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INTRODUCTION
The mathematical sciences provide the tools and the foundation on which the structure
of science and technology is built. This has been especially true for the development of
computational science in recent decades. The mathematical sciences contribute
fundamentally to the development of hardware, software, and networks for computational
science, and to the development of human resources for that field--in other words, to all
the major components of high-performance computing and communications. Mathematics
is also critical to the modeling that translates important problems into computable form,
to the numerical analysis enabling the computation, and to the statistical analysis for
assimilating physical data and numerical output.
The United States is now embarking on a program directed at building the
high-performance computing and communications infrastructure necessary for the solution
of "Grand Challenge" problems of major scientific and societal importance.] This report
documents the essential role of the mathematical sciences both in building this
infrastructure, according to the plan of the federal High Performance Computing and
Communications (HPCC) program, and in ultimately rising to the grand challenges of
computational science. A broad collection of mathematical tools will be required, and the
continued development of new mathematics must be an integral part of both the HPCC
program and ongoing attacks on grand challenge problems.
The primary conclusions of this report are as follows:
. The goals of the HPCC program cannot be met
challenge problems cannot continue, without the
mathematical sciences community. Therefore.
, and progress against grand
active involvement of the
~ , Therefore, relevant mathematical sciences
research should be a significant part of the heightened research effort associated
with the HPCC program.
1The 1991 report Grand Challenges: High Performance Computing and
Communications, from the White House Office of Science and Technology Policy, offers
this definition: "A Grand Challenge is a fundamental problem in science and engineering,
with broad economic and scientific impact, whose solution could be advanced by applying
high performance computing techniques and resources." There is no exhaustive list of such
problems, but examples such as weather and climate prediction, structural biology,
semiconductor design and modeling of turbulence are indicative of the range and
complexity of the targeted problems.
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. The mathematical research topics listed in Section 5 are particularly germane to
the HPCC program, as evidenced by their frequent mention in Sections 2 through
4.
. Research and education relative to high-performance computing and
communications and grand challenge problems must link a broad range of physical
and life sciences, the mathematical sciences, and computational science. Therefore
multidisciplinary settings offer the best chance for successes. Many of the advances
profiled in Sections 2 through 4 were achieved in such settings.
Section 2 below identifies where the mathematical sciences have contributed in the past
to progress in high-performance computing and communications, Section 3 surveys
potential near-term advances relevant to the goals of the HPCC program and beyond, and
Section 4 samples the role of mathematical research in selected grand challenge problems.
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