Parallel Numerical Algorithms: an Introduction

The rapidly evolving field of parallel computing has seen four eras, substantially overlapping, yet progressive. The first, which we could label the Stone Age, was characterized by having speed-up as its primary objective (" Solve my problem faster... "). The tyranny of Amdahl's Law, combined with architectural convergence to systems that added memory in fixed proportion to processors, led to the Bronze Age, characterized by pursuit of scaled speed-up (" Solve my problem bigger, in constant time... "). The cost associated with special purpose high-performance hardware and the even greater cost of developing reliable special purpose system-level software led to the Iron Age of commodity processors — clusters of full-function computers connected by either a special purpose network or a commodity network like Ethernet or FDDI (" Solve my problem cheaper... "). Though technology and market forces have not been eclipsed in their influence on parallel tool-building and parallel applications, we can now point to a growing influence of algorithmic development and software environment development on the envelope of computabil-ity (" Solve my problem smarter... "). Perhaps, through continued progress in architecture-adaptive algorithmic design that improves upon " best fit " flop-for-flop algorithmic porting, we will soon be able to refer to a Golden Age of parallel computing. The goals of the ICASE program in parallel numerical algorithms are to accelerate, widen, and enhance the use of high performance parallel scientific computing within NASA computational applications. The first goal refers to hastening the transition to parallel