Year 2019, Volume 3 , Issue 1, Pages 23 - 31 2019-06-24

Meshless solution of the neutron diffusion equation by the RBF collocation method using optimum shape parameters

Tayfun Tanbay [1]


The meshless radial basis function collocation method is an efficient numerical technique for solving partial differential equations. The multiquadric is the most widely utilized radial function for this purpose; but it contains a shape parameter, which has a significant effect on the performance of the method. In this study, the meshless collocation method employing multiquadric as the radial function with optimum shape parameters is applied to the numerical solution of the multigroup neutron diffusion equation. The optimization of the shape parameter is performed by minimizing the Madych-Nelson function. One external and two fission source problems are solved to investigate the performance of the method. The results show that the meshless collocation method with optimized shape parameters yield a high level of accuracy with an exponential convergence rate.

Meshless, RBF, Collocation, Optimum shape parameter, Neutron diffusion
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Primary Language en
Subjects Engineering
Journal Section Research Articles
Authors

Orcid: 0000-0002-0428-3197
Author: Tayfun Tanbay (Primary Author)
Institution: BURSA TECHNICAL UNIVERSITY
Country: Turkey


Dates

Publication Date : June 24, 2019

Bibtex @research article { jise570328, journal = {Journal of Innovative Science and Engineering (JISE)}, issn = {}, eissn = {2602-4217}, address = {ursa Technical University, Mimar Sinan Campus, Mimar Sinan Mah. Mimar Sinan Blv. Eflak Cad. No:177 16310 Yıldırım, Bursa / Turkey}, publisher = {Bursa Teknik Üniversitesi}, year = {2019}, volume = {3}, pages = {23 - 31}, doi = {}, title = {Meshless solution of the neutron diffusion equation by the RBF collocation method using optimum shape parameters}, key = {cite}, author = {Tanbay, Tayfun} }
APA Tanbay, T . (2019). Meshless solution of the neutron diffusion equation by the RBF collocation method using optimum shape parameters. Journal of Innovative Science and Engineering (JISE) , 3 (1) , 23-31 . Retrieved from http://jise.btu.edu.tr/en/issue/44666/570328
MLA Tanbay, T . "Meshless solution of the neutron diffusion equation by the RBF collocation method using optimum shape parameters". Journal of Innovative Science and Engineering (JISE) 3 (2019 ): 23-31 <http://jise.btu.edu.tr/en/issue/44666/570328>
Chicago Tanbay, T . "Meshless solution of the neutron diffusion equation by the RBF collocation method using optimum shape parameters". Journal of Innovative Science and Engineering (JISE) 3 (2019 ): 23-31
RIS TY - JOUR T1 - Meshless solution of the neutron diffusion equation by the RBF collocation method using optimum shape parameters AU - Tayfun Tanbay Y1 - 2019 PY - 2019 N1 - DO - T2 - Journal of Innovative Science and Engineering (JISE) JF - Journal JO - JOR SP - 23 EP - 31 VL - 3 IS - 1 SN - -2602-4217 M3 - UR - Y2 - 2019 ER -
EndNote %0 Journal of Innovative Science and Engineering (JISE) Meshless solution of the neutron diffusion equation by the RBF collocation method using optimum shape parameters %A Tayfun Tanbay %T Meshless solution of the neutron diffusion equation by the RBF collocation method using optimum shape parameters %D 2019 %J Journal of Innovative Science and Engineering (JISE) %P -2602-4217 %V 3 %N 1 %R %U
ISNAD Tanbay, Tayfun . "Meshless solution of the neutron diffusion equation by the RBF collocation method using optimum shape parameters". Journal of Innovative Science and Engineering (JISE) 3 / 1 (June 2019): 23-31 .
AMA Tanbay T . Meshless solution of the neutron diffusion equation by the RBF collocation method using optimum shape parameters. JISE. 2019; 3(1): 23-31.
Vancouver Tanbay T . Meshless solution of the neutron diffusion equation by the RBF collocation method using optimum shape parameters. Journal of Innovative Science and Engineering (JISE). 2019; 3(1): 31-23.