The Fast Multipole Method (FMM) is a generic name for a set of computational techniques for rapidly evaluating pairwise interactions in multi-particle systems, and, more generally, for rapidly applying various operators to vectors.

Areas of application for the FMM include:

Fast solvers for PDEs: The FMM can be used to construct fast solvers for many linear PDEs. The resulting methods are in many cases faster, and more accurate, than any other existing techniques.

Particle simulations: The FMM can be used to accelerate simulations involving large numbers of particles. Dramatic increases in the size of problems that can be simulated have been achieved in astro-physics, biochemistry, design of semi-conductors, and many other areas.

Numerical linear algebra: There exist FMM-accelerated algorithms for computing matrix decompositions (such as, e.g., the SVD) that are asymptotically extremely fast. The break-even point is currently quite high, but ongoing research may soon make such techniques standard practice.

The purpose of these pages is to:

• Briefly describe the FMM and what it can do.
• List some tutorials and research papers.
• Link to existing software libraries.
• Describe some recent research.