Convolution quadrature for the wave equation with a nonlinear impedance boundary condition

Banjai, Lehel; Rieder, Alexander

doi:10.1090/mcom/3279

Convolution quadrature for the wave equation with a nonlinear impedance boundary condition
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by Lehel Banjai and Alexander Rieder PDF

Math. Comp. 87 (2018), 1783-1819 Request permission

Abstract:

A rarely exploited advantage of time-domain boundary integral equations compared to their frequency counterparts is that they can be used to treat certain nonlinear problems. In this work we investigate the scattering of acoustic waves by a bounded obstacle with a nonlinear impedance boundary condition. We describe a boundary integral formulation of the problem and prove without any smoothness assumptions on the solution the convergence of a full discretization: Galerkin in space and convolution quadrature in time. If the solution is sufficiently regular, we prove that the discrete method converges at optimal rates. Numerical evidence in 3D supports the theory.

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