Optimized finite difference iterative scheme based on POD technique for 2D viscoelastic wave equation

被引：0
作者：
Hong Xia
Zhendong Luo
机构：
[1] North China Electric Power University,School of Control and Computer Engineering
[2] North China Electric Power University,School of Mathematics and Physics
来源：
Applied Mathematics and Mechanics | 2017年 / 38卷
关键词：
optimized finite difference iterative (OFDI) scheme; viscoelastic wave equation; proper orthogonal decomposition (POD); existence; stability; convergence; numerical simulation; O241; 65M60; 65N30; 65N15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This study develops an optimized finite difference iterative (OFDI) scheme for the two-dimensional (2D) viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition (POD) method. It has sufficiently high accuracy with very few unknowns for the 2D viscoelastic wave equation. Existence, stability, and convergence of the OFDI solutions are analyzed. Numerical simulations verify efficiency and feasibility of the proposed scheme.
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页码：1721 / 1732
页数：11
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[21]  
Luo Z. D.(2017)Comparison of POD reduced order strategies for the nonlinear 2D shallow water equations Applied Mathematics and Mechanics 38 289-310
[22]  
Zhu J.(2015)Reduced-order proper orthogonal decomposition extrapolating finite volume element format for two-dimensional hyperbolic equations Annals of the Academy of Romanian Scientists 7 173-188
[23]  
Wang R. W.(2014)POD-DEIM approach on dimension reduction of a multi-species host-parasitoid system Advances in Difference Equations 2014 1-18
[24]  
Navon I. M.(2015)A POD-based reduced-order finite difference extrapolating model for the non-stationary incompressible Boussinesq equations Frontiers of Mathematics in China 10 1025-1040
[25]  
Luo Z. D.(2016)Reduced-order extrapolation spectral-finite difference scheme based on POD method and error estimation for three-dimensional parabolic equation Journal of Mathematical Analysis and Applications 444 433-451
[26]  
Chen J.(2016)A POD-based reduced-order finite difference time-domain extrapolating scheme for the 2D Maxwell equations in a lossy medium Applied Mathematics and Computation 289 396-408
[27]  
Navon I. M.(2007)A reduced-order extrapolation central difference scheme based on POD for two dimensional fourth-order hyperbolic equations SIAM Journal on Numerical Analysis 45 837-869
[28]  
Yang X. Z.(2008)Stability and convergence of the Crank-Nicolson/Adams-Bashforth scheme for the time-dependent Navier-Stokes equations Mathematics of Computation 77 2097-2124
[29]  
Luo Z. D.(undefined)The Euler implicit/explicit scheme for the 2D time-dependent Navier-Stokes equations with smooth or non-smooth initial data undefined undefined undefined-undefined
[30]  
Yang X. Z.(undefined)undefined undefined undefined undefined-undefined
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