Performance comparison of a set of periodic and non-periodic tridiagonal solvers on SP2 and Paragon parallel computers

Abstract

Various tridiagonal solvers have been proposed in recent years for different parallel platforms. In this paper, the performance of three tridiagonal solvers, namely, the parallel partition LU algorithm, the parallel diagonal dominant algorithm, and the reduced diagonal dominant algorithm, is studied. These algorithms are designed for distributed‐memory machines and are tested on an Intel Paragon and an IBM SP2 machine. Measured results are reported in terms of execution time and speedup. Analytical studies are conducted for different communication topologies and for different tridiagonal systems. The measured results match the analytical results closely. In addition to addressing implementation issues, performance considerations such as problem sizes and models of speedup are also discussed. © 1997 John Wiley & Sons, Ltd.

A parallel two-level hybrid method for tridiagonal systems and its application to fast poisson solvers

“…2. As shown in [12], [13], [15], for most diagonal dominant systems, when the subsystem size is greater than 64, the reduced matrix Z is equivalent to e Z Z within machine accuracy for numerical computing. PDD uses e Z Z for the solution and needs only two neighboring communications.…”

“…We first use the measured results to confirm the performance formulas and then use the formulas to predict the performance on even larger computing systems. Since PDD is well-studied in [13], only PPD and the pipelined method are studied here.…”

“…It requests diagonal dominance. Studies of the application, accuracy, and performance of PDD algorithm can be found in [12], [13].…”