My research focuses on fast algorithms, integral equations, potential theory, and their applications in electromagnetics, solid and fluid dynamics, molecular mechanics and quantum chemistry. Past and current projects include:
- Fast multipole methods (FMM) for the Helmholtz, Yukawa, biharmonic, and diffusion equations.
- Direct adaptive solvers for linear differential equations based on potential theory.
- New integral formulations for lattice sums.
- A new class of ODE/DAE initial value problem solvers.
- Analysis based fast algorithms for large-scale long-time simulations.
- Applications: biomolecular electrostatic interactions; biofludic device simulations; efficient step flow simulation scheme using potential theory; new surface integral formulations of EMQS impedance extraction; fast integral equation methods for the incompressible Navier-Stokes equations, porous media, dislocation dynamics, and nonlinear shallow water waves.