Computational mathematics

The Computational Mathematics research program actively studies theoretical aspects of computational algorithms, both in the continuous and discrete settings, as well addressing implementation issues to ensure efficient and reliable solution techniques.

The program runs a regular seminar (usually 4pm on a Monday afternoon). If you would like to be notified of these seminars and associated notifications consider joining our mailing list.

The specific areas addressed by the program include:

  • high-dimensional approximation and sparse grid methods
  • efficient solution of large scale problems
  • numerical linear algebra
  • numerical solution of partial differential equations
  • parallel numerical methods
  • inverse problems
  • optimisation techniques
  • parameter estimation
  • uncertainty quantification
  • regularisation methods
  • thin plate spline smoothing
  • tsunami and flood modelling
  • plasma theory and modelling

 

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Project Supervisors
Adaptive sparse grids
Advanced computational techniques
Clustering techniques
Computational applications of Multiple Region relaXed MHD (MRxMHD)
Computational Methods in Real Algebraic Geometry and Applications
Discontinuous Galerkin method for the shallow water wave equation using physics based numerical fluxes
Domain decomposition/Multiscale physics
Edge Localised Modes – linear stability and dynamics
Energetic Particle Physics of the International Thermonuclear Experimental Reactor (ITER)
Evaluation of hydrological models
Exploring Adaptive Mesh Refinement strategies for dynamic earthquake rupture modeling with ExaHyPE
Fault tolerant algorithms
High dimensional approximation
Navier Stokes equation with free boundaries
Parallel high-dimensional density estimation
Parallel optimisation algorithms for large-scale machine learning
Particle orbits in magnetic islands and chaotic magnetic field
Reduced models in Plasma Cylinder
Regularised black-box optimisation algorithms for least-squares problems
Scalable Fault-tolerant PDE Solvers
Sensitivity Analysis of environmental models
Shaping value of information to real world conditions in water decision making
Symbolic and Numeric Computation in Algebraic Geometry
Synthetic diagnostics for global computer networks and fusion power experiments
The thermodynamics (and entropy) of redistribution of energetic ions due to wave-particle interaction
Thin plate splines
Topological Data Analysis for detecting consistent patterns of spread for extremist content
Tsunami and flood modelling
Upwind summation-by-parts (SBP) finite difference methods for 3D seismic wave propagation in complex geometries
Using methods from algebraic geometry to develop numerical approximations