Integral Equations, Fast Algorithms, and Potential Theory
Spring 2006
Professor Leslie Greengard

Wednesday, 9:30-11:20, 813 Warren Weaver Hall

In this course, we will discuss integral equation methods for the classical partial differential equations of mathematical physics. We will focus on the fast algorithms that have recently become available for the Poisson, heat and wave equations including the fast multipole method and the fast Gauss transform. Additional topics covered include elements of functional analysis, numerical quadrature, iterative and direct solvers, and applications. Familiarity with partial differential equations, complex analysis, numerical methods, and programming is recommended.

Textbook: There will be no course textbook. Readings will be drawn from the journal literature.

For further information, please contact me, preferably via email.

Tel: (212) 998-3306

Selected Readings:

  • A Short Course on Fast Mutipole Methods
  • An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
  • Spectral Integration and Two-Point Boundary Value Problems
  • A Fast Algorithm for Particle Simulations - (distributed in class 02/15/06)
  • A Fast Adpative Multipole Algorithm for Particle Simulations
  • Potential Flow in Channels