Edinburgh Research Explorer

A hybrid approach for extreme scalability when solving linear systems

Research output: Contribution to conferenceAbstract


Iterative methods for solving large sparse systems of linear equations are widely used in many HPC applications. Extreme scaling of these methods can be difficult, however, since global synchronisation to form dot products is typically required at every iteration.

To try to overcome this limitation we propose a hybrid approach, where the solution space is partitioned up into blocks. The solving of these blocks occurs at two levels; interblock communication is performed synchronously and intrablock asynchronously. Following this approach it is possible to completely separate the concerns involved at the block and intra block level, allowing one to choose a highly optimised (parallel) internal block solver and an asynchronous method operating at the global level. Using this approach one can achieve extreme scalability - when the limits of conventional solvers start to be reached the system can be partitioned into one or more blocks, each operating with the same conventional solver but at a high level employing asynchronous block Jacobi or some other multisplitting technique.

Our block framework has been built to use PETSc, a popular scientific suite for solving sparse linear systems, as the synchronous interblock solver, and we demonstrate results on up to 32768 cores of a Cray XE6 system.

ID: 21942275