The solution of the wave equation in a polyhedral domain admits an
asymptotic expansion in a neighborhood of the corners and edges.
In this article we formulate boundary and screen problems for the
wave equation as an equivalent boundary integral equations in time
domain and study the regularity properties and numerical approximation
of the solution. Guided by the theory for elliptic equations, graded
meshes are shown to recover the optimal approximation rates expected
for smooth solutions. Numerical experiments illustrate the theory
for screen problems. In particular, we discuss the Dirichlet problem,
the Dirichlet-to-Neumann operator and applications to the sound emitted
by a tire.