Analysis, Modeling and Simulation of Multiscale Problems

Mielke, Alexander

doi:10.1007/3-540-35657-6

2006

DOI: 10.1007/3-540-35657-6

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Analysis, Modeling and Simulation of Multiscale Problems

Alexander Mielke¹

Abstract: The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

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Cited by 21 publications

References 98 publications

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A block Krylov subspace time‐exact solution method for linear ordinary differential equation systems

Botchev

2013

Numerical Linear Algebra App

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SUMMARYWe propose a time‐exact Krylov‐subspace‐based method for solving linear ordinary differential equation systems of the form y ′ = − Ay + g(t) and y ′ ′ = − Ay + g(t), where y(t) is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of the source term g(t), constructed with the help of the truncated singular value decomposition. The second stage is a special residual‐based block Krylov subspace method. The accuracy of the method is only restricted by the accuracy of the piecewise polynomial approximation and by the error of the block Krylov process. Because both errors can, in principle, be made arbitrarily small, this yields, at some costs, a time‐exact method. Numerical experiments are presented to demonstrate efficiency of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.

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A block Krylov subspace time‐exact solution method for linear ordinary differential equation systems

Botchev

2013

Numerical Linear Algebra App

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On dispersive stability of Hamiltonian systems on lattices

Patz¹

2007

Proc Appl Math and Mech

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We study the long-time dynamics of oscillations in lattices of infinitely many particles interacting via certain non-linear potentials. The aim is to proof dispersive stability of such Hamiltonian systems analogously to results known for PDEs. To do so we first recapitulate the dynamics of linear Hamiltonian systems on an infinite chain and give optimal decay rates based on the dispersion relation. Based on this we proof that if the non-linearity is weak enough, the non-linear system shows a similar behaviour like its linearization. *

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Derivation of a plate theory for incompressible materials

Conti

Dolzmann

2007

Comptes Rendus. Mathématique

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Analysis, Modeling and Simulation of Multiscale Problems

Abstract: The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Cited by 21 publications

References 98 publications

A block Krylov subspace time‐exact solution method for linear ordinary differential equation systems

A block Krylov subspace time‐exact solution method for linear ordinary differential equation systems

On dispersive stability of Hamiltonian systems on lattices

Derivation of a plate theory for incompressible materials

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