A symplectic procedure for two-dimensional coupled elastic wave equations using radial basis functions interpolation. (1st November 2018)

• Record Type: Journal Article
• Authors: Zhang, Shengliang
• Is Part Of: Computers & mathematics with applications. Volume 76:issue 9(2018)
• Page Start: 2167
• Page End: 2178
• Publication Date: 2018-11-01
• Subjects: Two-dimensional elastic wave equations -- Radial basis functions -- Meshless method -- Symplectic integrator -- Energy conserving; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.08.014
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This study proposes a meshless symplectic algorithm for two-dimensional coupled elastic waves, which satisfy the equations of linear isotropic elasticity on a rectangular domain with appropriate initial and boundary conditions. This method is based on a combination of radial basis functions (RBFs) collocation and geometric integrators. The method involves two steps, first the spatial discretization by using RBFs interpolation transforms the seismic waves into a finite-dimensional Hamiltonian system, then evolves the semi-discretized system by using symplectic integrators. Furthermore, the conservations of energy and symplectic structure are investigated. The truncation error and global error of the method are estimated. Numerical experiments show that the scheme is efficient, easy to implement with the scattered knots and possesses a good behavior in the long time integration.