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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.