1Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran
International Journal of Partial Differential Equations and Applications.
2016,
Vol. 4 No. 1, 1-6
DOI: 10.12691/ijpdea-4-1-1
Copyright © 2016 Science and Education PublishingCite this paper: Hassan Ghassemi, Saeed Fazelifar, 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.
Correspondence to: Hassan Ghassemi, Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran. Email:
gasemi@aut.ac.irAbstract
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.
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