Methodologies
OCCAM's research in methodologies spans asymptotic techniques, multiscale methods, statistical methods, development of new algorithms for solving partial differential equations, visualisation techniques and optimisation methods. It covers analytical and numerical methods for models that may be discrete or continuous, deterministic or stochastic.
In addition to the research undertaken by OCCAM's faculty and research fellows, the following projects are currently being undertaken by PDRAs and students:
- M1: The numerical solution of coupled multiphysics problems
- M2: Design optimisation
- M3: Visualisation for applied mathematics
- M4: Adaptive spectral methods in 1D and 2D
- M5: Reaction and steric effects in stochastic models of drift diffusion
- M6: The closest point finite element method for numerical computing on surfaces
- M7: The numerical linear algebra of approximation involving radial basis functions (RBFs)
- M8: Multiscale methods based on unstructured data
- M9: Multiscale modelling in liquid crystal science
- M10: Chemical Fokker-Planck equation and multiscale modelling of (bio)chemical systems
- M11: Stochastic modelling of reaction-diffusion processes
- M12: Numerical fluid flow on dynamic implicit surfaces
- M13: Solvers for optimal control of time-dependent partial differential equations (PDEs)
- M14: Preconditioning in surface computing
- M15: Preconditioning non-symmetric systems for high performance computing (HPC)
- M16: Robust and efficient modelling, simulation and validation techniques for space fractional models
- M17: Bayesian inverse problems and seismic inversion
- M18: Software development for reaction-diffusion modelling
As our research programme evolves we expect to become ever more heavily involved in data handling of all kinds. We will undertake a close collaboration with the Oxford e-Research Centre (OeRC) to support our computational needs and to develop visualization capabilities for simulations spanning all of our application areas.