### Parallel Numerical Computations with Applications

#### Abstract

Edited by Tianruo Yang

Kluwer Academic Publisher, Dordrech, Netherlands, 1999, 248 pp.

ISBN 0-7923-8588-8, $135.00

This book contains a selection of contributed and invited papers presented and the workshop *Frontiers of Parallel Numerical Computations and Applications,* in the *IEEE 7th Symposium on the Frontiers on Massively Parallel Computers* (Frontiers '99) at Annapolis, Maryland, February 20-25, 1999. Its main purpose is to update the designers and users of parallel numerical algorithms with the latest research in the field. A broad spectrum of topics on parallel numerical computations, with applications to some of the more challenging engineering problems, is covered. Parallel algorithm designers and engineers who use extensively parallel numerical computations, as well as graduate students in Computer Science, Scientific Computing, various engineering fields and applied mathematics should benefit from reading it.

The first part is addressed to a larger audience and presents papers on parallel numerical algorithms. Two new libraries are presented: PSPASSES and PoLAPACK. PSPASSES is a collection of parallel direct solvers, for sparse symmetric positive definite linear systems, which are characterized by high performance and good scalability. PoLAPACK library contains LU and QR codes based on a new blocking strategy that guarantees good performance regardless of the physical block size. Next, an efficient approach to solving stiff ordinary differential equations by diagonal implicitly iterated Runge-Kutta (DIIRK) method is described. DIIRK renders a fast parallel implementation due to a reduced number of function evaluation and an automatic stepsize control mechanism. Finally, minimization of sufficiently smooth non-linear functionals is sought via parallel space decomposition. Here, a theoretical background of the problem and two equivalent algorithms are presented. New research directions for classical solvers are treated in the next three papers: first, reduction of the global synchronization in the biconjugate gradient method, second, a new more efficient Jacobi ordering for the multiple-port hypercubes, and finally, an analysis of the theoretical performance of an improved version of the Quasi-minimal residual method.

Parallel numerical applications constitute the second part of the book, with results from fluid mechanics, material sciences, applications to signal and image processing, dynamic systems, semiconductor technology and electronic circuits and systems design. With one exception, the authors expose in detail parallel implementations of the algorithms and numerical results. First, a 3D-elasticity problem is solved using an additive overlapping domain decomposition algorithm. Second, an overlapping mesh technique is used in a parallel solver for the compressible flow problem. Then, a parallel version of a complex numerical algorithm to solve a lubrication problem studied in tribology is introduced. Next, a timid approach to parallel computing of the cavity flow by the finite element method is presented. The problem solved is rather small for today's needs and only up to 6 processors are used. This is also the only paper that does not present results from numerical experiments. The remaining applications discussed in the subsequent chapters are: large scale multidisciplinary design optimization problem with application to the design of a supersonic commercial aircraft, a report on progress in parallel solution of an electromagnetic scattering problem using boundary integral methods and an optimal solution to the convection-diffusion equation modeling the concentration of a pollutant in the air.

The book is of definite interest to readers who keep up-to-date with the parallel numerical computation research. The main purpose, to present the novel ideas, results and work in progress and advancing state-of-the-art techniques in the area of parallel and distributed computing for numerical and computational optimization problems in scientific and engineering application is clearly achieved. However, due to its content it cannot serve as a textbook for a computer science or engineering class. Overall, is a reference type book to be kept by specialists and in a library rather than a book to be purchased for self-introduction to the field. Most of the papers presented are results of ongoing research and so they rely heavily on previous results. On the other hand, with only one exception, the results presented in the papers are a great source of information for the researchers currently involved in the field.

Michelle Pal,

Los Alamos National Laboratory

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