Long-Time Stability Analysis of Acoustic Absorbing Boundary Conditions for Regular-Shaped Surfaces

Hélène Barucq; Julien Diaz; Véronique Duprat

Long-Time Stability Analysis of Acoustic Absorbing Boundary Conditions for Regular-Shaped Surfaces

Hélène Barucq ^{1, 2} Julien Diaz ^{1, 2} Véronique Duprat ^{1, 2}

1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics

LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest

2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

Abstract : 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 we 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.

Document type :

Journal articles

Domain :

Mathematics [math] / Analysis of PDEs [math.AP]

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https://hal.inria.fr/hal-00759451
Contributor : Julien Diaz <>
Submitted on : Friday, November 21, 2014 - 2:26:34 PM
Last modification on : Monday, July 8, 2019 - 2:12:15 PM
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Long-Time Stability Analysis of Acoustic Absorbing Boundary Conditions for Regular-Shaped Surfaces

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