Frontiers in Physics (Aug 2023)
A space-time domain RBF method for 2D wave equations
Abstract
In the present study, we demonstrate the feasibility to reveal the numerical solution of the multi-dimensional wave equations. A simple semi-analytical meshless method was proposed to obtain the numerical solution of the wave equation with a newly-proposed space-time radial basis function to enhance the numerical stability. The wave equation was discretized into equivalent algebraic equations. By specifying boundary and initial conditions, the wave propagation in a two-dimensional domain can be virtually reconstructed. Our results exhibit that the semi-analytical meshless method is suitable and efficient for solving multi-dimensional wave equations.
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