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Research Output 2002 2019

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Article
2019
2 Citations (Scopus)
18 Downloads (Pure)
Open Access
File
Tensors
Maximum entropy methods
Probability density function
Mathematical operators
Decomposition

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

Open Access
Tensor Decomposition
Multivariate Distribution
Rejection
Probability Distribution
Tensor
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
File

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

High-performance dune modules for solving large-scale, strongly anisotropic elliptic problems with applications to aerospace composites

Butler, R., Dodwell, T., Reinarz, A., Sandhu, A., Scheichl, R. & Seelinger, L., 25 Oct 2019, In : Computer Physics Communications. 106997.

Research output: Contribution to journalArticle

Open Access
1 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 journalArticle

Open Access
2018
6 Citations (Scopus)
21 Downloads (Pure)

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 journalArticle

Open Access
File
Random Field
Regular hexahedron
Positive Definiteness
Circulant Matrix
Correlation Length
2 Citations (Scopus)

Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients

Graham, I., Kuo, F. Y., Nuyens, D., Scheichl, R. & Sloan, I. H., 1 Oct 2018, In : Numerische Mathematik. 140, 2, p. 479-511 33 p.

Research output: Contribution to journalArticle

Open Access
Quasi-Monte Carlo
Elliptic PDE
Monte Carlo methods
Random Field
Sampling
3 Citations (Scopus)

Dune-composites – A new framework for high-performance finite element modelling of laminates

Reinarz, A., Dodwell, T., Fletcher, T., Seelinger, L., Butler, R. & Scheichl, R., 15 Jan 2018, In : Composite Structures. 184, p. 269-278 10 p.

Research output: Contribution to journalArticle

Open Access
Laminates
Composite materials
Aircraft models
Innovation
Finite element method
3 Citations (Scopus)
20 Downloads (Pure)

Multilevel Monte Carlo and Improved Timestepping Methods in Atmospheric Dispersion Modelling

Katsiolides, G., Müller, E. H., Scheichl, R., Shardlow, T., Giles, M. B. & Thomson, D. J., 1 Feb 2018, In : Journal of Computational Physics. 354, p. 320-343 24 p.

Research output: Contribution to journalArticle

Open Access
File
Numerical methods
Ashes
Monte Carlo method
Differential equations
Monte Carlo methods
2017

Quasi-Monte Carlo and Multilevel Monte Carlo Methods for Computing Posterior Expectations in Elliptic Inverse Problems

Scheichl, R., Stuart, A. M. & Teckentrup, A. L., 31 Dec 2017, In : SIAM/ASA Journal on Uncertainty Quantification. 5, 1, p. 493-518 26 p.

Research output: Contribution to journalArticle

Open Access
File
Quasi-Monte Carlo
Multilevel Methods
Elliptic Problems
Monte Carlo method
Ratio Estimator
25 Downloads (Pure)

Scheduling Massively Parallel Multigrid for Multilevel Monte Carlo Methods

Drzisga, D., Gmeiner, B., Rüde, U., Scheichl, R. & Wohlmuth, B., 26 Oct 2017, In : SIAM Journal on Scientific Computing. 39, 5, p. S873-S897

Research output: Contribution to journalArticle

Open Access
File
Multilevel Methods
Monte Carlo method
Monte Carlo methods
Scheduling
Uncertainty Quantification
2016
1 Citation (Scopus)
25 Downloads (Pure)

An euler-poisson scheme for Lévy driven SDEs

Ferreiro-Castilla, A., Kyprianou, A. & Scheichl, R., Mar 2016, In : Journal of Applied Probability. 53, 1, p. 262-278

Research output: Contribution to journalArticle

Open Access
File
3 Citations (Scopus)
104 Downloads (Pure)
Open Access
File
Flow simulation
Flow Simulation
Aspect Ratio
Preconditioner
Aspect ratio
12 Citations (Scopus)
61 Downloads (Pure)
Open Access
File
Multilevel Methods
Mixed Finite Elements
Monte Carlo method
Finite Element Discretization
Error Bounds
13 Citations (Scopus)
144 Downloads (Pure)

Resin treatment of free edges to aid certification of through thickness laminate strength

Fletcher, T. A., Kim, T., Dodwell, T. J., Butler, R., Scheichl, R. & Newley, R., 20 Jun 2016, In : Composite Structures. 146, p. 26-33 8 p.

Research output: Contribution to journalArticle

Open Access
File
9 Citations (Scopus)
103 Downloads (Pure)

Robust numerical upscaling of elliptic multiscale problems at high contrast

Peterseim, D. & Scheichl, R., 1 Oct 2016, In : Computational Methods in Applied Mathematics. 16, 4, p. 579-603 25 p.

Research output: Contribution to journalArticle

Open Access
File
Multiscale Problems
Upscaling
Quasi-interpolation
Elliptic Problems
Mathematical operators
2015
36 Citations (Scopus)
115 Downloads (Pure)

A hierarchical multilevel Markov chain Monte Carlo algorithm with applications to uncertainty quantification in subsurface flow

Dodwell, T., Ketelsen, C., Scheichl, R. & Teckentrup, A. L., 31 Dec 2015, In : SIAM/ASA Journal on Uncertainty Quantification. 3, 1, p. 1075-1108 34 p.

Research output: Contribution to journalArticle

Open Access
File
Markov processes
Costs
Porous materials
Monte Carlo methods
Uncertainty
2 Citations (Scopus)
110 Downloads (Pure)
Open Access
File
Langevin Equation
Stochastic Equations
Differential equation
Discrete random variable
Strong Approximation
6 Citations (Scopus)

Optimized Schwarz and 2-Lagrange multiplier methods for multiscale elliptic PDEs

Loisel, S., Nguyen, H. & Scheichl, R., 2015, In : SIAM Journal on Scientific Computing. 37, 6, p. A2896-A2923

Research output: Contribution to journalArticle

Lagrange multiplier Method
Elliptic PDE
Lagrange multipliers
Preconditioner
Dirichlet-to-Neumann Map
7 Citations (Scopus)
110 Downloads (Pure)

Petascale solvers for anisotropic PDEs in atmospheric modelling on GPU clusters

Mueller, E., Scheichl, R. & Vainikko, E., 1 Dec 2015, In : Parallel Computing. 50, p. 53-69 20 p.

Research output: Contribution to journalArticle

Open Access
File
Data storage equipment
Modeling
Unknown
Fast Solvers
Iterative Solvers
39 Citations (Scopus)

Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients

Graham, I. G., Kuo, F. Y., Nichols, J. A., Scheichl, R., Schwab, C. & Sloan, I. H., Oct 2015, In : Numerische Mathematik. 131, 2, p. 329-368 40 p.

Research output: Contribution to journalArticle

Quasi-Monte Carlo Methods
Elliptic PDE
Random Coefficients
Finite Element Method
Finite element method

Regularity for Maxwell eigenproblems in photonic crystal fibre modelling

Dauge, M., Norton, R. A. & Scheichl, R., Mar 2015, In : BIT Numerical Mathematics. 55, 1, p. 59-80 22 p.

Research output: Contribution to journalArticle

Eigenproblem
Photonic crystal fibers
Photonic Crystal
Regularity
Fiber
2014
64 Citations (Scopus)

Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps

Spillane, N., Dolean, V., Hauret, P., Nataf, F., Pechstein, C. & Scheichl, R., Apr 2014, In : Numerische Mathematik. 126, 4, p. 741-770 30 p.

Research output: Contribution to journalArticle

Generalized Eigenproblem
Systems of Partial Differential Equations
Partial differential equations
Overlap
Partial differential equation
27 Citations (Scopus)
78 Downloads (Pure)
File
climate prediction
weather
fluid dynamics
anisotropy
spatial resolution
12 Citations (Scopus)
99 Downloads (Pure)

Multilevel Monte Carlo simulation for Lévy processes based on the Wiener–Hopf factorisation

Ferreiro-Castilla, A., Kyprianou, A. E., Scheichl, R. & Suryanarayana, G., Feb 2014, In : Stochastic Processes and their Applications. 124, 2, p. 985-1010 26 p.

Research output: Contribution to journalArticle

Open Access
File
Wiener-Hopf Factorization
Lévy Process
Factorization
Monte Carlo Simulation
Optimal Rate of Convergence
2013
75 Citations (Scopus)

Finite element error analysis of elliptic PDEs with random coefficients and its application to multilevel Monte Carlo methods

Charrier, J., Scheichl, R. & Teckentrup, A. L., 2013, In : SIAM Journal on Numerical Analysis (SINUM). 51, 1, p. 322-352 31 p.

Research output: Contribution to journalArticle

Multilevel Methods
Elliptic PDE
Random Parameters
Random Coefficients
Coercivity
71 Citations (Scopus)

Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients

Teckentrup, A. L., Scheichl, R., Giles, M. B. & Ullmann, E., Nov 2013, In : Numerische Mathematik. 125, 3, p. 569-600 32 p.

Research output: Contribution to journalArticle

Multilevel Methods
Elliptic PDE
Random Coefficients
Monte Carlo method
Monte Carlo methods
11 Citations (Scopus)
114 Downloads (Pure)

Matrix-free GPU implementation of a preconditioned conjugate gradient solver for anisotropic elliptic PDEs

Mueller, E., Guo, X., Scheichl, R. & Shi, S., Apr 2013, In : Computing and Visualization in Science. 16, 2, p. 41-58 18 p.

Research output: Contribution to journalArticle

Open Access
File
Preconditioned Conjugate Gradient
Elliptic Partial Differential Equations
Graphics Processing Unit
Partial differential equations
Numerical Weather Prediction
11 Citations (Scopus)
110 Downloads (Pure)

Planewave expansion methods for photonic crystal fibres

Norton, R. A. & Scheichl, R., Jan 2013, In : Applied Numerical Mathematics. 63, p. 88-104 17 p.

Research output: Contribution to journalArticle

Open Access
File
Photonic crystal fibers
Photonic Crystal
Plane Wave
Fiber
Discontinuous Coefficients
21 Citations (Scopus)

Weighted Poincaré inequalities

Pechstein, C. & Scheichl, R., 2013, In : IMA Journal of Numerical Analysis. 33, 2, p. 652-686 35 p.

Research output: Contribution to journalArticle

Weighted Inequalities
Poincaré Inequality
Poincaré
Decomposition
Coefficient
2012
32 Citations (Scopus)

Algebraic multigrid for discontinuous Galerkin discretizations of heterogeneous elliptic problems

Bastian, P., Blatt, M. & Scheichl, R., Mar 2012, In : Numerical Linear Algebra with Applications. 19, 2, p. 367-388 22 p.

Research output: Contribution to journalArticle

Algebraic multigrid
Discontinuous Galerkin
Elliptic Problems
Linear systems
Discretization
41 Citations (Scopus)

Analysis of a two-level Schwarz method with coarse spaces based on local Dirichlet-to-Neumann maps

Dolean, V., Nataf, F., Spillane, N. & Scheichl, R., Oct 2012, In : Computational Methods in Applied Mathematics. 12, 4, p. 391-414 24 p.

Research output: Contribution to journalArticle

Two-level Method
Schwarz Methods
Dirichlet-to-Neumann Map
Domain decomposition methods
Coefficient
18 Citations (Scopus)
95 Downloads (Pure)

Multilevel methods for elliptic problems with highly varying coefficients on nonaligned coarse grids

Scheichl, R., Vassilevski, P. S. & Zikatanov, L. T., 2012, In : SIAM Journal on Numerical Analysis (SINUM). 50, 3, p. 1675-1694 20 p.

Research output: Contribution to journalArticle

Open Access
File
Multilevel Methods
Varying Coefficients
Elliptic Problems
Boundary value problems
Grid
2011
36 Citations (Scopus)
98 Downloads (Pure)

Analysis of FETI methods for multiscale PDEs. Part II: interface variation

Pechstein, C. & Scheichl, R., 1 Jul 2011, In : Numerische Mathematik. 118, 3, p. 485-529 45 p.

Research output: Contribution to journalArticle

Open Access
File
Contrast media
Finite Element
Coefficient
Condition number
Jump
2 Citations (Scopus)

A robust numerical method for the potential vorticity based control variable transform in variational data assimilation

Buckeridge, S., Cullen, M. J. P., Scheichl, R. & Wlasak, M., Apr 2011, In : Quarterly Journal of the Royal Meteorological Society. 137, 657, p. 1083-1094 12 p.

Research output: Contribution to journalArticle

potential vorticity
data assimilation
numerical method
transform
tolerance
25 Citations (Scopus)

A robust two-level domain decomposition preconditioner for systems of PDEs

Spillane, N., Dolean, V., Hauret, P., Nataf, F., Pechstein, C. & Scheichl, R., Dec 2011, In : Comptes Rendus Mathematique. 349, 23-24, p. 1255-1259 5 p.

Research output: Contribution to journalArticle

Domain Decomposition
Preconditioner
Generalized Eigenvalue Problem
Elasticity Problem
Domain Decomposition Method
205 Citations (Scopus)

Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients

Cliffe, K. A., Giles, M. B., Scheichl, R. & Teckentrup, A. L., 1 Jan 2011, In : Computing and Visualization in Science. 14, 3, p. 3-15 13 p.

Research output: Contribution to journalArticle

Multilevel Methods
Elliptic PDE
Groundwater flow
Random Coefficients
Monte Carlo method
76 Citations (Scopus)
106 Downloads (Pure)

Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications

Graham, I. G., Kuo, F. Y., Nuyens, D., Scheichl, R. & Sloan, I. H., 10 May 2011, In : Journal of Computational Physics. 230, 10, p. 3668-3694 27 p.

Research output: Contribution to journalArticle

Open Access
File
pulse detonation engines
Monte Carlo method
Monte Carlo methods
coefficients
functionals
15 Citations (Scopus)

Weak approximation properties of elliptic projections with functional constraints

Scheichl, R., Vassilevski, P. S. & Zikatanov, L. T., 2011, In : Multiscale Modeling and Simulation. 9, 4, p. 1677-1699 23 p.

Research output: Contribution to journalArticle

Weak Approximation
Approximation Property
projection
Projection
pulse detonation engines
2010
8 Citations (Scopus)
106 Downloads (Pure)
File
Periodic Potential
Convergence Analysis
Plane Wave
Optical devices
Operator
12 Citations (Scopus)

Parallel geometric multigrid for global weather prediction

Buckeridge, S. & Scheichl, R., 1 Apr 2010, In : Numerical Linear Algebra with Applications. 17, 2-3, p. 325-342 18 p.

Research output: Contribution to journalArticle

Coarsening
Weather
Anisotropy
Algebraic multigrid
Grid
2009
26 Citations (Scopus)

Energy-minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs

Van Lent, J., Scheichl, R. & Graham, I. G., Oct 2009, In : Numerical Linear Algebra with Applications. 16, 10, p. 775-799 25 p.

Research output: Contribution to journalArticle

Two-level Method
Schwarz Methods
Energy
Preconditioner
Overlapping
17 Citations (Scopus)

Scaling up through domain decomposition

Pechstein, C. & Scheichl, R., Oct 2009, In : Applicable Analysis. 88, 10-11, p. 1589-1608 20 p.

Research output: Contribution to journalArticle

Domain Decomposition
Computational complexity
Scaling
Decomposition
Domain decomposition methods
2008
47 Citations (Scopus)

Analysis of FETI methods for multiscale PDEs

Pechstein, C. & Scheichl, R., 1 Dec 2008, In : Numerische Mathematik. 111, 2, p. 293-333 41 p.

Research output: Contribution to journalArticle

2007
29 Citations (Scopus)

Additive Schwarz with aggregation-based coarsening for elliptic problems with highly variable coefficients

Scheichl, R. & Vainikko, E., May 2007, In : Computing. p. 1--24 24 p.

Research output: Contribution to journalArticle

98 Citations (Scopus)

Domain decomposition for multiscale PDEs

Graham, I. G., Lechner, P. O. & Scheichl, R., Jun 2007, In : Numerische Mathematik. 106, 4, p. 589-626 38 p.

Research output: Contribution to journalArticle

Coarsening
Domain Decomposition
Preconditioner
Decomposition
Porous materials
32 Citations (Scopus)

Robust domain decomposition algorithms for multiscale PDEs

Graham, I. G. & Scheichl, R., 2007, In : Numerical Methods for Partial Differential Equations. 23, 4, p. 859-878 20 p.

Research output: Contribution to journalArticle

Decomposition Algorithm
Coarsening
Domain Decomposition
Decomposition
Groundwater flow
2005
23 Citations (Scopus)

Permeation of gases in polymers: parameter identification and nonlinear regression analysis

Scheichl, R., Klopffer, M. H., Benjelloun Dabaghi, Z. & Flaconneche, B., Jun 2005, In : Journal of Membrane Science. 254, p. 275--293 19 p.

Research output: Contribution to journalArticle