Numerical Analysis and Scientific Computing

Numerical Analysis and Scientific Computing Group at Leicester is evolved in a number of research directions such as

  • approximation theory,
  • computational dynamical systems,
  • numerical solution of partial differential equations,
  • computational fluid dynamics,
  • lattice Boltzmann methods
  • numerical solution of stochastic differential equations,
  • numerical methods for stochastic processes,  
  • data mining.

The group is involved both in analysis of numerical methods and in the development of new numerical algorithms.

The Department of Mathematics hosted the  2011 European Conference in Numerical Mathematics and Advanced Applications (ENUMATH).

Current members

 

 

 

Publications

Below are some representative journal publications by members of the group:

  1. RL Davidchack, TE Ouldridge, MV Tretyakov, New Langevin and gradient thermostats for rigid body dynamics, The Journal of chemical physics 142 (14), 144114 (2015).
  2. A Cangiani, EH Georgoulis, S Metcalfe, Adaptive discontinuous Galerkin methods for nonstationary convection–diffusion problems, IMA Journal of Numerical Analysis 34 (4) (2014), 1578-1597.
  3. P Antonelli, A Athanassoulis, Z Huang, PA Markowich, Numerical Simulations of X-Ray Free Electron Lasers (XFEL), Multiscale Modeling & Simulation 12 (4) (2014), 1607-1621.
  4. A Cangiani, EH Georgoulis, P Houston, hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshesMathematical Models and Methods in Applied Sciences 24 (10), 2009-2041 (2014).
  5. AN Gorban, DJ Packwood, Enhancement of the stability of lattice Boltzmann methods by dissipation control, Physica A 414 (2014), 285-299,
  6. T Hangelbroek, J. Levesley, On the density of polyharmonic splines, Journal of Approximation Theory 167,  94–108 (2013).
  7. A Cangiani, EH Georgoulis, M Jensen, Discontinuous Galerkin Methods for Mass Transfer through Semipermeable Membranes, SIAM Journal on Numerical Analysis 51 (5), 2911-2934 (2013).
  8. Beirão da Veiga, L., Brezzi, F., Cangiani, A., Manzini, G., Marini, L. D., & Russo, A. Basic principles of virtual element methods. Mathematical Models and Methods in Applied Sciences, 23(01), 199-214  (2013).
  9. A Cangiani, J Chapman, E Georgoulis, M Jensen, On the Stability of Continuous–Discontinuous Galerkin Methods for Advection–Diffusion–Reaction Problems, Journal of Scientific Computing 57 (2), 313-330 (2013).
  10. Y. Xie, H. Dong, J. Liu, R. L. Davidchack, J.A. Dantzig, G. Duggan, M. Tongd, D.J. Browne, A Multi-Scale Approach to Simulate Solidification Structure Evolution and Solute Segregation in a Weld Pool, Journal of Algorithms & Computational Technology 7 (4), 489-508 (2013).
  11. E.H.Georgoulis, J. Levesley, F. Subhan,   Multilevel sparse kernel-based interpolation. SIAM Journal on Scientific Computing, 35(2), A815-A831 (2013).
  12. A Athanassoulis, T Paul, On the selection of the classical limit for potentials with BV derivatives, Journal of Dynamics and Differential Equations 25 (1), 33-47 (2013).
  13. RA Brownlee, J Levesley, D Packwood, AN Gorban, RA Brownlee, Add-ons for Lattice Boltzmann Methods: Regularization, Filtering and LimitersProgress in Computational Physics, 2013, vol. 3, 31-52.
  14. RL Davidchack, Discretization errors in molecular dynamics simulations with deterministic and stochastic thermostats, Journal of Computational Physics 229 (24), 9323-9346 (2010).
  15. A. Cangiani and G. Manzini & A. Russo. Convergence analysis of the mimetic finite difference method for elliptic problems. SIAM J. on Numer. Anal. 47(4), pp. 2612–2637 (2009).
  16. P. Cvitanović, R. L. Davidchack, E. Siminos. On the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain. SIAM J. Appl. Dyn. Syst. 9(1), pp.1–33 (2010).
  17. E. H. Georgoulis, O. Lakkis and J.M. Virtanen. A posteriori error control for discontinuous Galerkin methods for parabolic problems. SIAM J. on Numer. Anal. 49(2), pp. 427-458 (2011)
  18. R. Beatson, O. Davydov, J. Levesley. Error bounds for anisotropic RBF interpolation. J. Approx. Theory 162(3), pp. 512–527 (2010).
  19. R.A. Brownlee, A. N. Gorban, J. Levesley, Nonequilibrium entropy limiters in lattice Boltzmann methods. Phys. A. 387, no. 2-3, pp. 385–406 (2008).

 

PhD Programme and Current Students

The group runs a successful Ph.D. programme (within the Ph.D. programme of the Department of Mathematics) with about 2-3 Ph.D.'s in the area of numerical analysis completed per academic year.

Current PhD students: Maria Krivko, Mengjiao Brian Li, Mykhailo Melnykov, Stephen Metcalfe, David Packwood, Mariam Pirashvili, Jian Xia Zhang

Some recently completed PhD's are:

  • "Multilevel Sparse Kernel-based Interpolation" by Fazli Subhan (2011)
  • "The Impact Of Hydrate Dissociation Coupled With Seismic Ground Motion On The Stability Of Submarine Slopes" by Alexandra Lemon (2011)
  • "Stabilizing Lattice Boltzmann simulation of flow past bluff bodies by introduction of Ehrenfests' limiters." by Tahir Khan (2011)
  • "Adaptive Discontinuous Galerkin Methods for Fourth Order Problems" by Juha Virtanen (2010)
  • "Selected topics in Dirichlet problems for linear parabolic stochastic partial differential equations" by Vasile Stanciulescu (2010)
  • "On Conditional Wiener Integrals and a Novel Approach to the Fermion Sign Problem" by Warwick Dumas (2010)
  • "Non-Oscillatory Finite Volume Methods for Conservation Laws on Unstructured Grids" by  Terhemen Aboiyar (2008)

Grants

The group has received funding in the last few years from the following grant-awarding institutions:

 

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Contact details

Department of Mathematics
University of Leicester
University Road
Leicester LE1 7RH
United Kingdom

Tel.: +44 (0)116 252 3917
Fax: +44 (0)116 252 3915

Campus Based Courses

Undergraduate: mathsug@le.ac.uk
Postgraduate Taught: mathspg@le.ac.uk

Postgraduate Research: pgrmaths@le.ac.uk

Distance Learning Course  

Actuarial Science:

dlstudy@le.ac.uk  

 

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