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Fast multigrid solver

Petr Vaněk (1995)

Applications of Mathematics

In this paper a black-box solver based on combining the unknowns aggregation with smoothing is suggested. Convergence is improved by overcorrection. Numerical experiments demonstrate the efficiency.

FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity

Axel Klawonn, Patrizio Neff, Oliver Rheinbach, Stefanie Vanis (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor εP := sym (P-1∇u) is redefined to include a matrix valued inhomogeneity P(x) which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field P induces a structural change of the elasticity equations. For such a model the FETI-DP method is...

FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity

Axel Klawonn, Patrizio Neff, Oliver Rheinbach, Stefanie Vanis (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor εP := sym (P-1∇u) is redefined to include a matrix valued inhomogeneity P(x) which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field P induces a structural change of the elasticity equations. For such a model the FETI-DP method is...

Finite element methods on non-conforming grids by penalizing the matching constraint

Eric Boillat (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.

Finite element methods on non-conforming grids by penalizing the matching constraint

Eric Boillat (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.

Frequency analysis of preconditioned waveform relaxation iterations

Andrzej Augustynowicz, Zdzisław Jackiewicz (1999)

Applicationes Mathematicae

The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting...

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