Numerical Analysis and Scientific Computing

Project ID: 2228cd1402 (You will need this ID for your application)

Research Theme: Mathematical Sciences

UCL Lead department: Mathematics

Department Website

Lead Supervisor: David Hewett

Project Summary:

The research will focus 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. Specific research areas include:

• 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.