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This IMA Volume in Mathematics and its Applications COMPUTATIONAL
WAVE PROPAGATION is based on the workshop with the same title and
was an integral part of the 1994-1995 IMA program on "Waves and
Scattering." We would like to thank Bjorn Engquist and Gregory A.
Kriegsmann for their hard work in organizing this meeting and in
editing the proceedings. We also take this opportunity to thank the
National Science Foundation, the Army Research Office, and the
Office of Naval Research, whose financial support made this
workshop possible. A vner Friedman Robert Gulliver v PREFACE
Although the field of wave propagation and scattering has its
classical roots in the last century, it has enjoyed a rich and
vibrant life over the past 50 odd years. Scientists, engineers, and
mathematicians have devel oped sophisticated asymptotic and
numerical tools to solve problems of ever increasing complexity.
Their work has been spurred on by emerging and maturing
technologies, primarily concerned with the propagation and
reception of information, and the efficient transmission of energy.
The vitality of this scientific field is not waning. Increased
demands to precisely quantify, measure, and control the propagation
and scattering of waves in increasingly complex settings pose
challenging scientific and mathematical problems. These push the
envelope of analysis and comput ing, just as their forerunners did
50 years ago. These modern technological problems range from using
underwater sound to monitor and predict global warming, to
periodically embedding phase-sensitive amplifiers in optical fibers
to insure long range digital communication."
This IMA Volume in Mathematics and its Applications COMPUTATIONAL
FLUID DYNAMICS AND REACTING GAS FLOWS is in part the proceedings of
a workshop which was an integral part of the 1986-87 IMA program on
SCIENTIFIC COMPUTATION. We are grateful to the Scientific
Committee: Bjorn Engquist (Chairman), Roland Glowinski, Mitchell
Luskin and Andrew Majda for planning and implementing an exciting
and stimulating year-long program. We especially thank the Workshop
Organizers, Bjorn Engquist, Mitchell Luskin and Andrew Majda, for
organizing a workshop which brought together many of the leading
researchers in the area of computational fluid dynamics. George R.
Sell Hans Weinberger PREFACE Computational fluid dynamics has
always been of central importance in scientific computing. It is
also a field which clearly displays the essential theme of
interaction between mathematics, physics, and computer science.
Therefore, it was natural for the first workshop of the 1986- 87
program on scientific computing at the Institute for Mathematics
and Its Applications to concentrate on computational fluid
dynamics. In the workshop, more traditional fields were mixed with
fields of emerging importance such as reacting gas flows and
non-Newtonian flows. The workshop was marked by a high level of
interaction and discussion among researchers representing varied
"schools of thought" and countries.
The first book to approach high oscillation as a subject of its
own, Highly Oscillatory Problems begins a new dialogue and lays the
groundwork for future research. It ensues from the six-month
programme held at the Newton Institute of Mathematical Sciences,
which was the first time that different specialists in highly
oscillatory research, from diverse areas of mathematics and
applications, had been brought together for a single intellectual
agenda. This ground-breaking volume consists of eight review papers
by leading experts in subject areas of active research, with an
emphasis on computation: numerical Hamiltonian problems, highly
oscillatory quadrature, rapid approximation of functions, high
frequency wave propagation, numerical homogenization,
discretization of the wave equation, high frequency scattering and
the solution of elliptic boundary value problems.
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