Amirkabir Journal of Civil Engineering

Amirkabir Journal of Civil Engineering

A Comparison between the Performance of RBF-MQ Method and Cell-Centered Finite Volume Method in Solving 2d Wave Equation

Document Type : Research Article

Authors
Nasrin Tavakkoli 1
Majid Akbari 2
Reza Babaee 3
Ehsan Jabbari 3
1 University Of Qom, Qom, Iran
2 Sistan and Balouchestan University
3 University of Qom, Qom, Iran
10.22060/ceej.2026.23804.8245
Abstract
In this study, the performance of the multi-quadratic radial basis function (RBF-MQ) method is compared with the cell-centered finite volume method (FVM-CC) for solving the two-dimensional second-order wave equation. The wave equation describes wave propagation, such as sound waves, and relates the second derivatives in time and space to the wave speed. The finite volume method and radial basis function method are among the techniques used for modeling partial differential equations, such as the wave equation, in complex geometries. To compare the efficiency of these two methods, the finite volume method is first formulated based on triangular cell-centered volumes. The radial basis function superposition method is also developed using a multiquadric function for scattered points. Finally, time discretization is carried out using the explicit Euler method. The comparison of the performance and capabilities of both methods is made by performing several numerical tests on different geometries, initial and boundary conditions, scattered points, shape variables, and processing time for each method. For a more quantitative comparison, an analytical solution of the wave equation is obtained using the method of separation of variables for a simple rectangular geometry with specified initial and boundary conditions. The results of this study indicate lower computational cost and better efficiency of the multiquadric radial basis function method compared to the cell-centered finite volume method. However, the RBF-MQ method strongly depends on the shape parameter and the selected scattered point distribution. Additionally, the FVM-CC method provides higher relative accuracy compared to RBF-MQ, regardless of the shape parameter and selected scattered point distribution.
Keywords
Two-Dimensional Wave Equation
Finite Volume Method
Multiquadric Radial Basis Function Method
Cell-Centered Method
Meshless Method
Subjects
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Amirkabir Journal of Civil Engineering
Volume 58, Issue 4
2026
Pages 463-478