Convolution quadrature for the wave equation with impedance boundary conditions

Abstract

We consider the numerical solution of the wave equation with impedance boundary conditions and start from a boundary integral formulation for its discretization. We develop the generalized convolution quadrature (gCQ) to solve the arising acoustic retarded potential integral equation for this impedance problem.

For the special case of scattering from a spherical object, we derive representations of analytic solutions which allow to investigate the effect of the impedance coefficient on the acoustic pressure analytically. We have performed systematic numerical experiments to study the convergence rates as well as the sensitivity of the acoustic pressure from the impedance coefficients.

Finally, we apply this method to simulate the acoustic pressure in a building with a fairly complicated geometry and to study the influence of the impedance coefficient also in this situation.