.)
There is continuing research on improving the performance of existing
fast multipole methods. Recent work include
(a) very fast methods for 1D problems,
(b) improved kernel-independent FMMs,
(c) FMMs for general anisotropic elasticity in 3D.
Software development:
A principal reason FMM based methods have not reached wider adaptation levels than
they have is a lack of systematic software libraries. Writing a stable
and efficient implementation of an FMM is a major software development
project, especially for 3D codes. Work is currently under way on
standardizing call sequences for fast solvers, and putting together
libraries of "black-box" fast algorithms.
Customization of fast algorithms to specific applications:
FMMs have the potential for very significantly accelerating
computational models of biochemical processes. Construction of
of fast software for simulating ion channels (with
Bob Eisenberg and
Dirk Gillespie)
and large macro-molecules in ionic solutions in under way.
(Joint work with
Leslie Greengard
and Denis Gueyffier at NYU.)
The following project is work by