DOI 10.1007/s11831-013-9086-4 Implementation and Scalability Analysis of Balancing Domain Decomposition Methods

Abstract In this paper we present a detailed description of a high-performance distributed-memory implementation of balancing domain decomposition preconditioning tech-niques. This coverage provides a pool of implementation hints and considerations that can be very useful for scien-tists that are willing to tackle large-scale distributed-memory machines using these methods. On the other hand, the pa-per includes a comprehensive performance and scalability study of the resulting codes when they are applied for the solution of the Poisson problem on a large-scale multicore-based distributed-memory machine with up to 4096 cores. Well-known theoretical results guarantee the optimality (al-gorithmic scalability) of these preconditioning techniques for weak scaling scenarios, as they are able to keep the con-dition number of the preconditioned operator bounded by a constant with fixed load per core and increasing number of cores. The experimental study presented in the paper com-plements this mathematical analysis and answers how far can these methods go in the number of cores and the scale of the problem to still be within reasonable ranges of ef-ficiency on current distributed-memory machines. Besides, for those scenarios where poor scalability is expected, th