Projects per year
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Research interests
I am a member of the Numerical Analysis Group. My interests are in the design and analysis of efficient and robust parallel numerical methods for engineering and physical problems with heterogeneous material properties that vary over multiple scales. This is typical in energy and environmental applications, but also in material science and manufacturing. My research spans the whole range from the regularity analysis of solutions to the efficient parallel implementation of novel methods and their industrial application. I am particularly interested in multilevel and multiscale methods for partial differential equations with strongly varying and high contrast coefficients, in particular domain decomposition and multigrid methods, preconditioners for systems of PDEs, iterative eigensolvers, and multiscale discretisation techniques with applications in oil reservoir simulation, radioactive waste disposal, numerical weather and climate prediction, novel optical materials or composite materials.
More recently my particular focus has been on the interface between computational mathematics and statistics/probability. In most applications with heterogeneous material properties the coefficients are not known exactly. In fact, they are usually highly uncertain. One of the most popular ways to deal with uncertainty is stochastic modelling. However, most of the statistical tools for uncertainty quantification are either very inaccurate or computationally infeasible for typical engineering applications. Similar things can be said for data assimilation, for example in numerical weather prediction. My current research focusses mainly on two promising variants of the classical Monte Carlo method, namely multilevel Monte Carlo and quasi-Monte Carlo, which can provide highly accurate and efficient tools for uncertainty quantification. More recently we have extended the technology also to Bayesian inference by developing a multilevel Markov chain Monte Carlo method. The new methods are also of interest in time dependent problems with random noise (SDEs), e.g. in mathematical finance or in atmospheric dispersion modelling.
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Projects
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Re-shaping the Test Pyramid
Scheichl, R. & Anaya-Izquierdo, K.
Engineering and Physical Sciences Research Council
1/08/19 → 31/07/24
Project: Research council
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International Research Initiator Scheme - Santander Call 2015-16
20/09/16 → 20/09/18
Project: Research-related funding
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Research output
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A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data
Lang, J., Scheichl, R. & Silvester, D., 15 Oct 2020, In: Journal of Computational Physics. 419, 109692.Research output: Contribution to journal › Article › peer-review
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Error Analysis and Uncertainty Quantification for the Heterogeneous Transport Equation in Slab Geometry
Graham, I. G., Parkinson, M. J. & Scheichl, R., 8 Aug 2020, In: IMA Journal of Numerical Analysis. draa028.Research output: Contribution to journal › Article › peer-review
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Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3
Lykkegaard, M. B., Mingas, G., Scheichl, R., Fox, C. & Dodwell, T. J., 17 Nov 2020, (Acceptance date) In: Advances in Neural Information Processing Systems.Research output: Contribution to journal › Article › peer-review
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Multilevel Monte Carlo for quantum mechanics on a lattice
Jansen, K., Müller, E. & Scheichl, R., 18 Dec 2020, In: Physical Review D. 102, 24 p., 114512 .Research output: Contribution to journal › Article › peer-review
Open Access -
Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances
Bachmayr, M., Graham, I. G., Nguyen, V. K. & Scheichl, R., 2020, In: SIAM Journal on Numerical Analysis (SINUM). 58, 5, p. 2953–2980 28 p.Research output: Contribution to journal › Article › peer-review
Open Access