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

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.

Anahtar Kelimeler:

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

A New Trigonometric Based Radial Basis Function for Meshless Method Applications

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 2nd order engineering problems whereas the last test problem was a 4th order engineering problem. 2nd 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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