Uniform boundary stabilization for the finite difference semi-discretization of 2-D wave equation

2013 ◽  
Vol 25 (3) ◽  
pp. 623-643 ◽  
Author(s):  
H. Bouslous ◽  
H. El Boujaoui ◽  
L. Maniar
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Boundary Stabilization ◽  
D Wave

Uniform boundary stabilization for the finite difference discretization of the 1-D wave equation

2016 ◽  
Vol 27 (7-8) ◽  
pp. 1239-1262 ◽  
Author(s):  
H. El Boujaoui ◽  
L. Maniar ◽  
H. Bouslous
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Boundary Stabilization ◽  
Finite Difference Discretization ◽  
Difference Discretization ◽  
D Wave

Uniform boundary stabilization of the finite difference space discretization of the 1−d wave equation

2006 ◽  
Vol 26 (1-3) ◽  
pp. 337-365 ◽  
Author(s):  
Louis T. Tebou ◽  
Enrique Zuazua
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Boundary Stabilization ◽  
Space Discretization ◽  
D Wave

Uniform interior stabilization for the finite difference fully-discretization of the 1-D wave equation

2018 ◽  
Vol 29 (3-4) ◽  
pp. 557-574
Author(s):  
H. El Boujaoui
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
D Wave

Boundary Stabilization of a 1-D Wave Equation with In-Domain Antidamping

2010 ◽  
Vol 48 (6) ◽  
pp. 4014-4031 ◽  
Author(s):  
Andrey Smyshlyaev ◽  
Eduardo Cerpa ◽  
Miroslav Krstic
Keyword(s):  
Wave Equation ◽  
Boundary Stabilization ◽  
D Wave

scholarly journals The controllability for the internally controlled 1-D wave equation via a finite difference method

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Juntao Li ◽  
Yuhan Zheng ◽  
Guojie Zheng
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
D Wave

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

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