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Generalized Finite Difference Time Domain Method and Its Application to Acoustics
Joint Authors
Wei, Jianguo
Wang, Song
Hou, Qingzhi
Dang, Jianwu
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-06-23
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Wei, Jianguo& Wang, Song& Hou, Qingzhi& Dang, Jianwu. 2015. Generalized Finite Difference Time Domain Method and Its Application to Acoustics. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1074363
Modern Language Association (MLA)
Wei, Jianguo…[et al.]. Generalized Finite Difference Time Domain Method and Its Application to Acoustics. Mathematical Problems in Engineering No. 2015 (2015), pp.1-13.
https://search.emarefa.net/detail/BIM-1074363
American Medical Association (AMA)
Wei, Jianguo& Wang, Song& Hou, Qingzhi& Dang, Jianwu. Generalized Finite Difference Time Domain Method and Its Application to Acoustics. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1074363
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074363