Research

The main research interests of the department are reflected in four core groups:

• Our Numerical Analysis group has its strength in the development of novel, efficient, and accurate numerical methods that are capable of tackling complex problems of practical interest. We mainly focus on the development of algorithms for solving all kinds of problems of continuous mathematics; it is a wide-ranging discipline with close connections to computer science, engineering, and life sciences. We are currently conducting active research on numerical methods for partial differential equations, domain decomposition and multigrid methods, numerical linear algebra and computational inverse problems.
• Our Analysis of Differential Equations group focuses on the rigorous study of differential equations, especially those coming from applications in physics and engineering. The main topics include but are not limited to: homogenization, existence, uniqueness, and stability of partial differential equations, qualitative behaviour of solutions, singular limits of nonlinear partial differential equations, and calculus of variations.
• Our Optimisation and Control Theory group focuses on optimisation and control problems with constraints governed by ordinary differential equations or partial differential equations. The research topics cover calculus of variations, differential equations and numerical analysis. Interdisciplinary applications in various domains such as engineering, biology, and physics are also investigated.
• Our Operational Research group covers operations research and its applications in real life. Particularly, our expertise includes discrete optimisation model building (vehicle routing, shortest path, resource allocation, etc.), meta-heuristic algorithm design and implementation (using CPLEX and C++), discrete event simulation and performance analysis.

In addition, we also have staff interested in the areas of fluid dynamics, machine learning, probability theory, materials science, and more.