On the stability of the high-order Higdon Absorbing Boundary Conditions

2011 ◽  
Vol 61 (6) ◽  
pp. 768-784 ◽  
Author(s):  
Daniel Baffet ◽  
Dan Givoli
Keyword(s):  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
High Order ◽  
Absorbing Boundary ◽  
The Stability

Analysis of High-Order Absorbing Boundary Conditions for the Schrödinger Equation

2011 ◽  
Vol 10 (3) ◽  
pp. 742-766 ◽  
Author(s):  
Jiwei Zhang ◽  
Zhizhong Sun ◽  
Xiaonan Wu ◽  
Desheng Wang
Keyword(s):  
Boundary Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Absorbing Boundary Conditions ◽  
High Order ◽  
Absorbing Boundary ◽  
The Stability ◽  
Initial Boundary Value ◽  
Dimensional Domain ◽  
Convergence Of The Scheme

AbstractThe paper is concerned with the numerical solution of Schrödinger equations on an unbounded spatial domain. High-order absorbing boundary conditions for one-dimensional domain are derived, and the stability of the reduced initial boundary value problem in the computational interval is proved by energy estimate. Then a second order finite difference scheme is proposed, and the convergence of the scheme is established as well. Finally, numerical examples are reported to confirm our error estimates of the numerical methods.

LONG-TERM STABILITY ANALYSIS OF ACOUSTIC ABSORBING BOUNDARY CONDITIONS

2013 ◽  
Vol 23 (11) ◽  
pp. 2129-2154 ◽  
Author(s):  
HÉLÈNE BARUCQ ◽  
JULIEN DIAZ ◽  
VÉRONIQUE DUPRAT
Keyword(s):  
Stability Analysis ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Acoustic Wave Equation ◽  
Absorbing Boundary ◽  
Term Stability ◽  
Long Term Stability ◽  
The Stability

This work deals with the stability analysis of a one-parameter family of Absorbing Boundary Conditions (ABC) that have been derived for the acoustic wave equation. We tackle the problem of long-term stability of the wave field both at the continuous and the numerical levels. We first define a function of energy and show that it is decreasing in time. Its discrete form is also decreasing under a Courant–Friedrichs–Lewy (CFL) condition that does not depend on the ABC. Moreover, the decay rate of the continuous energy can be determined: it is exponential if the computational domain is star-shaped and this property can be illustrated numerically.

High order local absorbing boundary conditions for acoustic and elastic scattering

2020 ◽  
Vol 148 (4) ◽  
pp. 2451-2451
Author(s):  
Vianey Villamizar ◽  
Tahsin Khajah ◽  
Sebastian Acosta ◽  
Dane Grundvig ◽  
Jacob Badger ◽  
...  
Keyword(s):  
Elastic Scattering ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
High Order ◽  
Absorbing Boundary
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