Efficient resolution of wave scattering problems

The use of time-domain boundary integral equations to solve wave scattering problems has become a very active field of research in the last decade. In particular great progress has been achieved in the time discretization of these problems, being the so-called „convolution quadrature methods“ among the most accepted ones in this context. In this talk I will introduce convolution quadrature methods and will review some of their nice properties. I will present modern algorithms for their efficient implementation, either with a fixed time step or with a variable time step, and will show a few numerical results to illustrate the theory. Finally I will outline some open problems.