Efficient decomposition and performance of parallel PDE, FFT, Monte Carlo simulations, simplex, and Sparse solvers

Abstract

In this paper, we describe the decomposition of six algorithms: two partial differential equations (PDE) solvers (successive over-relaxation [SOR] and alternating direction implicit [ADI]), fast Fourier transform (FFT), Monte Carlo simulations, Simplex linear programming, and Sparse solvers. The algorithms were selected not only because of their importance in scientific applications, but also because they represent a variety of computational (structured to irregular) and communication (low to high) requirements. We present the performance results TM 1 of these algorithms on two shared-memory VAX/VMS multiprocessor prototypes: the VAX 6300 series with up to 8 processors and the M31 with up to 22 processors. We demonstrate that by efficient decomposition it is possible to achieve high performance for all algorithms on both prototypes. We describe the efficient decomposition techniques applied to optimize the performance of parallel algorithms. Also, we discuss the performance implications due to different cache designs on two multiprocessors.

Towards a practical parallelisation of the simplex method

“…A relatively early work which is representative of this era is due to Stunkel (1988) who implemented both the dense standard simplex method and the revised simplex method with a dense inverse on a 16-processor Intel hypercube, achieving a speed-up of between 8 and 12 for small problems from the Netlib set (Gay 1985). Cvetanovic et al (1991) report a speed-up of 12 when solving two small problems using the standard simplex method, a result that is notable for being achieved on a 16-processor shared memory machine. Luo and Reijns (1992) obtained speed-ups of more than 12 on 16 transputers when using the revised simplex method with a dense inverse to solve modest Netlib problems.…”

SPEED: A parallel platform for solving and predicting the performance of PDEs on distributed systems

“…Numerical weather prediction, oceanography, study of air and water pollutants also requires the solution of parabolic PDEs to model the time-dependent climate behavior with respect to a number of parameters[ 161. These different classes of PDEs are typically solved using different numerical methods [9,14]. SPEED focuses on the parallel solution of parabolic PDEs, which are also known as time-dependent PDEs.…”

A software platform for solving PDEs on distributed systems: implementation issues and performance prediction

“…Sequential numerical methods for solving time-dependent PDEs have been explored extensively [4], [SI. On the other hand, only a few attempts have been made toward parallel solutions using either transputers [7] or distributed-memory MlMD machines [2]. However, these parallel solu-tions are specific to particular kinds of problems and are not general in nature.…”