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Journal Articles Mathematical Models and Methods in Applied Sciences Year : 2013

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

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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Dates and versions

hal-00759451 , version 1 (21-11-2014)

Identifiers

  • HAL Id : hal-00759451 , version 1

Cite

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, 2013, 23 (11), pp.2129-2154. ⟨hal-00759451⟩
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