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IMA Hot Topics Workshop
Integral Equation Methods, Fast Algorithms and Applications
August 2-5, 2010

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Cosponsored with the NSF CCF Collaborative Research Group, Award # 0905473/0905395/0905164, "Integral-Equation-Based Fast Algorithms and Graph-Theoretic Methods for Large-Scale Simulations."

  Organizers
Jingfang Huang Mathematics, University of North Carolina, Chapel Hill
Shidong Jiang Mathematical Sciences, New Jersey Institute of Technology
Per-Gunnar J. Martinsson Applied Mathematics, University of Colorado, Boulder
Mark Tygert Courant Institute of Mathematical Sciences, New York University
Hong Xiao Mathematics, University of California, Davis
  Description

Techniques based on integral equations for the solution of linear boundary-value problems and computational simulations have become increasingly popular over the past several decades. The superior stability of such methods allows highly accurate solutions to be computed, and the development of efficient numerical techniques such as the fast multipole method have made integral-equation approaches significantly faster than many other currently available schemes. Integral-equation methods and associated fast algorithms have become important in many domains of computational science and engineering, including computational electromagnetics, solid and fluid mechanics, molecular dynamics, quantum physics and chemistry, and astrophysics.

The main objective of this workshop is to have timely reviews and discussions of recent results and current issues in (1) the mathematical foundations of integral-equation methods and associated fast algorithms, (2) implementations and performance assessments of such methods on a variety of computer architectures, and (3) existing and new application areas. A plethora of computational techniques already exists, and includes tree-codes, pre-corrected fast Fourier transforms, Ewald procedures, and the many classes of fast multipole methods. This workshop will help clarify the relative advantages of existing schemes, and elucidate the trajectories and applications of many methods now under development.

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