Paper Info
Title
The Conservative Time High-Order AVF Compact Finite Difference Schemes for Two-Dimensional Variable Coefficient Acoustic Wave Equations.
Abstract
In this paper, we develop and analyze the energy conservative time high-order AVF compact finite difference methods for variable coefficient acoustic wave equations in two dimensions. We first derive out an infinite-dimensional Hamiltonian system for the variable coefficient wave equations and apply the spatial fourth-order compact finite difference operator to the equations of the system to obtain a semi-discrete approximation system, which can be cast into a canonical finite-dimensional Hamiltonian form. We then apply the second-order and fourth-order AVF techniques to propose the fully discrete energy conservative time high-order AVF compact finite difference methods for wave equations in two dimensions. We prove that the proposed semi-discrete and fully-discrete schemes satisfy energy conservations in the discrete forms. We further prove that the semi-discrete scheme has the fourth-order convergence order in space and the fully-discrete AVF compact finite difference method has the fourth-order convergence order in both time and space. Numerical tests confirm the theoretical results.
Year
DOI
Venue
2019
10.1007/s10915-019-00983-6
Journal of Scientific Computing
Keywords
Field
DocType
AVF method, Compact finite difference, Energy conservation, Convergence analysis, Variable coefficient wave equation, Hamiltonian, 37K05, 65M06, 65N06, 65N12
Convergence (routing),Compact finite difference,Hamiltonian (quantum mechanics),Mathematical analysis,Spacetime,Hamiltonian system,Operator (computer programming),Wave equation,Acoustic wave,Mathematics
Journal
Volume
Issue
ISSN
80
2
0885-7474
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Baohui Hou100.34
Liang Dong232652.32
Hongmei Zhu321.42