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Personal profile

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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  • 2 Similar Profiles
Multilevel Methods Mathematics
Elliptic PDE Mathematics
Monte Carlo methods Engineering & Materials Science
Monte Carlo method Mathematics
Coefficient Mathematics
Partial differential equations Engineering & Materials Science
Domain Decomposition Mathematics
Preconditioner Mathematics

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Projects 2009 2024

Re-shaping the Test Pyramid

Scheichl, R. & Anaya-Izquierdo, K.


Project: Research council

Sustainable development
Numerical methods
Fusion reactions
Composite materials

Research Output 2002 2019

2 Citations (Scopus)
18 Downloads (Pure)
Open Access
Maximum entropy methods
Probability density function
Mathematical operators

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 journalArticle

Approximation and sampling of multivariate probability distributions in the tensor train decomposition

Dolgov, S., Anaya-Izquierdo, K., Fox, C. & Scheichl, R., 31 Dec 2019, In : Statistics and Computing. 2019, 23 p., s11222-019-09910-z.

Research output: Contribution to journalArticle

Open Access
Tensor Decomposition
Multivariate Distribution
Probability Distribution
1 Citation (Scopus)
3 Downloads (Pure)

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 journalArticle

Open Access

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 journalArticle

Open Access


Development Of A Performance-Portable Framework For Atomistic Simulations

Author: Saunders, W. R., 13 Feb 2019

Supervisor: Mueller, E. (Supervisor), Parker, S. (Supervisor), Grant, R. (Supervisor) & Scheichl, R. (Supervisor)

Student thesis: Doctoral ThesisPhD


Multilevel Monte Carlo Methods and Uncertainty Quantication

Author: Teckentrup, A., 19 Jun 2013

Supervisor: Scheichl, R. (Supervisor)

Student thesis: Doctoral ThesisPhD


Multi Level Monte Carlo Methods for Atmospheric Dispersion Modelling

Author: Cook, S., 22 Nov 2013

Supervisor: Scheichl, R. (Supervisor) & Mueller, E. (Supervisor)

Student thesis: Doctoral ThesisMPhil


Numerical computation of band gaps in photonic crystal fibres

Author: Norton, R., 1 Sep 2008

Supervisor: Scheichl, R. (Supervisor)

Student thesis: Doctoral ThesisPhD


Numerical solution of weather and climate systems

Author: Buckeridge, S., 31 Dec 2010

Supervisor: Scheichl, R. (Supervisor)

Student thesis: Doctoral ThesisPhD