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From: john@spectre.unm.edu (John Prentice)
Newsgroups: comp.sys.super
Subject: Re: Massively Parallel LINPACK on the Intel Touchstone Delta machine
Message-ID: <1991Jun06.205144.22611@ariel.unm.edu>
Date: 6 Jun 91 20:51:44 GMT
References: <1991Jun5.120653.7852@hubcap.clemson.edu> <1991Jun05.185818.1071@convex.com> <1991Jun6.144903.20456@chpc.utexas.edu>
Organization: Dept. of Math & Stat, University of New Mexico, Albuquerque
Lines: 53

In article <1991Jun6.144903.20456@chpc.utexas.edu> gary@chpc.utexas.edu (Gary Smith) writes:
>
>
>Continuing to paraphrase Snyder: The frequent challenge with physical
>phemomena models is not to solve a fixed-size problem faster, but to
>solve larger instances within a fixed time budget.  Simple rationale:
>Solutions are so computationally intensive that problem instances of an
>"interesting" size do not complete execution in a tolerable amount of
>time.  What is the effect of parallelism on problem size?  Keeping time
>fixed and UNREALISTICALLY assuming the best possible speedup, it follows
>that superlinear problems (the interesting, realistic ones) can only be
>improved sublineraly by parallel computation.  Specifically, if a problem
>takes t = c*n^x sequential steps, and if the application of p processors
>permits an increase in the problem size by a factor of m, t = c*(m*n)^x/p,
>then the problem size can increase by at most a factor of m = p^(1/x).
>For example, to increase by two orders of magnitude the size of a problem
>whose sequential performance is given by t = cn^4 (three spacial, one time
>demension) requires, WITH UNREALISTIC OPTIMISM, 100,000,000 processors!
>
>Again, it's time for the advocates of the promise of massive parallelism
>to acknowledge Synder's "corollary of modest potential."
>

So what would you suggest as an alternative.  By this analysis, anyway
you cut it, a serial processor will still take p times longer to do the
same problem (of course, you have ignored overhead, but that works in 
favor of your argument).  If I can do it 64,000 times faster on a CM-2
and I don't have any choice but to do the problem, then I am going to
use the CM-2.  The alternative is to just not do the problem. 

Your are both right and wrong about what the goal is in scientific
computing.  For many applications, the goal isn't to run bigger problems,
it is to make current ones less expensive.  Clearly parallelism buys
you something there.  For ones where bigger is better, I will grant
you that parallelism has many drawbacks, but I fail to see an alternative.
The main thing that bothers me in your analysis however is that you are
being far too simplistic.  You are assuming that numerical schemes are
not going to change or be developed which exploit the unique capabilities
of a parallel architecture.  But things like multi-grid, composite grid
domain decomposition, and so forth are being developed and these schemes
can by made to really fly on a parallel system.  Parallelism is 
largely a new way of thinking and as more people become involved in it,
I think you will see numerical methods undergo some major advances as
people learn to think in terms of this new paradigm.

By the way, I know an awful lot of physicists who would not agree with
you that the only problems of interest are superlinear ones  :-) .

John
-- 
John K. Prentice    john@spectre.unm.edu (Internet)
Computational Physics Group
Amparo Corporation, Albuquerque, NM