  We describe a parallel solver for the discretized weakly singular space-time
boundary integral equation of the spatially two-dimensional heat equation. The
global space-time nature of the system matrices leads to improved parallel
scalability in distributed memory systems in contrast to time-stepping methods
where the parallelization is usually limited to spatial dimensions. We present
a parallelization technique which is based on a decomposition of the input mesh
into submeshes and a distribution of the corresponding blocks of the system
matrices among processors. To ensure load balancing, the distribution is based
on a cylic decomposition of complete graphs. In addition, the solution of the
global linear system requires the use of an efficient preconditioner. We
present a robust preconditioning strategy which is based on boundary integral
operators of opposite order, and extend the introduced parallel solver to the
preconditioned system.
