  We consider the efficient numerical solution of the three-dimensional wave
equation with Neumann boundary conditions via time-domain boundary integral
equations. A space-time Galerkin method with $C^\infty$-smooth, compactly
supported basis functions in time and piecewise polynomial basis functions in
space is employed. We discuss the structure of the system matrix and its
efficient parallel assembly. Different preconditioning strategies for the
solution of the arising systems with block Hessenberg matrices are proposed and
investigated numerically. Furthermore, a C++ implementation parallelized by
OpenMP and MPI in shared and distributed memory, respectively, is presented.
The code is part of the boundary element library BEM4I. Results of numerical
experiments including convergence and scalability tests up to a thousand cores
on a cluster are provided. The presented implementation shows good parallel
scalability of the system matrix assembly. Moreover, the proposed algebraic
preconditioner in combination with the FGMRES solver leads to a significant
reduction of the computational time.
