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March 2830, 2005
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Biographies and Lecture Abstracts 
The primary goal of this workshop is to facilitate the use of the best computational techniques in important industrial applications. Key developers of three of the most significant recent or emerging paradigms of computation  fast multipole methods, level set methods, and multiscale computation will provide tutorial introductions to these classes of methods. Presentations will be particularly geared to scientists using or interested in using these approaches in industry. In addition the workshop will include research reports, poster presentations, and problem posing by industrial researchers, and offer ample time for both formal and informal discussion, related to the use of these new methods of computation. If you wish to describe a problem in the problem posing session, please contact Arnd Scheel at deputy@ima.umn.edu.
Organizer
Robert V. Kohn
Department of Mathematics
Courant Institute of Mathematical Sciences
New York University
kohn@courant.nyu.edu
http://www.math.nyu.edu/faculty/kohn/
Tutorial Lectures:
Overview of Multiscale Methods
Problems with Multiple Time Scales
Weinan E
Department of Mathematics and Program in Applied and Computational
Mathematics
Princeton University
weinan@princeton.edu
http://www.math.princeton.edu/~weinan/
Fast Multipole Methods and their Applications
Leslie F. Greengard
Department of Mathematics
Courant Institute of Mathematical Sciences
New York University
greengard@cims.nyu.edu
http://www.math.nyu.edu/faculty/greengar/
Advances in Advancing Interfaces: Level Set Methods, Fast Marching Methods, and Beyond
James A. Sethian
Department of Mathematics
University of CaliforniaBerkeley
sethian@math.berkeley.edu
http://math.berkeley.edu/~sethian/




MONDAY,
MARCH 28 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 


8:30  Coffee and Registration  Reception Room EE/CS 3176  
9:159:30  Douglas N. Arnold and Robert V. Kohn  Welcome and Introduction  
9:3010:30  James A. Sethian  Lecture 1: Advances in Advancing Interfaces: Level
Set Methods, Fast Marching Methods, and Beyond Link to online tutorial on fast marching and level set methods 

10:30  Coffee  
11:0012:00  Leslie F. Greengard  Lecture 1: Fast Multipole Methods
and their Applications For lecture notes, please see R. K. Beatson and L. Greengard, A short course on fast multipole methods, in Wavelets, Multilevel Methods and EllipticPDEs, M. Ainsworth, J. Levesley, W. Light, and M. Marletta, eds., Oxford University Press, 1997, pp. 1.37 A preprint is available at www.math.nyu.edu/faculty/greengar 

12:00  Lunch  
1:302:30  Weinan E  Lecture 1: Overview of Multiscale Methods  
2:30  Coffee 

3:004:00  Second chances (discussion and review of today's lectures)  
TUESDAY,
MARCH 29 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

9:00  Coffee  
9:3010:30  Industrial problems  Raju Mattikalli (Boeing): Observer Positioning  
10:30  Coffee  
11:0012:00  James A. Sethian  Lecture 2: Advances in Advancing Interfaces: Level
Set Methods, Fast Marching Methods, and Beyond Link to online tutorial on fast marching and level set methods 

12:00  Lunch  
1:302:30  Leslie F. Greengard  Lecture 2: Fast Multipole Methods and
their Applications
For lecture notes, please see R. K. Beatson and L. Greengard, A short course on fast multipole methods, in Wavelets, Multilevel Methods and EllipticPDEs, M. Ainsworth, J. Levesley, W. Light, and M. Marletta, eds., Oxford University Press, 1997, pp. 1.37 A preprint is available at www.math.nyu.edu/faculty/greengar 

2:30  Coffee  
3:004:00  Weinan E  Lecture 2: Problems with Multiple Time Scales  
4:004:15  Group Photos  
4:15  IMA
Tea and more (with POSTER SESSION) 400 Lind Hall


WEDNESDAY,
MARCH 30 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

9:00  Coffee  
9:302:30  Structured discussion of lectures and industrial problems 
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3:354:35 Wednesday 301 Vincent Hall 
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5:006:30 Wednesday 400 Lind Hall 
Public Lecture Reception  
7:008:00 Wednesday EE/CS 3210 
Thomas C. Hales University of Pittsburgh 
Math Matters: IMA Public Lecture
Computers and the Future of Mathematical Proof 
3:304:30 Thursday 16 Vincent Hall 
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School of Mathematics Colloquium Incompressibility 
Monday  Tuesday 
Biographies and Lecture Abstracts
Weinan E (Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University) http://www.math.princeton.edu/~weinan/
Biography: Weinan E received his PhD from the University of California at Los Angeles in 1989. He was visiting member at the Courant Institute from 1989 to 1991. He joined the IAS in Princeton as a long term member in 1992 and went on to take a faculty position at the Courant Institute at New York University in 1994. He is Professor of Mathematics at Princeton University since 1999. His awards include the Alfred P. Sloan Foundation Fellowship, a Presidential Faculty Fellowship, the Feng Kang Prize in Scientific Computing and the Collatz Prize awarded by the International Council of Industrial and Applied Mathematics. He serves on the editorial board of various journals including the Journal of American Mathematical Society, Acta Mathematica Sinica, Journal of Computational Mathematics, Communications of Contemporary Mathematics, and Journal of Statistical Physics.
Overview of Multiscale Methods
Abstract: We will begin by reviewing the basic issues and concepts in multiscale modeling, including the various models of multiphysics, serial and concurrent coupling strategies, and the essential features of the kind of multiscale problems that we would like to deal with. We then discuss some representative examples of successful multiscale methods, including the CarParrinello method and the quasicontinuum method. Finally we discuss several general methodologies for multiscale, multiphysics modeling, such as the domain decomposition methods, adaptive model refinement and heterogeneous multiscale methods. These different methodologies are illustrated on one example, the contact line problem. Throughout this presentation, we will emphasize the interplay between physical models and numerical methods, which is the most important theme in modern multiscale modeling.
Problems with Multiple Time Scales
Abstract: We will discuss the mathematical background and numerical techniques for three types of problems with multiple time scales: stiff ODEs, Markov chains with disparate rates and rare events.
Leslie F. Greengard (Department of Mathematics, Courant Institute of Mathematical Sciences, New York University)
Biography: Leslie F. Greengard was born in London, England, and grew up in New York, Boston, and New Haven. He received his B.A. in mathematics from Wesleyan University in 1979, his Ph.D. in computer science from Yale University in 1987, and his M.D. from Yale University in 1987. From 1987 89 he was a National Science Foundation Postdoctoral Fellow at Yale University in the Department of Computer Science. He is presently a professor of mathematics at the Courant Institute of New York University, where he has been a faculty member since 1989. In 2001, he was awarded the Leroy P. Steele Prize by the AMS Council. Much of his work has been in the development of analysisbased fast algorithms such as the Fast Multipole Method for gravitation and electromagnetics and the Fast Gauss Transform for diffusion.
Fast Multipole Methods and their Applications
Abstract: In these lectures, we will describe the analytic and computational foundations of fast multipole methods (FMMs), as well as some of their applications. They are most easily understood, perhaps, in the case of particle simulations, where they reduce the cost of computing all pairwise interactions in a system of N particles from O(N2) to O(N) or O(N log N) operations. FMMs are equally useful, however, in solving partial differential equations by first recasting them as integral equations. We will present examples from electromagnetics, elasticity, and fluid mechanics.
For lecture notes, please see R. K. Beatson and L. Greengard, A short course on fast multipole methods, in Wavelets, Multilevel Methods and EllipticPDEs, M. Ainsworth, J. Levesley, W. Light, and M. Marletta, eds., Oxford University Press, 1997, pp. 1.37
A preprint is available at www.math.nyu.edu/faculty/greengar
Robert V. Kohn (Department of Mathematics, Courant Institute of Mathematical Sciences)New York University) http://www.math.nyu.edu/faculty/kohn/
Biography: Robert V. Kohn received his A.B. from Harvard University in 1974, his M.Sc. from the University of Warwick in 1975, and a Ph.D. From Princeton in 1979. He spent two years as an NSF Postdoc at New York University's Courant Institute of Mathematical Sciences, before he joined the faculty. He has been a Professor of Mathematics at the Courant Institute since 1981. His honors include SIAM's Ralph Kleinman Prize, an Ordway Visiting Professorship at the University of Minnesota, and a Sloan Research Fellowship. His research interests include mathematical aspects of materials science, nonlinear partial differential equations, nonconvex variational problems, and mathematical finance. In addition, he is among the leaders of the Courant Institute's professional masters program in mathematical finance.
James A. Sethian (Department of Mathematics, University of CaliforniaBerkeley) http://math.berkeley.edu/~sethian/
Biography: James A. Sethian was born on May 10, 1954, in Washington, DC. He received a B.A. in mathematics from Princeton University in 1976 and a Ph.D. in Applied Mathematics from the University of California, Berkeley, in 1982. After a National Science Foundation Postdoctoral Fellowship at the Courant Institute of Mathematical Sciences, he joined the faculty at UC Berkeley, where he is now Professor of Mathematics as well as Head of the Mathematics Department at the Lawrence Berkeley National Laboratory. He has been a plenary speaker at the International Congress of Industrial and Applied Mathematicians, and has been an invited speaker at the International Congress of Mathematicians. He has received SIAM's I. E. Block Community Lecture Prize, and in 2004 was awarded the Norbert Wiener Prize in Applied Mathematics by the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics SIAM). He is an Associate Editor of SIAM Review, the Journal of Mathematical Imaging and Vision, and the Journal on Interfaces and Free Boundaries.
Advances in Advancing Interfaces: Level Set Methods, Fast Marching Methods, and Beyond
Abstract: Propagating interfaces occur in a variety of settings, including semiconductor manufacturing in chip production, the fluid mechanics of ink jet plotters, segmentation in cardiac medical imaging, computeraideddesign, optimal navigation in robotic assembly, and geophysical wave propagation. Over the past 25 years, a collection of numerical techniques have come together, including Level Set Methods and Fast Marching Methods for computing such problems in interface phenomena in which topological change, geometrydriven physics, and threedimensional complexities play important roles. These algorithms, based on the interplay between schemes for hyperbolic conservation laws and their connection to the underlying theory of curve and surface evolution, offer a unified approach to computing a host of interface problems.
In this tutorial, the author will cover (i) the development of these methods, (ii) the fundamentals of Level Set Methods and Fast Marching Methods, including efficient, adaptive versions, and the coupling of these schemes to complex physics, and (iii) new approaches to tackling more demanding interface problems. The emphasis in this tutorial will be on a practical, "handson" view, and the methods and algorithms will be discussed in the context of ongoing collaborative projects, including work on semiconductor processing, industrial ink jet design, and medical and biomedical imaging.
Raju Mattikalli (The Boeing Company)
Industrial Problem: Observer Positioning:
Abstract: Consider the museum guard problem, i.e. finding positions for guards in a museum so that they can have the largest number of museum artifacts within sight. This problem was first defined by Victor Klee in 1973. There are many variations of the museum guard problem.
My interest is in an outdoor version of the museum guard problem. Consider the problem of positioning cameras to monitor mountainous terrain, say over a section of the Grand Canyon. The terrain can be assumed to have vertical surfaces, but no overhangs. The field of view of a camera can be represented as a cone with a fixed half angle and height. The objective is to define camera positions and orientations to achieve maximum coverage of the terrain surface.
Cameras are either fixed or mobile. Fixed (both over space and time) cameras can be mounted at any point zero to six feet high along a normal to the ground surface. The camera cone can have any orientation. Mobile cameras can be assumed to be mounted on constant speed airplanes capable of making turns with a radius no smaller than R. Mobile cameras can have time varying orientation, with a maximum angular rotation speed of T.
I will present 3 variations of the above problem.
Name  Department  Affiliation 

Douglas N. Arnold  Institute for Mathematics and its Applications  University of Minnesota 
Donald G. Aronson  Institute for Mathematics and its Applications  University of Minnesota 
Gerard Awanou  University of Minnesota  
Paolo Biscari  Dipartimento di Matematica  Politecnico di Milano 
Olus N. Boratav  Science & Technology  Corning 
MariaCarme Calderer  School of Mathematics  University of Minnesota 
Qianyong Chen  Institute for Mathematics and its Applications  University of Minnesota 
David Day  Computational Mathematics and Algorithms  Sandia National Laboratories 
Antonio DeSimone  Applied Mathematics  SISSAItaly 
Brian DiDonna  Institute for Mathematics and its Applications  University of Minnesota 
Elena Dimitrova  Department of Mathematics  Virginia Tech 
Qiang Du  Department of Mathematics  Pennsylvania State University 
Weinan E  Department of Mathematics & Applied Computational Mathematics  Princeton University 
Charles M. Elliott  Centre for Mathematical Analysis and Its Applications  University of Sussex 
Ryan S. Elliott  University of Michigan  
Anthony Ervin  CPRL  3M 
Eugene C. Gartland Jr.  Department of Mathematical Sciences  Kent State University 
Donn W. Glander  Research & Development  General Motors 
Dmitry Golovaty  Department of Theoretical & Applied Mathematics  University of Akron 
Leslie F. Greengard  Courant Institute of Mathematical Sciences  New York University 
JeanLuc Guermond  Department of Mathematics  Texas A & M University 
Changfeng Gui  Department of Mathematics, U9  University of Connecticut 
Robert Gulliver  School of Mathematics  University of Minnesota 
Rohit Gupta  Department of Computer Science & Engineering  University of Minnesota 
Cushing Hamlen  Science and Technology  Medtronic, Inc. 
Viet Ha Hoang  Department of Applied Mathematics and Theoretical Physics  Cambridge University 
Richard D. James  Aerospace Engineering and Mechanics  University of Minnesota 
Slah Jendoubi  CRPL  3M 
Richard M. Jendrejack  Corporate Research Process Laboratory  3M 
Shi Jin  Department of Mathematics  University of Wisconsin  Madison 
Mitchell A. Johnson  Corporate Research Process Laboratory  3M 
Sookyung Joo  Institute for Mathematics and its Applications  University of Minnesota 
Lili Ju  Department of Mathematics  University of South Carolina 
Sung Chan Jun  Department of Biological and Quantum Physics  Los Alamos National Laboratory 
Chiu Yen Kao  Institute for Mathematics and its Applications  University of Minnesota 
Robert V. Kohn  Courant Institute of Mathematical Sciences  New York University 
Richard Kollar  University of Minnesota  
Matthias Kurzke  Institute for Mathematics and its Applications  University of Minnesota 
Namyong Lee  Department of Mathematics  Minnesota State University  Mankato 
Frederic Legoll  University of Minnesota  
Benedict Leimkuhler  Department of Mathematics and Computer Science  University of Leicester 
Melvin Leok  Department of Mathematics  University of Michigan 
Debra Lewis  Institute for Mathematics and its Applications  University of Minnesota 
Xiantao Li  University of Minnesota  
Julia Liakhova  Advanced Servo Integration Group  Seagate Technology 
Hua Lin  Department of Mathematics  Purdue University 
Chun Liu  Department of Mathematics  Pennsylvania State University 
Hailiang Liu  Department of Mathematics  Iowa State University 
Summer Locke  Mathematical Modeling  Boeing 
Mitchell Luskin  School of Mathematics  University of Minnesota 
Raju Mattikalli  Math and Computing Technologies  Boeing 
Anish Mohan  Computer Science  University of Minnesota 
Duane Nykamp  School of Mathematics  University of Minnesota 
Peter PalffyMuhoray  Liquid Crystal Institute  Kent State University 
Peter Philip  Institute for Mathematics and its Application  University of Minnesota 
Petr Plechac  Mathematics Institute  University of Warwick 
S. S. Ravindran  Department of Mathematical Sciences  University of Alabama  Huntsville 
Maria Reznikoff  University of Bonn  
Rolf Ryham  Department of Mathematics  Pennsylvania State University 
Arnd Scheel  Institute for Mathematics and its Applications  University of Minnesota 
Robert Secor  Corporate Research Process Lab  3M 
George R Sell  School of Math  University of Minnesota 
James A. Sethian  Mathematics  University of California  Berkeley 
Jie Shen  Department of Mathematics  Purdue University 
TienTsan Shieh  Department of Mathematics  Indiana University 
Suzanne Shontz  Department of Computer Science  University of Minnesota 
Devashish Shrivastava  Radiology Dept.  University of Minnesota 
Peter J. Sternberg  Department of Mathematics  Indiana University 
Vladimir Sverak  Department of Mathematics  University of Minnesota 
Eugene Terentjev  Cavendish Laboratory  Cambridge University 
Igor Tsukerman  Department of Electrical & Computer Engineering  University of Akron 
Qi Wang  Department of Mathematics  Florida State University 
Xiaoqiang Wang  Department of Mathematics  Pennsylvania State University 
Stephen J. Watson  ESAM  Northwestern University 
Jue Yan  Department of Mathematics  University of California  Los Angeles 
Aaron Nung Kwan Yip  Department of Mathematics  Purdue University 
Emmanuel Yomba  Faculty of Sciences  University of NgaoundÃ©rÃ© 
Pingwen Zhang  School of Mathematical Sciences  Peking University 