Parallelization of krylov subspace methods in multiprocessor PC clusters

Abstract

This chapter describes the parallelization of two Krylov subspace methods in multiprocessor clusters. The objective of this parallelization was the efficient solution of sparse and huge linear equations systems, resulting from the discretization of a hydrodynamics and mass transport model. The objective of this work is to compare of the use of different tools, as well as the use of different approaches to the exploration of intra-node parallelism, presenting an analysis of the results obtained. In this work, the computational performance is also compared obtained with the use of two processors in dual processor nodes, and the use of a single processor in each node, using more nodes to get the same number of processors. From the obtained results an analysis of the cost/benefit ratio of the use of dual machines versus mono-processed machines in PC clusters is done. An important issue that must be considered in the decision of using dual processor nodes or mono-processed nodes is memory contention. Some tests done with two processes in dual processor nodes showed that memory contention grows with the use of memory by the application. This result suggests that, in applications that use less memory and have a good scalability, the use of multiprocessor nodes is more viable, as it presents a similar result to that obtained using mono-processed nodes, by a lower cost. Other advantage in the use of multiprocessor nodes is the possibility of exploration intra-node parallelism through the use of multithreading.