Absorbing boundary conditions for the Westervelt equation

Igor  Shevchenko; Barbara  Kaltenbacher

doi:10.3934/proc.2015.1000

Article Contents

2015, Volume 2015: 1000-1008. Doi: 10.3934/proc.2015.1000 open access

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Absorbing boundary conditions for the Westervelt equation

Igor Shevchenko^1, and
Barbara Kaltenbacher^2,

1.
Imperial College London, Department of Mathematics, London, SW7 2AZ
2.
Alpen-Adria-Universität Klagenfurt, Institute of Mathematics, Klagenfurt, A-9020

Received: August 31, 2014

Revised: November 30, 2014

Published: October 2015

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Abstract

The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is pseudo-differential calculus. This approach enables to develop high order boundary conditions in a consistent way which are typically more accurate than their low order analogs. Under the hypothesis of small initial data, we establish local well-posedness for the Westervelt equation with the absorbing boundary conditions. The performed numerical experiments illustrate the efficiency of the proposed boundary conditions for different regimes of wave propagation.

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Mathematics Subject Classification: 35C07, 35L20, 35L70.

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