Günther Of

Stefan Dohr, Michal Merta, Günther Of et al.

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.

Christoph Erath, Günther Of, Francisco-Javier Sayas

As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we develop a new non-symmetric coupling between the vertex-centered finite volume and boundary element method. This discretization provides naturally conservation of local fluxes and with an upwind option also stability in the convection dominated case. We aim to provide a first rigorous analysis of the system for different model parameters; stability, convergence, and a~priori estimates. This includes the use of an implicit stabilization, known from the finite element and boundary element method coupling. Some numerical experiments conclude the work and confirm the theoretical results.