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We describe a parallel solver for the discretized weakly singular space-timeboundary integral equation of the spatially two-dimensional heat equation. Theglobal space-time nature of the system matrices leads to improved parallelscalability in distributed memory systems in contrast to time-stepping methodswhere the parallelization is usually limited to spatial dimensions. We presenta parallelization technique which is based on a decomposition of the input meshinto submeshes and a distribution of the corresponding blocks of the systemmatrices among processors. To ensure load balancing, the distribution is basedon a cylic decomposition of complete graphs. In addition, the solution of theglobal linear system requires the use of an efficient preconditioner. Wepresent a robust preconditioning strategy which is based on boundary integraloperators of opposite order, and extend the introduced parallel solver to thepreconditioned system.

A parallel solver for a preconditioned space-time boundary element method for the heat equation