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This IMA Volume in Mathematics and its Applications PARALLEL
SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS is based on the
proceedings of a workshop with the same title. The work shop was an
integral part of the 1996-97IMA program on "MATHEMAT ICS IN
HIGH-PERFORMANCE COMPUTING." I would like to thank Petter Bj0rstad
of the Institutt for Informatikk, University of Bergen and Mitchell
Luskin of the School of Mathematics, University of Minnesota for
their excellent work as organizers of the meeting and for editing
the proceedings. I also take this opportunity to thank the National
Science Founda tion (NSF), Department of Energy (DOE), and the Army
Research Office (ARO), whose financial support made the workshop
possible. Willard Miller, Jr., Professor and Director v PREFACE The
numerical solution of partial differential equations has been of
major importance to the development of many technologies and has
been the target of much of the development of parallel computer
hardware and software. Parallel computers offer the promise of
greatly increased perfor mance and the routine calculation of
previously intractable problems. The papers in this volume were
presented at the IMA workshop on the Paral lel Solution of PDE held
during June 9-13, 1997. The workshop brought together leading
numerical analysts, computer scientists, and engineers to assess
the state-of-the-art and to consider future directions.
This IMA Volume in Mathematics and its Applications GRID GENERATION
AND ADAPTIVE ALGORITHMS is based on the proceedings of a workshop
with the same title. The work shop was an integral part of the
1996-97 IMA program on "MATHEMAT ICS IN HIGH-PERFORMANCE COMPUTING.
" I would like to thank Marshall Bern (Xerox, Palo Alto Research
Cen ter), Joseph E. Flaherty (Department of Computer Science,
Rensselaer Polytechnic Institute), and Mitchell Luskin (School of
Mathematics, Uni versity of Minnesota), for their excellent work as
organizers of the meeting and for editing the proceedings. I also
take this opportunity to thank the National Science Founda tion
(NSF), Department of Energy (DOE), and the Army Research Office
(ARO), whose financial support made the workshop possible. Willard
Miller, Jr. , Professor and Director v PREFACE Scientific and
engineering computation has become so complex that traditional
numerical computation on uniform meshes is generally not pos sible
or too expensive. Mesh generation must reflect both the domain
geometry and the expected solution characteristics. Meshes should,
fur thermore, be related to the solution through computable
estimates of dis cretization errors. This, suggests an automatic
and adaptive process where an initial mesh is enriched with the
goal of computing a solution with prescribed accuracy
specifications in an optimal manner. While automatic mesh
generation procedures and adaptive strategies are becoming
available, major computational challenges remain. Three-dimensional
mesh genera tion is still far from automatic.
This IMA Volume in Mathematics and its Applications RECENT ADVANCES
IN ITERATIVE METHODS is based on the proceedings of a workshop that
was an integral part of the 1991-92 IMA program on "Applied Linear
Algebra. " Large systems of matrix equations arise frequently in
applications and they have the prop erty that they are sparse
and/or structured. The purpose of this workshop was to bring
together researchers in numerical analysis and various ap plication
areas to discuss where such problems arise and possible meth ods of
solution. The last two days of the meeting were a celebration
dedicated to Gene Golub on the occasion of his sixtieth birthday,
with the program arranged by Jack Dongarra and Paul van Dooren. We
are grateful to Richard Brualdi, George Cybenko, Alan George, Gene
Golub, Mitchell Luskin, and Paul Van Dooren for planning and
implementing the year-long program. We especially thank Gene Golub,
Anne Greenbaum, and Mitchell Luskin for organizing this workshop
and editing the proceed ings. The financial support of the National
Science Foundation and the Min nesota Supercomputer Institute made
the workshop possible. A vner Friedman Willard Miller, Jr. xi
PREFACE The solution of very large linear algebra problems is an
integral part of many scientific computations."
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.
This IMA Volume in Mathematics and its Applications MICROSTRUCTURE
AND PHASE TRANSITION is based on the proceedings of a workshop
which was an integral part of the 1990-91 IMA program on "Phase
Transitions and Free Boundaries." We thank R. Fosdick, M.E. Gurtin,
W.-M. Ni and L.A. Peletier for organizing the year-long program
and, especially, D. Kinderlehrer, R. James, M. Luskin and J.
Ericksen for organizing the meeting and editing these proceedings.
We also take this opportunity to thank those agencies whose
financial support made the workshop possible: the Army Research
Office, and the National Science Foun dation. A vner Friedman
Willard Miller. Jr. PREFACE Much of our traditional knowledge of
materials and processes is achievf'd by observa tion and analysis
of small departures from equilibrium. Many materials, especially
modern alloys, ceramics, and their composites, experience not only
larger but more dramatic changes, such as the occurrence of phase
transitions and t.he creation of defect structures, when viewed at
the microscopic scale. How is this observed, how can it be
interpreted, and how does it influence macroscopic behavior? These
are the principle concerns of this volume, which constitutes the
proceedings of an IMA workshop dedicated to these issues.
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