Parallel Performance Studies for an Elliptic Test Problem
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2008
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Abstract
The performance of parallel computer code depends on an intricate interplay of the processors, the architecture of the compute nodes, their interconnect network, the numerical algorithm, and the scheduling policy used. The solution of large, sparse, highly structured systems of linear equations by an iterative linear solver that requires communication between the parallel processes at every iteration is an instructive test of this interplay. This note considers the classical elliptic test problem of a Poisson equation with Dirichlet boundary conditions, whose approximation by the finite difference method results in a linear system of this
type. Our existing implementation of the conjugate gradient method for the iterative solution of this system is known to have the potential to perform well up to many parallel processes, provided the interconnect network has low latency. Since the algorithm is known to be memory bound, it is also vital for good performance that the architecture of the nodes in conjunction with the scheduling policy does not create a bottleneck. The results presented here show excellent performance the cluster hpc in the UMBC High Performance Computing Facility and give guidance on the scheduling policy to be implemented. Specifically, they confirm that it is beneficial to use all four cores of the two dual-core processors on each node simultaneously, giving us in
effect a computer that can run jobs efficiently with up to 128 parallel processes.