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Radial Basis Functions
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Radial Basis Functions

A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: 31 December 2024 | Viewed by 4177

Special Issue Editors

Prof. Dr. Benny Yiu-Chung Hon

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Guest Editor
Department of Mathematics, City University of Hong Kong, Hong Kong, China
Interests: meshfree methods; inverse problems; computational mechanics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Zhuojia Fu

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Guest Editor
College of Mechanics and Engineering Science, Hohai University, Nanjing 210098, China
Interests: acoustic and elastic waves; inverse problems; RBF-based meshless methods; Trefftz method; boundary element method
Special Issues, Collections and Topics in MDPI journals
Dr. Junpu Li

E-Mail Website
Guest Editor
School of Mechanics and Safety Engineering, Zhengzhou University, Zhengzhou 450001, China
Interests: radial basis functions; computational mechanics; computational wave dynamic

Special Issue Information

Dear Colleagues,

Radial basis functions (RBFs) are a type of real-value function which invariably involve only one-dimensional distance. With their merit of meshless and independence from dimensionality and geometric complexity, RBFs have gained substantial attention from various scientific computing and engineering applications, such as the recovery of functions from scattered data, the numerical solution of partial differential equations (PDEs), ill-posed and inverse problems, neural networks, machine learning algorithms, and so on. This Special Issue will present recent research results on radial basis functions and their applications in engineering and sciences.

Prof. Dr. Benny Y. C. Hon
Prof. Dr. Zhuojia Fu
Dr. Junpu Li
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematical and Computational Applications is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

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Published Papers (2 papers)

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Research

16 pages, 4439 KiB  
Article
Simulation of Temperature Field in Steel Billets during Reheating in Pusher-Type Furnace by Meshless Method
by Qingguo Liu, Umut Hanoglu, Zlatko Rek and Božidar Šarler
Math. Comput. Appl. 2024, 29(3), 30; https://doi.org/10.3390/mca29030030 - 24 Apr 2024
Cited by 1 | Viewed by 1528
Abstract
Using a meshless method, a simulation of steel billets in a pusher-type reheating furnace is carried out for the first time. The simulation represents an affordable way to replace the measurements. The heat transfer from the billets with convection and radiation is considered. [...] Read more.
Using a meshless method, a simulation of steel billets in a pusher-type reheating furnace is carried out for the first time. The simulation represents an affordable way to replace the measurements. The heat transfer from the billets with convection and radiation is considered. Inside each of the billets, the heat diffusion equation is solved on a two-dimensional central slice of the billet. The diffusion equation is solved in a strong form by the Local Radial Basis Function Collocation Method (LRBFCM) with explicit time-stepping. The ray tracing procedure solves the radiation, where the view factors are computed with the Monte Carlo method. The changing number of billets in the furnace at the start and the end of the loading and unloading of the furnace is considered. A sensitivity study on billets’ temperature evolution is performed as a function of a different number of rays used in the Monte Carlo method, different stopping times of the billets in the furnace, and different spacing between the billets. The temperature field simulation is also essential for automatically optimizing the furnace’s productivity, energy consumption, and the billet’s quality. For the first time, the LRBFCM is successfully demonstrated for solving such a complex industrial problem. Full article
(This article belongs to the Special Issue Radial Basis Functions)
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31 pages, 10410 KiB  
Article
Assessment of Local Radial Basis Function Collocation Method for Diffusion Problems Structured with Multiquadrics and Polyharmonic Splines
by Izaz Ali, Umut Hanoglu, Robert Vertnik and Božidar Šarler
Math. Comput. Appl. 2024, 29(2), 23; https://doi.org/10.3390/mca29020023 - 17 Mar 2024
Cited by 3 | Viewed by 1519
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Radial Basis Functions)
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