Publications

Preprints (Submitted)

• A.L. Teckentrup, R. Scheichl, M.B. Giles and E. Ullmann, Further Analysis of Multilevel Monte Carlo Methods for Elliptic PDEs with Random Coefficients, submitted 29 March 2012, arXiv:1204.3476v1, 2012 [Preprint]
  
  
• R. Norton and R. Scheichl, Planewave Expansion Methods for Photonic Crystal Fibres, submitted 3 November 2011 [Preprint]
  
  
• N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein and R. Scheichl, Abstract Robust Coarse Spaces for Systems of PDEs via Generalized Eigenproblems in the Overlaps , submitted 31 October 2011
  
  
• 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, submitted 21 April 2011, BICS Preprint 2/11, University of Bath, 2011 [Preprint]
  
  
• V. Dolean, F. Nataf, R. Scheichl and N. Spillane, Analysis of a Two-level Schwarz Method with Coarse Spaces Based on Local Dirichlet-to-Neumann Maps, submitted 15 Apr 2011, Preprint HAL-00586246, Hyper Articles en Ligne
  
  
• C. Pechstein and R. Scheichl, Weighted Poincare inequalities, submitted 10th December 2010, NuMa-Report 2010-10, Institute of Computational Mathematics, Johannes Kepler University Linz, 2010. [Preprint]

Journals and Refereed Proceedings

• M. Marletta and R. Scheichl, Eigenvalues in Spectral Gaps of Differential Operators, to appear in Journal of Spectral Theory, 2012. [Preprint]
  
  
• R. Scheichl, P.S. Vassilevski and L.T. Zikatanov, Mutilevel Methods for Elliptic Problems with Highly Varying Coefficients on Non-Aligned Coarse Grids, to appear in SIAM Journal on Numerical Analysis, 2012 [Preprint]
  
  
• P. Bastian, M. Blatt and R. Scheichl, Algebraic Multigrid for Discontinuous Galerkin Discretizations, to appear in Numerical Linear Algebra with Applications, 2012 [Preprint]
  
  
• R. Scheichl, Robust Coarsening in Multiscale PDEs, to appear in Proceedings of the 20th International Conference on Domain Decomposition Methods (DD20), San Diego, 2011 [Preprint]
  
  
• C. Pechstein, M. Sarkis and R. Scheichl, New Theoretical Coefficient Robustness Results for FETI-DP, to appear in Proceedings of the 20th International Conference on Domain Decomposition Methods (DD20), San Diego, 2011 [Preprint]
  
  
• V. Dolean, F. Nataf, R. Scheichl and N Spillane, A Two-Level Schwarz Preconditioner for Heterogeneous Problems, to appear in Proceedings of the 20th International Conference on Domain Decomposition Methods (DD20), San Diego, 2011 [Preprint]
  
  
• N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein and R. Scheichl, A Robust Two Level Domain Decomposition Preconditioner for Systems of PDEs, Comptes Rendus Mathematique 349 (23-24):1255-1259, 2011. [Preprint]
  
  
• R. Scheichl, P.S. Vassilevski and L.T. Zikatanov, Weak Approximation Properties of Elliptic Projections with Functional Constraints, Multiscale Modeling and Simulation and Analysis 9 (4):1677-1699, 2011. [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]
  
  
• S.D. Buckeridge, M.J.P. Cullen, R. Scheichl and M. Wlasak 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, 2011.
  
  
• C. Pechstein and R. Scheichl, Analysis of FETI Methods for Multiscale PDEs - Part II: Interface Variation, Numerische Mathematik 118 (3):485-529, 2011. [Preprint]
  
  
• I. G. Graham, F. Y. Kuo, D. Nuyens, R. Scheichl, and I. H. Sloan, Quasi-Monte Carlo Methods for for Elliptic PDEs with Random Coefficients and Applications, Journal of Computational Physics 230 (10):3668-3694, 2011. [Preprint]
  
  
• C. Pechstein and R. Scheichl, 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, 2011, 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, 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.), 2010.
  
  
• S.D. Buckeridge and R. Scheichl, Parallel Geometric Multigrid for Global Weather Prediction, Numerical Linear Algebra with Applications 17:325-342, 2010. [Preprint]
  
  
• R. Norton and R. Scheichl, Convergence Analysis of Planewave Expansion Methods for Schroedinger Operators with Discontinuous Periodic Potentials, SIAM Journal for Numerical Analysis 47 (6):4356-4380, 2010. [Preprint]
  
  
• C. Pechstein and R. Scheichl, Robust FETI Solvers for Multiscale Elliptic PDEs, in Proceedings of the 6th Int. Conf. on Scientific Computing in Electrical Engineering (SCEE 2008, Helsinki, September 2008), Roos, J., Costa, L.R.J. (Eds.), volume 14 of Mathematics in Industry, Springer, 2010, pp. 421-428. [Preprint]
  
  
• C. Pechstein and R. Scheichl, Scaling Up through Domain Decomposition, Applicable Analysis 88(10):1589-1608, 2009. [Preprint]
  
  
• J. Van lent, R. Scheichl and I.G. Graham, Energy Minimizing Coarse Spaces for Two-level Schwarz Methods for Multiscale PDEs, Numerical Linear Algebra with Applications 16(10):775-799, 2009. [Preprint]
  
  
• C. Pechstein and R. Scheichl, Analysis of FETI Methods for Multiscale PDEs, Numerische Mathematik 111(2):293-333, 2008. [Preprint]
  
  
• B. Aksoylu, I.G. Graham, H. Klie and R. Scheichl, Towards a Rigorously Justified Algebraic Preconditioner for High-Contrast Diffusion Problems, Computing and Visualization in Science 11, pp. 319-331, 2008. [Preprint]
  
  
• I.G. Graham and R. Scheichl, 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, 2008. [Preprint]
  
  
• R. Scheichl and E. Vainikko, Additive Schwarz with Aggregation-Based Coarsening for Elliptic Problems with Highly Variable Coefficients, Computing 80(4):319-343, 2007. [Preprint]
  
  
• I.G. Graham, P. Lechner and R. Scheichl, Domain Decomposition for Multiscale PDEs, Numerische Mathematik 106:589-626, 2007. [Preprint]
  
  
• I.G. Graham and R. Scheichl, Robust Domain Decomposition Algorithms for Multiscale PDEs, Numerical Methods for Partial Differential Equations 23(4):859-878, 2007. [Preprint]
  
  
• R. Scheichl and E. Vainikko, 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, 2006. [Preprint]
  
  
• R. Scheichl, M.-H. Klopffer, Z. Benjelloun-Dabaghi, B. Flaconneche, Permeation of Gases in Polymers: Parameter Identification and Nonlinear Regression Analysis, Journal of Membrane Science 254, pp. 275-293, 2005. [PostScript file]
  
  
• R. Masson, P. Quandalle, S. Requena, R. Scheichl, 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, 2004. [Abstract ] [PostScript file]
  
  
• R. Scheichl, R. Masson, J. Wendebourg, Decoupling and Block Preconditioning for Sedimentary Basin Simulations, Computational Geosciences 7(4), pp. 295-318, 2003. [Abstract ] [Preprint]
  
  
• R. Scheichl, Decoupling Three-dimensional Mixed Problems Using Divergence-free Finite Elements. (SIAM Student Paper Prize 2000) SIAM Journal of Scientific Computing 23 (5):1752-1776, 2002. [Abstract ] [Preprint]
  
  
• K.A. Cliffe, I.G. Graham, R. Scheichl, and L. Stals, Parallel Computation of Flow in Heterogeneous Media Modelled by Mixed Finite Elements. Journal of Computational Physics 164:258-282, 2000. [Abstract] [Preprint]
  
  
• R. Scheichl, Parallel Solvers for the Transient Multigroup Neutron Diffusion Equations. International Journal for Numerical Methods in Engineering 47:1751-1771, 2000. [Abstract] [Preprint]
  
  
• R. Scheichl, 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.), 1999. [PostScript file]
  
  
• H. Finnemann and R. Scheichl, Efficiency Enhancements of Coupled RELAP5/PANBOX Calculations Using Adaptive Methods. Transactions of the American Nuclear Society for the Annual Meeting, Boston, June 1999. [WordDocument]

Books and Theses

• I.G. Graham, T.Y. Hou, O. Lakkis and R. Scheichl (Editors), Numerical Analysis of Multiscale Problems, to appear in Lecture Notes in Computational Science and Engineering, Vol. 83, Springer, Heidelberg, 2011.
  
  
• S.D. Buckeridge, Numerical Solution of Weather and Climate Systems. PhD Thesis, University of Bath, 2010. [PDF]
  
  
• R. Norton, Numerical Computation of Band Gaps in Photonic Crystal Fibres. PhD Thesis, University of Bath, 2008. [PDF]
  
  
• R. Scheichl, Iterative Solution of Saddle Point Problems Using Divergence-free Finite Elements with Applications to Groundwater Flow. PhD Thesis, University of Bath, 2000. [PostScript file (without large colour pictures)]
  
  
• R. Scheichl, 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, 1997. [PostScript file (without large colour picture)]

Extended Abstracts and Other Publications

• C. Pechstein and R. Scheichl, 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, 2010. [PDF] [Full Report]
  
  
• R. Scheichl, 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, 2009. [PDF] [Full Report]
  
  
• B. Aksoylu, I.G. Graham, H. Klie and R. Scheichl, 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, 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, Sensitivity of Markov chains for wireless protocols, Study Group Report, 56th European Study Group with Industry, Bath, 2006. [PDF]
  
  
• R. Scheichl, 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]

Last updated 07/11/2011