Numerical Analysis and Scientific Computing

The Numerical Analysis and Scientific Computing Group at Leicester is involved in a number of research directions such as approximation theory, computational dynamical systems, numerical solution of partial differential equations, computational fluid dynamics, numerical solution of stochastic differential equations, numerical methods for stochastic processes and 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:

• 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).
• 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).
• 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).
• 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).
• R. Beatson, O. Davydov, J. Levesley. Error bounds for anisotropic RBF interpolation. J. Approx. Theory 162(3), pp. 512–527 (2010).

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:

• Engineering and Physical Sciences Research Council (EPSRC)
  
• The Royal Society
• The Leverhulme Trust
• The London Mathematical Society (LMS)
  
• Institute of Mathematics and its Applications (IMA)