Melting and natural convection in a square cavity (Dr John Mackenzie)
Research activity in the Numerical Analysis and Scientific Computing Teaching and Research Group is concentrated mainly on the construction and analysis of methods for numerical solution of nonlinear differential equations, and on computational solution of problems of practical interest. There is also related research activity in several aspects of numerical linear algebra.
Numerical solutions of PDEs
Topics that are being investigated in the area of numerical solution of partial differential equations 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.
Stochastic Computation
Research also takes place in the area of stochastic computation, with a focus on differential equations driven by random noise.
Topics include:
- 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
Topics being studied in the area of numerical linear algebra are:
- Effects of nonnormality on the performance of linear algebra routines: in particular, the stability of algorithms for finding a single eigenvalue-eigenvector pair
- Influence of finite precision arithmetic in models of dynamical systems
- Iterative solution of large sparse linear systems arising from finite element discretisation of problems in computational fluid dynamics.
Computational Physics and Engineering
Computational solution of problems in physics and engineering is currently focused on
- 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
- Nonlinear elasticity - biomechanics (developing nonlinearly elastic models of intestinal organs), buckling and barrelling of nonlinear elastic columns under axial compression.
Academic collaborations exist with:
- Austin (Texas)
- Boulder (Colorado)
- Maryland
- Dundee
- Frankfurt
- Heriot-Watt
- Kaiserslautern
- Kiel
- Kansas
- Magdeburg
- Manchester
- Manitoba
- Oxford
- Simon Fraser (Vancouver)
- Sussex
- Swansea
- UMIST (Manchester)
- UNSW (Sydney)
- Uppsala
- Warwick.