The Maxwell Institute unifies a wide range of research activities in applied and computational mathematics.
We strive to be a UK leader in the development of mathematical methods and numerical algorithms, together with their rigorous analysis, and the application of those techniques in direct collaboration with scientists and engineers. In recent years, our research portfolio has been greatly expanded in the area of numerical analysis, boosted by the creation of Centre for Numerical Algorithms and Intelligent Software,and by an increased reliance on stochastic methods (SDEs and SPDEs), and further through increased collaboration with biology. Today, our research activities can be divided into the following overlapping themes:
- Numerics and Computation: numerical analysis, applications to ordinary and partial differential equations, geometric integrators, numerical methods for stochastic differential equations, algorithms and software for high performance computing.
- Modelling and Applications, covering a broad range of multidisciplinary work aimed at delivering valuable methods and understanding for scientists and engineerings. Collaborative work has been addressed to problems in engineering (microstructure and dislocations in materials, metamaterials, fire safety, multiscale modelling), biology (cancer evolution, ecological modelling, cell dynamics), chemistry (molecular dynamics algorithms), physics (gravitational fluids, optical materials), fluid dynamics and geosciences (porous media, rare event modelling, ocean/atmosphere dynamics).
- Applied analysis, including work on asymptotics, dynamical systems and PDEs. There are close interactions here with work in Analysis & PDEs, especially through involvement in CANPDE, and staff are associated with both groups
Related applied mathematics work is being undertaken in the Operational Research and Probability, Statistics and Applications groups. Mathematical Physics is further identified as a separate topic within the Maxwell Institute research organisation. Staff and students freely transcend the somewhat artificial boundaries between the various groups.