A parallel solver for a preconditioned space-time boundary element method for the heat equation
For researchers in computational science and engineering, this work addresses the parallel scalability bottleneck of time-stepping methods for the heat equation by enabling efficient distributed memory computation of space-time boundary integral equations.
The paper presents a parallel solver for a space-time boundary element method for the 2D heat equation, achieving improved parallel scalability over time-stepping methods by using a cyclic decomposition of complete graphs for load balancing and a robust preconditioner based on boundary integral operators of opposite order.
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.