Forwarded: Mon, 19 Apr 1999 14:36:32 -0400
Forwarded: linda@rice.edu
Replied: Mon, 19 Apr 1999 14:36:09 -0400
Replied: John Salmon <johns@fishnet.caltech.edu>
Date: Mon, 19 Apr 1999 09:12:51 -0700
Message-Id: <199904191612.JAA07783@fishnet.caltech.edu>
From: John Salmon <johns@fishnet.caltech.edu>
To: gcf@npac.syr.edu
Subject: abstract
Content-Type: text
Content-Length: 3340


Here it is.  I thought about disappearing to the Far East, but there
just weren't any flights available to Cambodia this time :-)

John


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<h2>Computational Cosmology</h2>
<!-- I think it should be called Computational Cosmology rather than
    Computational Astrophysics.  The latter is much broader and I will
    focus on the narrower topic in the case study.  -->

<p>
A very brief review of the problem domain emphasizes the different
length scales and relevant physics.  Length scales encompass stars,
galaxies, clusters, filaments, sheets and voids.  Observations provide
redshifts, ages, masses, and correlations in position and velocity.
The "missing mass" implies a dominant dark matter component.  Theory
allows for a density parameter, a cosmological constant and various
flavors of dark matter in addition to "normal" baryonic matter.  At the
largest scales, Newtonian gravity dominates and numerical methods that
follow gravitating particles are good models of the real Universe.
Analytic approaches are hampered by the nonlinearity, positive
feedback and negative heat-capacity of gravitating systems.
<p>
Supercomputers have played a significant role for at least the last 30
years in understanding the large scale structure of the Universe.
Computational methods include Poisson solvers, O(N<sup>2</sup>), and
"Fast" (O(NlgN) and O(N)) methods.  Parallel implementations exist for
each of these algorithmic approaches.  Poisson solvers can use FFT
methods or multi-grid (both of which exist in parallel).
O(N<sup>2</sup>) methods have perhaps the best parallel efficiency of
any non-trivial parallel application (Tcomm/Tcalc is proportional to
P/N).  At least two approaches to Fast methods have been shown to be
workable.  Orthogonal Recursive Bisection with explicit assembly of
"locally essential" data works when the locally essential data is
predictable in advance.  It has difficulty supporting improved
sequential algorithms with dynamic "acceptability criteria", however.
A new approach based on space-filling curves is required.  It has the
additional benefit of being "cache friendly".  It also naturally
supports both out-of-core and parallel computations
which is important because one consequence of "Fast"ness is that one
tends to run out of memory before one runs out of patience.
<p>
Computation has allowed us to understand the implications of different
scenarios and parameter sets, including the effects of the input power
spectrum of fluctuations, the evolution of non-linear clustering and
correlation functions, and the effects of the density parameter and
the cosmological constant on observational data.  Computations
continue to be challenged by ever improving observations, but they are
important tools for understanding and effectively rule out many
scenarios by demonstrating them to be inconistent with observation.
<p>
Similar numerical methods (indeed the first "Fast" method) apply to
potential and scattering problems for the Poisson, Helmholz and
Maxwell equations.  Other application areas include electrostatic
interactions in chemical dynamics, stress-strain interactions in solid
mechanics/geophysics and vortex dynamics from incompressible CFD.

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