Dr Catherine Powell - research
My research falls under the umbrella of numerical analysis (a branch of applied mathematics) and is centered on approximation schemes and efficient computational tools for finding approximate solutions to partial differential equations (PDEs). The applications I deal with include fluid flow in porous media, image processing and electromagnetics.
The goal is to develop and implement appropriate approximation schemes and solve the resulting large systems of algebraic equations on a computer in real time. Often, the last step - the solution of a matrix problem - is a bottleneck in practical computations and fast solvers are crucial. This topic is my primary interest. By exploiting properties of the matrices of the system and properties of the underlying PDEs, we can often design fast solvers and so-called preconditioners to speed up the solution process. This is the focus of most of my research.
In 2006, I began investigating the numerical solution of models of physical processes whose input parameters are subject to uncertainty. This is important in modelling groundwater flow in porous medium, where a complete description of the permability coefficients of material in the flow domain is lacking. Developing fast solvers for such problems is even more challenging due to their stochastic nature and increased dimensionality.
For more details and a complete list of my publications (not the automatically generated one shown in the next tab), please visit my official research web page: www.ma.man.ac.uk/~cp/research.html