2014/08/21 by Barbara Kaltenbacher, Kaltenbacher, Barbara, Igor Shevchenko +1
Engineering · Mathematics · #35C07 #35L20 #35L70 #Advanced Mathematical Physics Problems #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1408.5031
openalex publication_date 2014/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.