| Title: | Assessment of local radial basis function collocation method for diffusion problems structured with multiquadrics and polyharmonic splines |
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| Authors: | ID Ali, Izaz (Author)
ID Hanoglu, Umut (Author)
ID Vertnik, Robert (Author)
ID Šarler, Božidar (Author) |
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| Files: |  PDF - Presentation file, download (2,79 MB)
MD5: E4256383DE996CECAC34F8C6E8ED264A
 URL - Source URL, visit https://www.mdpi.com/2297-8747/29/2/23
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMT - Institute of Metals and Technology
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| Abstract: | This paper aims to systematically assess the local radial basis function collocation method, structured with multiquadrics (MQs) and polyharmonic splines (PHSs), for solving steady and transient diffusion problems. The boundary value test involves a rectangle with Dirichlet, Neuman, and Robin boundary conditions, and the initial value test is associated with the Dirichlet jump problem on a square. The spectra of the free parameters of the method, i.e., node density, timestep, shape parameter, etc., are analyzed in terms of the average error. It is found that the use of MQs is less stable compared to PHSs for irregular node arrangements. For MQs, the most suitable shape parameter is determined for multiple cases. The relationship of the shape parameter with the total number of nodes, average error, node scattering factor, and the number of nodes in the local subdomain is also provided. For regular node arrangements, MQs produce slightly more accurate results, while for irregular node arrangements, PHSs provide higher accuracy than MQs. PHSs are recommended for use in diffusion problems that require irregular node spacing. |
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| Keywords: | meshless method, polyharmonic splines, multiquadrics, augmentation, heat diffusion equation |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 17.03.2024 |
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| Publisher: | MDPI |
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| Year of publishing: | 2024 |
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| Number of pages: | str. 1-31 |
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| Numbering: | Vol. 29, iss. 2, [article no.] 23 |
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| Source: | Švica |
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| PID: | 20.500.12556/DiRROS-18602  |
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| UDC: | 519.62 |
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| ISSN on article: | 2297-8747 |
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| DOI: | 10.3390/mca29020023 |
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| COBISS.SI-ID: | 189462019 |
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| Copyright: | © 2024 by the authors |
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| Note: | Nasl. z nasl. zaslona;
Opis vira z dne 19. 3. 2024;
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| Publication date in DiRROS: | 04.04.2024 |
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| Views: | 74 |
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| Downloads: | 32 |
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| Metadata: |     |
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