Research Interests

Roughly speaking, my research interests lie in the intersection of scientific computing, numerical methods for linear PDEs, and numerical linear algebra. The goal of my work (at a high level) is to design efficient and accurate numerical methods of simulating physical phenomena. To achieve this goal, I exploit the physics of the problems under consideration, develop high order discretizations and low rank matrices. My recent work has focused on the following areas:

• “Fast” algorithms such as the Fast Multipole Method and fast direct solvers.

• Integral equation formulations for the mathematical modeling of physics and other real world applications.

• Wave scattering, acoustics, variable media.

• Techniques for handling challenging geometries such as corners, edges, and periodic domains.

The methods I develop can be applied to a variety of problems including the simulation of composite materials and design of microfluidic devices.