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- Ivan G. Graham, P. O. Lechner, Robert Scheichl
- Numerische Mathematik
- 2007

We consider additive Schwarz domain decomposition preconditioners for piecewise linear finite element approximations of elliptic PDEs with highly variable coefficients. In contrast to standard analyses, we do not assume that the coefficients can be resolved by a coarse mesh. This situation arises often in practice, for example in the computation of flows in… (More)

- Nicole Spillane, Victorita Dolean, Patrice Hauret, Frédéric Nataf, Clemens Pechstein, Robert Scheichl
- Numerische Mathematik
- 2014

Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. Here, we introduce in a varia-tional setting a… (More)

In this paper we present a new preconditioner suitable for solving linear systems arising from finite element approximations of elliptic PDEs with high-contrast coefficients. The construction of the preconditioner consists of two phases. The first phase is an algebraic one which partitions the degrees of freedom into " high " and " low " permeability… (More)

- K. A. Cliffe, Michael B. Giles, Robert Scheichl, Aretha L. Teckentrup
- Computat. and Visualiz. in Science
- 2011

We consider the numerical solution of elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification for groundwater flow. We describe a novel variance reduction technique for the standard Monte Carlo method, called the multilevel Monte Carlo method. The main result is that in certain… (More)

- Julia Charrier, Robert Scheichl, Aretha L. Teckentrup
- SIAM J. Numerical Analysis
- 2013

We consider a finite element approximation of elliptic partial differential equations with random coefficients. Such equations arise, for example, in uncertainty quantification in subsurface flow modelling. Models for random coefficients frequently used in these applications, such as log-normal random fields with exponential covariance, have only very… (More)

- Victorita Dolean, Frédéric Nataf, Robert Scheichl, Nicole Spillane
- Comput. Meth. in Appl. Math.
- 2012

Coarse grid correction is a key ingredient in order to have scalable domain decomposition methods. For smooth problems, the theory and practice of such two-level methods is well established, but this is not the case for problems with complicated variation and high contrasts in the coefficients. Stable coarse spaces for high contrast problems are also… (More)

- Robert Scheichl, Panayot S. Vassilevski, Ludmil Zikatanov
- SIAM J. Numerical Analysis
- 2012

nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process,… (More)

- Eike Hermann Müller, Robert Scheichl
- ArXiv
- 2013

The demand for substantial increases in the spatial resolution of global weather-and climate-prediction models makes it necessary to use numerically efficient and highly scalable algorithms to solve the equations of large scale atmospheric fluid dynamics. For stability and efficiency reasons several of the operational forecasting centres, in particular the… (More)

- Richard Norton, Robert Scheichl
- SIAM J. Numerical Analysis
- 2010

In this paper we consider the problem of computing the spectrum of a Schrödinger operator with discontinuous, periodic potential in two dimensions using Fourier (or planewave expansion) methods. Problems of this kind are currently of great interest in the design of new optical devices to determine band gaps and to compute localised modes in photonic crystal… (More)

- I. G. Graham, R. Scheichl
- 2006

In this paper we describe a new class of domain deomposition preconditioners suitable for solving elliptic PDEs in highly fractured or heterogeneous media, such as arise in groundwater flow or oil recovery applications. Our methods employ novel coarsening operators which are adapted to the heterogeneity of the media. In contrast to standard methods (based… (More)