Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature

by   Lehel Banjai, et al.

Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes materials with a thin coating (with the thickness of the coating as the small scale) and strongly absorbing materials. For the acoustic scattering from generalized impedance boundary conditions, the approach taken here first determines the Dirichlet and Neumann boundary data from a system of time-dependent boundary integral equations with the usual boundary integral operators, and then the scattered wave is obtained from the Kirchhoff representation. The system of time-dependent boundary integral equations is discretized by boundary elements in space and convolution quadrature in time. The well-posedness of the problem and the stability of the numerical discretization rely on the coercivity of the Calderón operator for the Helmholtz equation with frequencies in a complex half-plane. Convergence of optimal order in the natural norms is proved for the full discretization. Numerical experiments illustrate the behaviour of the proposed numerical method.



There are no comments yet.


page 23


Time-dependent electromagnetic scattering from thin layers

The scattering of electromagnetic waves from obstacles with wave-materia...

Absorbing boundary conditions for the time-dependent Schrödinger-type equations in R^3

Absorbing boundary conditions are presented for three-dimensional time-d...

Integral boundary conditions in phase field models

Modeling the microstructure evolution of a material embedded in a device...

The Time Domain Linear Sampling Method for Determining the Shape of a Scatterer using Electromagnetic Waves

The time domain linear sampling method (TD-LSM) solves inverse scatterin...

PML and high-accuracy boundary integral equation solver for wave scattering by a locally defected periodic surface

This paper studies the PML method for wave scattering in a half space of...

Generalized Internal Boundaries (GIB)

Representing large-scale motions and topological changes in the finite v...

Helmholtz scattering by random domains: first-order sparse boundary elements approximation

We consider the numerical solution of time-harmonic acoustic scattering ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.