Title:  Design Considerations and Open Problems in Fast Solvers

Speaker:   Jacob White, Electrical Engineering and Computer Science, MIT


Abstract:
 In the last fifteen years a wide variety of fast methods have been
 developed for solving integral equations, and these methods have been
 used for problems in integrated circuit interconnect and packaging
 analysis, electromagnetic and acoustic scattering, aircraft drag
 analysis, microscale fluid flow analysis, biomolecular analysis, and
 even Casimir force analysis.  In parallel, a wide range of fast methods
 have been developed based on translation invariance and the
 Fast-Fourier transform, the singular-value decomposition and other
 low-rank approximations, multipole and Taylor series expansions, and
 exponential expansions.  In this talk, we will try to provide developers
 faced with new problems some guidance as to which methods to use, and
 how these methods interact with problem formulation and appropriate
 preconditioning.  Finally, we will discuss the issue of higher order 
 methods, and the open problem  of higher order methods on moving bodies 
 in close proximity.