University of Warwick
The aims of applied mathematics include satisying curiosity about nature and the
provision of quantitative tools in technology and engineering which are directed
towards simulation, prediction and control. The astonishing increase of computing
power together with the capacity of accumulating and storing large amounts of
data fuel the growth in complexity and scale of systems which can be studied.
This is achieved by the use of mathematical models. A major mathematical
domain which features in such models is the analysis of partial differential
Partial differential equations are ubiquitous in almost all applications of
mathematics, where they provide a natural mathematical description of
phenomena in the physical, natural and social sciences, often arising from
fundamental conservation laws. Consequently they provide the fundamental
objects which are used to model the world around us and their practical
importance cannot be overemphasized. They have become a central tool in
providing mathematical models of the processes under investigation.
The research will address fundamental issues in computational
aspects of the mathematical sciences. Nevertheless it is aimed at providing
methodologies which will aid scientists to develop their theories and
understanding with the potential for useful technological and medical advances.
My aim is to create a rigorous
mathematical theory and methodology for the development of accurate and
efficient computational tools to solve complex and large scale problems which
are currently intractable.