AUTHOR=Wang Fu-Zhang , Shao Ming-Yu , Li Jia-Le , Zhang Zhong-Liang TITLE=A space-time domain RBF method for 2D wave equations JOURNAL=Frontiers in Physics VOLUME=11 YEAR=2023 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1241196 DOI=10.3389/fphy.2023.1241196 ISSN=2296-424X 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.