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
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.
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Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2013, 23 (11), pp.2129-2154
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Hélène Barucq, Julien Diaz, Véronique Duprat. Long-Time Stability Analysis of Acoustic Absorbing Boundary Conditions for Regular-Shaped Surfaces. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2013, 23 (11), pp.2129-2154. 〈hal-00759451〉

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