The broad area of my research is numerical analysis/computational mathematics. I work on
the development, rigorous analysis and efficient implementation of computational algorithms for
problems coming from physics and engineering.

I have worked on boundary and finite element and also on space-time methods for both steady state and and time-domain problems. These include wave scattering problems, both acoustic and electromagnetic,  and Schroedinger equations. There has been a strong emphasis in my work on the development and analysis of fast methods for non-local problems. These include both boundary integral equations and non-local/fractional differential operators.

Further, I am active in the development and analysis of numerical eigenvalue computations and in computational complex analysis.  Here I have worked on pseudospectral, finite element and multigrid methods.