In many areas of mathematics and the physical sciences, systems of differential, stochastic and algebraic equations must be solved.
In most realistic models these equations are extremely difficult to solve through analytical methods and approximate numerical methods of solution are used.
The development of new algorithms and the analysis of these methods to ensure an accurate solution is found in the fastest time possible is the area of numerical analysis and scientific computing.
With increasing complexity in mathematical models, numerical methods must be more sophisticated and more efficient.
Research activity in the Numerical Analysis and Scientific Computing group is therefore concentrated on the construction and analysis of methods for numerical solution of nonlinear differential equations, the computational solution of problems of practical interest and several aspects of numerical linear algebra.
If you're interested in collaborating with us or wish to enquire about postgraduate or postdoctoral research positions then please contact one of the group members listed below.
Our research activities are focused on:
Numerical solutions of partial differential equations (PDEs)
Topics that we're investigating in the area of numerical solution of PDEs include:
- hp finite elements for Maxwell's equations
- Mixed hp finite element methods
- Hierarchic modelling
- Domain decomposition methods
- Adaptive moving mesh methods based on the idea of equidistribution
- Adaptive solution of phase change and moving boundary value problems
- Uniform convergence of discrete methods on adaptive meshes for problems with near-singular solutions
- A posteriori error estimates for finite element methods
- Adaptive methods for steady and unsteady problems based on high order pseudospectral discretisations.
- Numerical simulation of stochastic differential equations
- Applications to mathematical finance
- Computation with large, noisy data sets such as those arising in genomics.
Numerical linear algebra
- Preconditioning large unstructured sparse matrices
- Algorithms and analysis of matrix balancing
- Applications and algorithms for complex networks
- Iterative solution of large sparse linear systems arising from finite element discretisation of problems in computational fluid dynamics
- Preconditioning large block matrices
- Preconditioning matrices with Toeplitz, or related, structure
- Analysing convergence rates of iterative methods for linear systems
Computational physics & engineering
- Fluid flow calculations in two and three dimensions using boundary-fitted coordinates and adaptivity
- Solution of fluid flows in industrial problems such as flow on rotating circular and elliptic cylinders and rivulets
- Computational electromagnetics - stability and convergence of numerical time marching algorithms of the electric field integral equation on flat plate, thin wire and curved scatterers
- Non-linear elasticity - biomechanics (developing nonlinearly elastic models of intestinal organs), buckling and barrelling of nonlinear elastic columns under axial compression. (Head of Group)