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Parareal operator splitting techniques for multi-scale reaction waves: Numerical analysis and strategies

Max Duarte, Marc Massot, Stéphane Descombes (2011)

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

In this paper, we investigate the coupling between operator splitting techniques and a time parallelization scheme, the parareal algorithm, as a numerical strategy for the simulation of reaction-diffusion equations modelling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive...

Parareal operator splitting techniques for multi-scale reaction waves: Numerical analysis and strategies

Max Duarte, Marc Massot, Stéphane Descombes (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we investigate the coupling between operator splitting techniques and a time parallelization scheme, the parareal algorithm, as a numerical strategy for the simulation of reaction-diffusion equations modelling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive...

Penrose transform and monogenic sections

Tomáš Salač (2012)

Archivum Mathematicum

The Penrose transform gives an isomorphism between the kernel of the 2 -Dirac operator over an affine subset and the third sheaf cohomology group on the twistor space. In the paper we give an integral formula which realizes the isomorphism and decompose the kernel as a module of the Levi factor of the parabolic subgroup. This gives a new insight into the structure of the kernel of the operator.

Perona-Malik equation: properties of explicit finite volume scheme

Angela Handlovičová (2007)

Kybernetika

The Perona–Malik nonlinear parabolic problem, which is widely used in image processing, is investigated in this paper from the numerical point of view. An explicit finite volume numerical scheme for this problem is presented and consistency property is proved.

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