Research Papers
My research consists of designing computational procedures to solve mathematical problems;
primarily problems that are expressed in terms of partial differential equations. The general orientation of my
efforts is towards the development of algorithms/procedures that are synthesized from several algorithmic
components. For example, to solve Poisson's equation on infinite domains, one combines discrete
Fourier methods with fast Poisson solvers (Solution of Poisson's
Equations on Infinite Domains.) Alternately, procedures developed for the solution of the
incompressible Navier-Stokes equations require combining methods for solving convection equations, diffusion equations,
and methods for solving Poisson's equation. References to the procedures I've worked are given in Vortex
Methods for Incompressible Flow and Finite
Difference Methods for Incompressible Flow.
Additionally, since the solution of partial differential equations tends to be computationally
time consuming, I've been interested in the development of procedures that are computationally efficient. In particular,
as described in "Fast Computational Techniques",
I've worked on problems for accelerating the solution of Poisson's equation.