Absorbing boundary conditions for the Westervelt equation
Numerical Analysis
2014-08-22 v1
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.
Cite
@article{arxiv.1408.5031,
title = {Absorbing boundary conditions for the Westervelt equation},
author = {Barbara Kaltenbacher and Igor Shevchenko},
journal= {arXiv preprint arXiv:1408.5031},
year = {2014}
}