Assessment of local radial basis function collocation method for diffusion problems structured with multiquadrics and polyharmonic splines

Ali, Izaz (author), Hanoglu, Umut (author), Vertnik, Robert (author), Šarler, Božidar (author)

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.

• Language: English
• Keywords: meshless method, polyharmonic splines, multiquadrics, augmentation, heat diffusion equation
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 31 str.
• Numbering: Vol. 29, iss. 2, art. 23
• PID: 20.500.12556/RUL-155074
• UDC: 519.62
• ISSN on article: 2297-8747
• DOI: 10.3390/mca29020023
• COBISS.SI-ID: 189462019
• Publication date in RUL: 19.03.2024

Record is a part of a journal

• Title: Mathematical and computational applications
• Shortened title: Math. comput. appl.
• Publisher: MDPI
• ISSN: 2297-8747
• COBISS.SI-ID: 20008470

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: brezmrežna metoda, poliharmonični zlepki, multikvadrike, povečanje, enačba toplotne difuzije