International Journal of Partial Differential Equations and Applications
ISSN (Print): 2376-9548 ISSN (Online): 2376-9556 Website: http://www.sciepub.com/journal/ijpdea Editor-in-chief: Mahammad Nurmammadov
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International Journal of Partial Differential Equations and Applications. 2016, 4(1), 1-6
DOI: 10.12691/ijpdea-4-1-1
Open AccessArticle

DRBEM Applied to the 3D Helmholtz Equation and Its Particular Solutions with Various Radial Basis Functions

Hassan Ghassemi1, , Saeed Fazelifar1 and Alireza Nadery1

1Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran

Pub. Date: May 03, 2016

Cite this paper:
Hassan Ghassemi, Saeed Fazelifar and Alireza Nadery. DRBEM Applied to the 3D Helmholtz Equation and Its Particular Solutions with Various Radial Basis Functions. International Journal of Partial Differential Equations and Applications. 2016; 4(1):1-6. doi: 10.12691/ijpdea-4-1-1

Abstract

This paper presents to solve the 3D Helmholtz equation using dual reciprocity boundary element method (DRBEM) and its particular solutions with various radial basis functions (RBFs). The important function in this method is to employ the RBF. Here, we find the particular solution of the Helmholtz equation (∇2±k2)h= f(r), where f(r) is the RBF. Various RBFs are chosen and the particular solutions are obtained. The dual reciprocity method (DRM) is a method that converts the domain integral into the boundary integral. Mathematical formulations and discretization forms are described and discussed. Numerical results with three RBF with and without polynomial terms are presented and discussed. Algorithm of the method is also presented.

Keywords:
3D Helmholtz equation radial basis function particular solution dual reciprocity method

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