Research interests

My research interests lie in numerical analysis and uncertainty quantification. The majority of my work is related to the numerical solution of partial differential equations with random coefficients. Such equations arise, for example, in stochastic groundwater flow modelling, where rock properties such as permeability are often highly uncertain due to lack of data.

In my PhD, I worked on the development and analysis of Multilevel Monte Carlo methods for the above model problems, with particular focus on coefficients which are rough and highly oscillatory. These multilevel methods greatly reduce the cost of the classical Monte Carlo estimators, and allow to compute quantities of interest to a high accuracy in a feasible amount of time.

More recently, I have also started working on stochastic collocation type methods, which work very well for smooth coefficients, and on problems in Bayesian inference.

Submitted papers

  • A.L. Teckentrup, P. Jantsch, C.G. Webster and M. Gunzburger . A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data.. Submitted April 2014, available as arXiv:1404.2647. Preprint

  • C. Ketelsen, R. Scheichl and A.L. Teckentrup . A Hierarchical Multilevel Markov chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow.. Submitted March 2013, available as arXiv:1303.7343. Preprint

    • Publications

  • A.L. Teckentrup . Multilevel Monte Carlo methods for highly hetereogeneous media. Proceedings of the Winter Simulation Conference 2012. Available at http://informs-sim.org/. Preprint

  • A.L. Teckentrup, R. Scheichl, M.B. Giles and E. Ullmann . Further Analysis of Multilevel Monte Carlo Methods for elliptic PDEs with random coefficients. Numerische Mathematik, 125(3):569-600, 2013. Preprint

  • J. Charrier, R. Scheichl and A.L. Teckentrup. Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and its Application to Multilevel Monte Carlo Methods. SIAM Journal on Numerical Analysis, 51(1):322-352, 2013. Preprint

  • K.A. Cliffe, M.B. Giles, R. Scheichl and A.L. Teckentrup. Multilevel Monte Carlo Methods and Applications to Elliptic PDEs with Random Coefficients. Computing and Visualization in Science, 14(1):3-15, 2011. Preprint

    • Theses

  • A.L. Teckentrup . Multilevel Monte Carlo methods and uncertainty quantification.. PhD thesis, University of Bath (UK), June 2013. PDF