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Mathematical Problems in Engineering
Volume 2015, Article ID 640305, 13 pages
Research Article

Generalized Finite Difference Time Domain Method and Its Application to Acoustics

1School of Computer Software, Tianjin University, Tianjin 300072, China
2Tianjin Key Laboratory of Cognitive Computing and Application, Tianjin University, Tianjin 300072, China
3Japan Advanced Institute of Science and Technology, Ishikawa 923-1292, Japan

Received 28 August 2014; Revised 11 January 2015; Accepted 11 January 2015

Academic Editor: Shaofan Li

Copyright © 2015 Jianguo Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A meshless generalized finite difference time domain (GFDTD) method is proposed and applied to transient acoustics to overcome difficulties due to use of grids or mesh. Inspired by the derivation of meshless particle methods, the generalized finite difference method (GFDM) is reformulated utilizing Taylor series expansion. It is in a way different from the conventional derivation of GFDM in which a weighted energy norm was minimized. The similarity and difference between GFDM and particle methods are hence conveniently examined. It is shown that GFDM has better performance than the modified smoothed particle method in approximating the first- and second-order derivatives of 1D and 2D functions. To solve acoustic wave propagation problems, GFDM is used to approximate the spatial derivatives and the leap-frog scheme is used for time integration. By analog with FDTD, the whole algorithm is referred to as GFDTD. Examples in one- and two-dimensional domain with reflection and absorbing boundary conditions are solved and good agreements with the FDTD reference solutions are observed, even with irregular point distribution. The developed GFDTD method has advantages in solving wave propagation in domain with irregular and moving boundaries.