Latest Research (over the past 3 years). Most of the papers can be found either in Journal of Computational Physics or IEEE Transactions on Antennas and Propagation

Fast time domain integral equation techniques

Provalbly scalable parallel wideband FMM techniques

Accelerated Cartesian Harmonics--A method for accelerating non-oscillary poetntials

Applied to
1. Potentials of the form 1/R^\nu
2. Low frequency retarded potential
3. Low frequency Helmholtz
4. Diffusion
5. Klien Gordon
6. Dispersion
7. Periodic Coulomb, Helmholtz, Yulawa in 1-, 2-, and 3-D
8. Periodic retared potentials

Molecular Dynamics using Cartesian Harmonics

Nanostructure crystal growth

Surface enhanced Raman Spectra (for a full description, see our papers in J. Raman Spectroscopy)

Generalized method of moments

1. Enlarges function space, permits easy p-adaptivity, handles non-conformal meshes, and results in stable condition numbers
2. Applied to scattering from perfect conductors
3. Applied to scattering from dielectric objects
4. Developing these techniques on smooth surface approximations to further applicability

Time domain Floquet Modes

Broadband accelerators in frequency and time domain using (i) ACE + PWTD and (ii) ACE + FMM