  The solution of the wave equation in a polyhedral domain in $\mathbb{R}^3$
admits an asymptotic singular expansion in a neighborhood of the corners and
edges. In this article we formulate boundary and screen problems for the wave
equation as equivalent boundary integral equations in time domain, study the
regularity properties of their solutions and the numerical approximation.
Guided by the theory for elliptic equations, graded meshes are shown to recover
the optimal approximation rates known for smooth solutions. Numerical
experiments illustrate the theory for screen problems. In particular, we
discuss the Dirichlet and Neumann problems, as well as the Dirichlet-to-Neumann
operator and applications to the sound emission of tires.
