Publications
(see also my page on Google Scholar)
Preprints (Submitted)
- S. Dolgov and R. Scheichl (2017), A hybrid Alternating Least Squares - TT Cross algorithm for parametric PDEs, submitted 14 July 2017
[Preprint]
- A. Reinarz, T. Dodwell, T. Fletcher, L. Seelinger, R. Butler and R. Scheichl (2017), dune-composites - A New Framework for High-Performance Finite Element Modelling of Laminates, submitted 13 July 2017
[Preprint]
- G. Katsiolides, E.H. Müller, R. Scheichl, T. Shardlow, M.B. Giles and D.J. Thomson (2016), Multilevel Monte Carlo and Improved Timestepping Methods in Atmospheric Dispersion Modelling, submitted 22 December 2016
[Preprint]
- I.G. Graham, M.J. Parkinson and R. Scheichl (2016), Modern Monte Carlo Variants for Uncertainty Quantification in Neutron Transport, submitted 9 December 2016
[Preprint]
Journals
- B. Gmeiner, D Drzisga, U. Rüde, R. Scheichl and B. Wohlmuth (2017), Scheduling Massively Parallel Multigrid for Multilevel Monte Carlo Methods, to appear in SIAM Journal on Scientific Computing
[Preprint]
- F.Y. Kuo, R. Scheichl, Ch. Schwab, I.H. Sloan and E. Ullmann (2017), Multilevel Quasi-Monte Carlo Methods for Lognormal Diffusion Problems, Mathematics of Computation 86:2827-2860
[Preprint]
- R. Scheichl, A. Stuart and A.L. Teckentrup (2017), Quasi-Monte Carlo and Multilevel Monte Carlo Methods for Computing Posterior Expectations in Elliptic Inverse Problems, SIAM/ASA Journal on Uncertainty Quantification 5(1):493-518. [Preprint]
- D. Peterseim and R. Scheichl (2016), Robust Numerical Upscaling of Elliptic Multiscale Problems at High Contrast, Computational Methods in Applied Mathematics 16(4):579-603. [Preprint]
- T.A. Fletcher, T. Kim, T.J. Dodwell, R. Butler, R. Scheichl and R. Newley (2016), Resin Treatment of Free Edges to Aid Certification of Through Thickness Laminate Strength, Composite Structures 146:26-33.
- A. Ferreiro-Castilla, A.E. Kyprianou and R. Scheichl (2016), An Euler-Poisson Scheme for Levy driven SDEs, Journal of Applied Probability 53(1):262-278. [Preprint (Sept 2013)]
- A. Dedner, E.H. Mueller and R. Scheichl (2016), Efficient Multigrid Preconditioners for Atmospheric Flow Simulations at High Aspect Ratio, International Journal for Numerical Methods in Fluids 80(1):76-102
[Preprint]
- I.G. Graham, R. Scheichl and E. Ullmann (2015), Mixed Finite Element Analysis of Lognormal Diffusion and Multilevel Monte Carlo Methods,
Stochastics and Partial Differential Equations: Analysis and Computations 4(1):41-75,
[Preprint (Dec 2013)]
- S. Loisel, H. Nguyen and R. Scheichl (2015), Optimized Schwarz and 2-Lagrange Methods for Multiscale PDEs, SIAM Journal of Scientific Computing 37(6):A2896–A2923
[Preprint]
- E.H. Mueller, R. Scheichl and E. Vainikko (2015), Petascale Solvers for Anisotropic PDEs in atmospheric modelling on GPU Clusters, Parallel Computing 50:53-69 [Preprint]
- T.J. Dodwell, C. Ketelsen, R. Scheichl and A.L. Teckentrup (2015), A Hierarchical Multilevel Markov Chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow, SIAM/ASA Journal on Uncertainty Quantification 3(1):1075-1108 [Preprint (v1: Mar 2013)]
- E.H. Mueller, R. Scheichl and T. Shardlow (2015), Improving MLMC for SDEs with Application to the Langevin Equation, Proceedings of the Royal Society A 471:20140679 [Preprint]
- I.G. Graham, F.Y. Kuo, J.A. Nicholls, R. Scheichl, Ch. Schwab and I.H. Sloan (2015), Quasi-Monte Carlo Finite Element Methods for Elliptic PDEs with Log-normal Random Coefficients, Numerische Mathematik 131(2):329-368
[Preprint (May 2013)]
- M. Dauge, R.A. Norton and R. Scheichl (2014), Regularity of Maxwell Eigenproblems in Photonic Crystal Fibre Modelling, BIT Numerical Mathematics 55(1):59-80 [Preprint]
- E.H. Mueller and R. Scheichl (2014), Massively Parallel Solvers for Elliptic PDEs in Numerical Weather- and Climate Prediction, Quarterly J Royal Meteorological Society 140(685):2608-2624
[Preprint]
- A. Ferreiro-Castilla, A.E. Kyprianou, R. Scheichl and G. Suryanarayana (2014), Multilevel Monte Carlo Simulation for Levy Processes Based on the Wiener-Hopf Factorisation, Stochastic Processes and their Applications 124(2):985-1010 [Preprint (Oct 2012)]
- N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein and R. Scheichl (2014),
Abstract Robust Coarse Spaces for Systems of PDEs via Generalized Eigenproblems in the Overlaps , Numerische Mathematik 126(4):741-770
[Preprint (Nov 2011)]
- E. Mueller, X. Guo, R. Scheichl and S. Shi (2013), Matrix-free GPU implementation of a preconditioned conjugate gradient solver for anisotropic elliptic PDEs, Computing and Visualization in Science 16(2):41-58
[Preprint]
- A.L. Teckentrup, R. Scheichl, M.B. Giles and E. Ullmann (2013), Further Analysis of Multilevel Monte Carlo Methods for Elliptic PDEs with Random Coefficients, Numerische Mathematik 125(3):569-600
[Preprint]
- J. Charrier, R. Scheichl and A.L. Teckentrup (2013), 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
[Preprint (April 2011)]
- R. Norton and R. Scheichl (2012), Planewave Expansion Methods for Photonic Crystal Fibres, Applied Numerical Mathematics 63:88-104 [Preprint]
- C. Pechstein and R. Scheichl (2012),
Weighted Poincare Inequalities, IMA Journal on Numerical
Analysis 33 (2):652--686 [Preprint (Dec 2010)]
- V. Dolean, F. Nataf, R. Scheichl and N. Spillane (2012), Analysis of a Two-level Schwarz Method with Coarse Spaces Based on Local Dirichlet-to-Neumann Maps, Computational Methods in Applied Mathematics 12 (4):391-414, [Preprint]
- R. Scheichl, P.S. Vassilevski and L.T. Zikatanov (2012),
Mutilevel Methods for Elliptic Problems with Highly Varying Coefficients
on Non-Aligned Coarse Grids, SIAM Journal on Numerical
Analysis 50 (3):1675-1694 [Preprint (Aug 2010)]
- M. Marletta and R. Scheichl (2012),
Eigenvalues in Spectral Gaps of Differential Operators,
Journal of Spectral Theory 2 (3):293-320
[Preprint (Sept 2010)]
- P. Bastian, M. Blatt and R. Scheichl (2012), Algebraic Multigrid for Discontinuous Galerkin Discretizations, Numerical Linear Algebra with Applications 19 (2):367-388 [Preprint]
- N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein and R. Scheichl (2011),
A Robust Two Level Domain Decomposition Preconditioner for Systems of PDEs, Comptes Rendus Mathematique 349 (23-24):1255-1259
[Preprint]
- R. Scheichl, P.S. Vassilevski and L.T. Zikatanov (2011),
Weak Approximation Properties of Elliptic Projections with Functional Constraints, Multiscale Modeling and Simulation and Analysis 9 (4):1677-1699 [Preprint]
- K.A. Cliffe, M.B. Giles, R. Scheichl and A.L. Teckentrup (2011),
Multilevel Monte Carlo Methods and Applications to Elliptic PDEs with Random Coefficients, Computing and Visualization in Science 14 (1):3-15
[Preprint]
- S.D. Buckeridge, M.J.P. Cullen, R. Scheichl and M. Wlasak (2011),
A Robust Numerical Method for the Potential Vorticity Based Control Variable Transform in Variational Data Assimilation, Quarterly J Royal Meteorological Soc 137 (657):1083-1094
- C. Pechstein and R. Scheichl (2011),
Analysis of FETI Methods for Multiscale PDEs - Part II:
Interface Variation, Numerische Mathematik 118 (3):485-529
[Preprint (July 2009)]
- I. G. Graham, F. Y. Kuo, D. Nuyens, R. Scheichl, and I. H. Sloan (2011),
Quasi-Monte Carlo Methods for for Elliptic PDEs with Random Coefficients and Applications,
Journal of Computational Physics 230 (10):3668-3694
[Preprint]
- S.D. Buckeridge and R. Scheichl (2010),
Parallel Geometric Multigrid for Global Weather Prediction,
Numerical Linear Algebra with Applications 17:325-342
[Preprint]
- R. Norton and R. Scheichl (2010),
Convergence Analysis of Planewave Expansion Methods for Schroedinger
Operators with Discontinuous Periodic Potentials, SIAM
Journal for Numerical Analysis 47 (6):4356-4380
[Preprint]
- C. Pechstein and R. Scheichl (2009),
Scaling Up through Domain Decomposition, Applicable Analysis
88(10):1589-1608
[Preprint]
- J. Van lent, R. Scheichl and I.G. Graham (2009),
Energy Minimizing Coarse Spaces for Two-level Schwarz Methods for
Multiscale PDEs, Numerical Linear Algebra with Applications 16(10):775-799 [Preprint]
- C. Pechstein and R. Scheichl (2008),
Analysis of FETI Methods for Multiscale PDEs, Numerische Mathematik
111(2):293-333
[Preprint]
- B. Aksoylu, I.G. Graham, H. Klie and R. Scheichl (2008),
Towards a Rigorously Justified Algebraic Preconditioner for High-Contrast
Diffusion Problems, Computing and Visualization in Science 11,
pp. 319-331 [Preprint]
- R. Scheichl and E. Vainikko (2007),
Additive Schwarz with Aggregation-Based Coarsening for Elliptic
Problems with Highly Variable Coefficients, Computing 80(4):319-343
[Preprint]
- I.G. Graham, P. Lechner and R. Scheichl (2007),
Domain Decomposition for Multiscale PDEs, Numerische Mathematik
106:589-626
[Preprint]
- I.G. Graham and R. Scheichl (2007),
Robust Domain Decomposition Algorithms for Multiscale
PDEs, Numerical Methods for Partial Differential Equations
23(4):859-878
[Preprint]
- R. Scheichl, M.-H. Klopffer, Z. Benjelloun-Dabaghi, B.
Flaconneche (2005),
Permeation of Gases in Polymers: Parameter Identification and
Nonlinear Regression Analysis, Journal of Membrane Science
254, pp. 275-293
[PostScript file]
- R. Scheichl, R. Masson, J. Wendebourg (2003),
Decoupling and Block Preconditioning for Sedimentary Basin
Simulations, Computational Geosciences 7(4), pp. 295-318
[Abstract ]
[Preprint]
- R. Scheichl (2002),
Decoupling Three-dimensional Mixed Problems Using
Divergence-free Finite Elements. (SIAM Student Paper Prize 2000)
SIAM Journal of Scientific Computing 23 (5):1752-1776
[Abstract ]
[Preprint]
- K.A. Cliffe, I.G. Graham, R. Scheichl, and L. Stals (2000),
Parallel Computation of Flow in Heterogeneous Media Modelled by Mixed
Finite Elements. Journal of Computational Physics
164:258-282
[Abstract]
[Preprint]
- R. Scheichl (2000),
Parallel Solvers for the Transient Multigroup Neutron Diffusion Equations.
International Journal for Numerical Methods in Engineering
47:1751-1771
[Abstract]
[Preprint]
Books
- M. Cullen, M.A. Freitag, S. Kindermann and R. Scheichl (Editors) (2013),
Large Scale Inverse Problems: Computational Methods and Applications in the Earth Sciences, Radon Series on Computational and Applied Mathematics, Vol. 13,
De Gruyter, Berlin
[De Gruyter Link]
- P. Bastian, J. Kraus, R. Scheichl and M.F. Wheeler (Editors) (2013),
Simulation of Flow in Porous Media:
Applications in Energy and Environment,
Radon Series on Computational and Applied Mathematics, Vol. 12,
De Gruyter, Berlin
[De Gruyter Link]
- I.G. Graham, T.Y. Hou, O. Lakkis and R. Scheichl (Editors) (2012),
Numerical Analysis of Multiscale Problems,
Lecture Notes in Computational Science and Engineering, Vol. 83,
Springer, Heidelberg
[Springer Link]
- R. Scheichl (1997),
Parallel Solution of the Transient Multigroup Neutron Diffusion Equations
with Multi-Grid and Preconditioned Krylov-Subspace Methods (Master's Thesis).
Schriften der Johannes Kepler Universitaet Linz, Vol. C21 ,
Trauner-Verlag, Linz [PostScript
file (without large colour picture)]
Refereed Proceedings
- T.J. Dodwell, A. Sandhu and R. Scheichl (2017), Customized Coarse Models for Highly Heterogeneous Materials, in "Bifurcation and Degradation of Geomaterials with Engineering Applications" (Papamichos E, Papanastasiou P, Pasternak E, Dyskin A, Eds.), IWBDG 2017, Springer Series in Geomechanics and Geoengineering, Springer
[Preprint]
- T. Fletcher, A. Reinarz, T.J. Dodwell, R. Butler, R. Scheichl and R. Newley (2016), Efficient Modelling and Accurate Certification of Curved Aerospace Laminates, 17th European Conference on Composite Materials, Munich, 26-30 June 2016 [Link]
- R. Butler, T.J. Dodwell, T. Kim, S. Kynaston, R. Scheichl, R.T. Haftka and N.H. Kim (2015), Uncertainty Quantification of Composite Structures with Defects using Multilevel Monte Carlo Simulations, AIAA SciTech Conference, Kissimmee, 5-9 January 2015 [Link]
- T. Kim, T. Fletcher, T.J. Dodwell, R. Butler, R. Scheichl, J. Ankersen and R. Newley
(2015), The Effect of Free Edges on Inter-Laminar Performance of Curved Laminates, AIAA SciTech Conference, Kissimmee, 5-9 January 2015 [Link]
- R. Scheichl (2014),
Robust Numerical Upscaling at High Contrast, Oberwolfach Workshop on
"Reactive Flows in Deformable, Complex Media"
(Organisers: M.~Gerritsen, J.M.~Nordbotten, I.S.~Pop, B.~Wohlmuth), 21-27 September 2014, Oberwolfach Report 43/2014
[PDF]
- N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein and R
Scheichl (2014), Achieving Robustness Through Coarse Space Enrichment
in the Two Level Schwarz Framework, to appear in Proceedings of the 21st International Conference on Domain Decomposition Methods (DD21), Rennes, June 2012
[Preprint]
- R. Scheichl (2013), MLMCMC -- Multilevel Markov Chain Monte Carlo, Oberwolfach Miniworkshop on "Numerical Upscaling for Media with Deterministic and Stochastic Heterogeneity"
(Organisers: Y. Efendiev, O. Iliev, P. Vassilevski), 10-16 February
2013, Oberwolfach Report 07/2013
[PDF]
- R. Scheichl (2013), Robust Coarsening in Multiscale PDEs, in Domain Decomposition Methods in Science and Engineering XX (R. Bank, M. Holst, O. Widlund, J. Xu, Eds.), Vol. 91 of Lecture Notes in Computational Science and Engineering, Springer, pp. 51-62.
[Preprint]
- C. Pechstein, M. Sarkis and R. Scheichl (2013), New Theoretical Coefficient Robustness Results for FETI-DP, in Domain Decomposition Methods in Science and Engineering XX (R. Bank, M. Holst, O. Widlund, J. Xu, Eds.), Vol. 91 of Lecture Notes in Computational Science and Engineering, Springer, pp. 313-320.
[Preprint]
- V. Dolean, F. Nataf, R. Scheichl and N Spillane (2013), A Two-Level Schwarz Preconditioner for Heterogeneous Problems, in Domain Decomposition Methods in Science and Engineering XX (R. Bank, M. Holst, O. Widlund, J. Xu, Eds.), Vol. 91 of Lecture Notes in Computational Science and Engineering, Springer, pp. 87-94.
[Preprint]
- C. Pechstein and R. Scheichl (2011),
Weighted Poincare Inequalities and Applications in Domain
Decomposition, Domain Decomposition Methods in Science and Engineering XIX
(Y. Huang, R. Kornhuber, O. Widlund, and J. Xu, eds.), Lecture Notes in Computational Science and Engineering, vol. 78, pp. 197-204 (Proceedings of 19th
Int. Conf. Domain Decomposition Methods, 17-22 Aug 2009, Zhangjiajie, China).
[Preprint]
- E. Dodgson, D.A.S. Rees and R. Scheichl (2010),
Vortex Instability of Free Convection Boundary Layers in Porous Media,
in Proceedings of 3rd Internat. Conf. Porous Media and its Applications in Science, Engineering and Industry, June 20-25 2010, Montecatini, Italy, AIP Conference Proceedings, Vol. 1254, K. Vafai (Ed.)
- C. Pechstein and R. Scheichl (2010),
Robust FETI Solvers for Multiscale Elliptic PDEs, in
Proceedings of the 6th Int. Conf. on Scientific Computing in Electrical
Engineering (SCEE 2008, Helsinki, Sep 2008), Roos, J., Costa, L.R.J. (Eds.), volume 14 of Mathematics in Industry, Springer, pp. 421-428
[Preprint]
- C. Pechstein and R. Scheichl (2010),
Weighted Poincare Inequalities for High-Contrast Coefficients,
Oberwolfach Workshop on "Computational Electromagnetism and Accoustics"
(Organisers: R Hiptmair, RHW Hoppe, P Joly, U Langer), 14-20 February 2010,
Oberwolfach Report 10/2010
[PDF]
[Full Report]
- R. Scheichl (2009),
Domain Decomposition and Upscaling, Oberwolfach Miniworkshop on
"Numerical Upscaling for Flow Problems: Theory and Applications"
(Organisers: A. Brandt, Y. Efendiev, O. Iliev), 1-7 March
2009, Oberwolfach Report 12/2009
[PDF]
[Full Report]
- I.G. Graham and R. Scheichl (2008),
Coefficient-explicit Condition Number Bounds for Overlapping
Additive Schwarz, in Proceedings of the 17th International
Conference on Domain Decomposition Methods, Strobl, Austria, 3-7 July
2006, Langer, U., Discacciati, M. Keyes, D. et al.
(Eds.), Domain Decomposition Methods in Science and
Engineering XVII, Lecture Notes in Computational Science and Engineering,
Vol. 60, Springer, New York
[Preprint]
- R. Scheichl and E. Vainikko (2006),
Robust Aggregation-Based Coarsening for Additive Schwarz in the
Case of Highly Variable Coefficients, in Proceedings of the European
Conference on Computational Fluid Dynamics, ECCOMAS CFD 2006
(P. Wesseling, E. Onate, J. Periaux, Eds.), TU Delft
[Preprint]
- R. Masson, P. Quandalle, S. Requena, R. Scheichl (2004),
Parallel Preconditioning for Sedimentary Basin
Simulations, Lecture Notes in Computer Science 2907
(Lirkov I., Margenov S. et al., Eds.),
Proceedings 4th Int. Conf. on Large Scale Scientific Computations, June 4-8,
2003, Sozopol, Bulgaria, Springer
[Abstract ]
[PostScript file]
- R. Scheichl (1999),
Parallel Solvers for the Two-Group Neutron Diffusion Equations of
Reactor Kinetics. Proceedings of the 11th International
Conference on Domain Decomposition Methods, Greenwich, July 1998 (edited by
C.H. Lai et al.) [PostScript
file]
- H. Finnemann and R. Scheichl (1999),
Efficiency Enhancements of Coupled RELAP5/PANBOX Calculations Using
Adaptive Methods. Transactions of the American Nuclear Society for the
Annual Meeting, Boston, June 1999 [WordDocument]
Theses
- S.E. Cook (2013), Multilevel Monte Carlo Methods for Atmospheric Dispersion Modelling. MPhil Thesis, University of Bath
[PDF]
- A.L. Teckentrup (2013), Multilevel Monte Carlo Methods and Uncertainty Quantification. PhD Thesis, University of Bath
[PDF]
- E. Dodgson (2011),
Thermoconvective Instability in Porous Media.
PhD Thesis, University of Bath
[PDF]
- S.D. Buckeridge (2010),
Numerical Solution of Weather and Climate Systems.
PhD Thesis, University of Bath
[PDF]
- R. Norton (2008),
Numerical Computation of Band Gaps in Photonic Crystal Fibres.
PhD Thesis, University of Bath
[PDF]
- R. Scheichl (2000),
Iterative Solution of Saddle Point Problems Using Divergence-free
Finite Elements with Applications to Groundwater Flow. PhD
Thesis, University of Bath
[PostScript file (without large colour pictures)]
Extended Abstracts and Other Publications
- E. Mueller, R. Scheichl and E. Vainikko (2013),
Matrix-free multi-GPU implementation of elliptic solvers for strongly anisotropic PDEs, Extended Abstract for the 5th UK Manycore Developer Conference,
Oxford, 16 December 2013
[PDF]
- B. Aksoylu, I.G. Graham, H. Klie and R. Scheichl (2008),
A Rigorously Justified Robust Algebraic Preconditioner for High-Contrast
Diffusion Problems, Extended Abstract for the 8th World Congress on
Computational Mechanics (WCCM8) and the 5th European Congress on
Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008),
Venice, 30 June - 4 July 2008
[PDF]
- R. Norton and R. Scheichl (2007),
Convergence Analysis of Planewave Expansion for Band Gap Computations in
Photonic Crystal Fibres, Extended Abstract for the 8th International
Conference on Mathematical and Numerical Aspects of Waves (Waves 2007),
University of Reading, July 23-27, 2007.
[PDF]
- D. Allwright, K. Briggs, P. Dellar, J. Gravesen, R. Scheichl,
J. Van lent and M. Zyskin (2006),
Sensitivity of Markov chains for wireless protocols, Study Group
Report, 56th European Study Group with Industry, Bath
[PDF]
- R. Scheichl (2000),
A Decoupled Iterative Method for Mixed Problems
using Divergence-free Finite Elements. Extended Abstract, SIAM Student
Paper Prize 2000, SIAM Annual Meeting, Rio
Grande, Puerto Rico, July 10-14, 2000
[PDF]
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Last updated 20/12/2013