Numerical Analysis and Scientific Computing

The numerical analysis group at UCL is a relatively recent addition. The main focus is on the design and implementation of efficient and accurate computational methods for the approximation of solutions to partial differential equations. A wide range of applications are considered, including continuum mechanics, electro-magnetics, stochastic optimisation and inverse problems. Research interest and staff can be broadly classed into the following categories:

• Computational methods in continuum mechanics - finite element methods for fluid and solid mechanics including multiphysics coupling, such as fluid-structure interaction or contact, and ficititious domain methods.
• Analysis and computational methods for wave scattering - boundary integral equations, wavenumber dependent stability, fractal domains, boundary element methods, fast solvers.
• Inverse problems - robust and accurate finite element methods with Carleman estimate based analysis, medical imaging. An example of a multidisciplinary research project in this context is the computational optimisation of treatment plans for high intensity focused ultrasound (HIFU) cancer treatment.
• Numerical methods in stochastic optimal control, a posteriori error estimation and adaptivity, parallel solvers.

The group has also participated in several research software developments, such as BEM++ and the Fenics based Cutfemlib.

Researchers

Dr Masoud Ahmadi
Prof Timo Betcke
Dr Freya Bull
Prof Erik Burman
Dr Fabian Heimann
Prof David Hewett
Dr Max Jensen
Dr Iain Smears
Dr Harry Wells