Mathematics & statisticsApplied & Computational Mathematics
Continuum Mechanics & Industrial Mathematics
Continuum Mechanics and Industrial Mathematics (CMIM) is an internationally leading research group in applied mathematics. The CMIM has long-standing expertise in applying mathematics to real-world challenges and industrial problems, with a global reputation in the mathematics of liquid crystals, fluid dynamics (including complex fluids and droplet dynamics), polymer physics, poroelasticity and more. The group’s mathematical expertise spans mechanics, modelling, nonlinear partial differential equations, asymptotics, homogenisation, statistical mechanics and scientific computing, to name a few. The CMIM is firmly committed to interdisciplinary research and maintains collaborations across diverse sectors e.g., with the pharmaceutical company Boehringer Ingelheim in Germany. CMIM is the lead node for two national networks in soft matter, funded by the Royal Society of Edinburgh and the Isaac Newton Institute and is proud to have an international network in four continents - Europe, Asia, North and South America.
Group members:
- Debasish Das
- Geoff McKay
- Apala Majumdar (Co-lead)
- Dr Laura Miller
- Mikhail Osipov
- David Pritchard
- Alexander Wray (Co-lead)
Numerical Analysis
The Numerical Analysis (NA) group is a long-standing and internationally recognised group of mathematicians dedicated to the analysis and development of numerical methods to solve complex problems in science and engineering.
The group possesses specific expertise and interest in numerical linear algebra, encompassing preconditioners for iterative solution techniques employed in the numerical solution of partial differential equations. Additionally, members of the group focus on numerical linear algebra aspects of variational data assimilation and matrix function theory. Research conducted within the group also focuses on the area of networks science, addressing pertinent questions such as centrality measures of networks and network resilience.
The group places a strong emphasis on the numerical solution of partial differential equations and their practical applications. The group engages in mathematical analysis and the design of novel finite element methods for problems in fluid dynamics, electric heating and the modelling of bulk-surface processes in biological cell migration.
Currently, the group is investigating methods that guarantee provable accuracy and stability while preserving known physical properties, such as conservation of mass or bounds on solution behaviour. Research in the group also encompasses uncertainty quantification (UQ), global sensitivity analysis (GSA) and scientific machine learning (SML). Analysis is conducted to identify and analyse efficient numerical approximation and quadrature techniques for high-dimensional quadrature problems that frequently arise in UQ, GSA and SML. The group actively participates in a diverse range of interdisciplinary and industrial projects, collaborating with for example the National Physics Laboratory and BAE Systems. The group is very outward-looking in its collaboration with a wide range of international partners across the globe.