Improving the Scalability of the ABCD Solver with a Combination of New Load Balancing and Communication Minimization Techniques.

The hybrid scheme block row-projection method implemented in the ABCD Solver is designed for solving large sparse unsymmetric systems of equations on distributed memory parallel computers. The method implements a block Cimmino iterative scheme, accelerated with a stabilized block conjugate gradient algorithm. An augmented pseudo-direct variant has also been developed to overcome convergence issues. Both methods are included in the ABCD solver with a hybrid parallelization scheme. The parallel performance of the ABCD Solver is improved in the first non-beta release, version 1.0, which we present in this paper. Novel algorithms for the distribution of partitions to processes are introduced to minimize communication as well as to balance the workload. Furthermore, the master-workers approach on each subsystem is also improved in order to achieve higher scalability through run-time placement of processes. We illustrate the improved parallel scalability of the ABCD Solver on a distributed memory architecture by solving several problems from the SuiteSparse Matrix Collection.