muzik, J., Bulko, R. (2018). Regularized singular boundary method for groundwater flow in a cofferdam. MATEC Web of Conferences, 196, 03025.
[5] Fan, C., Huang, Y., Chen, C., & Kuo, S. (2019). Localized method of fundamental solutions for solving two-dimensional Laplace and biharmonic equations. Engineering Analysis With Boundary Elements, 101, 188–197.
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This contribution is the result of the project funded by the Scientific Grant Agency of Slovak Republic (VEGA) No. 1/0879/21.
conference
https://doi.org/10.5593/sgem2023/1.1/s02.34
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Proceedings of 23rd International Multidisciplinary Scientific GeoConference SGEM 2023
23rd International Multidisciplinary Scientific GeoConference SGEM 2023, 03 - 09 July, 2023
Proceedings Paper
STEF92 Technology
International Multidisciplinary Scientific GeoConference-SGEM
SWS Scholarly Society; Acad Sci Czech Republ; Latvian Acad Sci; Polish Acad Sci; Russian Acad Sci; Serbian Acad Sci and Arts; Natl Acad Sci Ukraine; Natl Acad Sci Armenia; Sci Council Japan; European Acad Sci, Arts and Letters; Acad Fine Arts Zagreb Croatia; Croatian Acad Sci and Arts; Acad Sci Moldova; Montenegrin Acad Sci and Arts; Georgian Acad Sci; Acad Fine Arts and Design Bratislava; Russian Acad Arts; Turkish Acad Sci.
285-292
03 - 09 July, 2023
website
9023
fundamental solution, groundwater, Trefftz methods