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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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Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients
Gilbert, A. D., Graham, I. G., Kuo, F. Y., Scheichl, R. & Sloan, I. H., 1 Aug 2019, In: Numerische Mathematik. 142, 4, p. 863-915 53 p.Research output: Contribution to journal › Article › peer-review
Open Access1 Citation (Scopus) -
Continuous Level Monte Carlo and Sample-Adaptive Model Hierarchies
Detommaso, G., Dodwell, T. & Scheichl, R., 31 Dec 2019, In: SIAM/ASA Journal on Uncertainty Quantification. 7, 1, p. 93-116 24 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile2 Citations (Scopus)18 Downloads (Pure) -
Correction of coarse-graining errors by a two-level method: Application to the Asakura-Oosawa model
Kobayashi, H., Rohrbach, P. B., Scheichl, R., Wilding, N. B. & Jack, R. L., 14 Oct 2019, In: Journal of Chemical Physics. 151, 14, p. 144108 144108.Research output: Contribution to journal › Article › peer-review
Open Access1 Citation (Scopus) -
Multilevel Markov chain Monte Carlo
Dodwell, T. J., Ketelsen, C., Scheichl, R. & Teckentrup, A. L., 2019, In: Siam Review. 61, 3, p. 509-545 37 p.Research output: Contribution to journal › Article › peer-review
Open Access5 Citations (Scopus) -
Analysis of circulant embedding methods for sampling stationary random fields
Graham, I. G., Kuo, F. Y., Nuyens, D., Scheichl, R. & Sloan, I. H., 31 Dec 2018, In: SIAM Journal on Numerical Analysis (SINUM). 56, 3, p. 1871-1895 25 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile13 Citations (Scopus)33 Downloads (Pure)