Meshless local radial point interpolation (MLRPI) to two dimensional wave equation with Neumann’s boundary conditions

Document Type : Research Paper

Authors

Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran

Abstract

In this article, the meshless local radial point interpolation (MLRPI) methods are applied to simulate two dimensional wave equation subject to given appropriate initial and Neumann’s boundary conditions. In MLRPI method, all integrations are carried out locally over small quadrature domains of regular shapes such as square or circle. The radial point interpolation method is proposed to construct shape functions for MLRPI. A weak formulation with a Heaviside step function transforms the set of governing equations into local integral equations on local sub domains where Neumann’s boundary condition is imposed naturally. A two-step time discretization method with the help of Crank-Nicolson technique is employed to approximate the time derivatives. Convergence studies in the numerical example show that MLRPI method possesses excellent rates of convergence.

Keywords


Volume 8, Issue 1
January 2020
Pages 155-172
  • Receive Date: 06 May 2018
  • Revise Date: 05 September 2018
  • Accept Date: 23 September 2018
  • First Publish Date: 01 January 2020