Ağsız Yöntem Uygulamaları için Trigonometri Tabanlı Radyal Özelliğe Sahip Yeni Bir Temel Fonksiyon

Year 2020, Volume: 32 Issue: 1, 96 - 110, 31.03.2020

Atakan Altınkaynak

https://doi.org/10.7240/jeps.581959

Cited By: 2

Abstract

Bu çalışmada,
ağsız yöntemler için radyal özelliğe sahip yeni bir temel fonksiyon
önerilmiştir. Önerilen fonksiyon, iki boyutta, dört farklı problemde, ağsız
yöntemlerde sıklıkla kullanılan Ters Multikuadrik ve Gauss fonksiyonlarıyla
birlikte test edilmiştir. Test problemlerinin üç tanesi 2. mertebeden
mühendislik problemlerini içerirken son test problemi 4. mertebeden bir
mühendislik problemi uygulaması olmuştur. 2. mertebeden test problemlerinde
farklı sınır koşulları ve problem türleri incelenmiştir. Yapılan sayısal deneyler,
önerilen fonksiyonun Ters Multikuadrik ve Gauss fonksiyonlarına kıyasla daha az
nokta sayılarında benzer mertebedeki hatalara ulaşabildiğini göstermiştir.
Ayrıca nokta sayısının artmasıyla aynı mertebedeki hatalar için
kullanılabilecek şekil/ölçek parametresinin (epsilon) diğer iki fonksiyona kıyasla daha geniş bir aralıkta seçilebildiği
gösterilmiştir. Dolayısıyla, önerilen fonksiyon, ağsız yöntem uygulamalarında
bir alternatif olarak kullanılabilecektir.

Keywords

Radyal özelliğe sahip temel fonksiyon, trigonometri, ağsız yöntemler, Multikuadrik, Gauss

A New Trigonometric Based Radial Basis Function for Meshless Method Applications

Abstract

In this study, a new radial basis function
for meshless method is proposed. The proposed function was tested on four
different 2D problems along with the two well-known IMQ and Gauss functions.
Three of the test problems include 2^nd order engineering problems
whereas the last test problem was a 4^th order engineering problem. 2^nd
order engineering problems were used to investigate the type of boundary
conditions and problems. Numerical experiments suggested that similar order of
error can be obtained using the proposed function with less number of nodes
compared to IMQ and Gauss functions. Besides that, with an increase on the
number of nodes, the range of shape/scale parameter (epsilon) for the proposed function is broader
that that for the other two functions. Thus, the proposed function is a good
candidate for meshless method applications. 

Keywords

Radial basis function, trigonometry, meshless methods, Multiquadric, Gauss

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