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Scientific Programming
Volume 3 (1994), Issue 1, Pages 13-32

On the Parallel Elliptic Single/Multigrid Solutions about Aligned and Nonaligned Bodies Using the Virtual Machine for Multiprocessors

A. Averbuch, E. Gabber, S. Itzikowitz, and B. Shoham

School of Mathematical Sciences, Department of Compater Science, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel

Received 30 March 1992; Accepted 30 July 1993

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Parallel elliptic single/multigrid solutions around an aligned and nonaligned body are presented and implemented on two multi-user and single-user shared memory multiprocessors (Sequent Symmetry and MOS) and on a distributed memory multiprocessor (a Transputer network). Our parallel implementation uses the Virtual Machine for Muli-Processors (VMMP), a software package that provides a coherent set of services for explicitly parallel application programs running on diverse multiple instruction multiple data (MIMD) multiprocessors, both shared memory and message passing. VMMP is intended to simplify parallel program writing and to promote portable and efficient programming. Furthermore, it ensures high portability of application programs by implementing the same services on all target multiprocessors. The performance of our algorithm is investigated in detail. It is seen to fit well the above architectures when the number of processors is less than the maximal number of grid points along the axes. In general, the efficiency in the nonaligned case is higher than in the aligned case. Alignment overhead is observed to be up to 200% in the shared-memory case and up to 65% in the message-passing case. We have demonstrated that when using VMMP, the portability of the algorithms is straightforward and efficient.