Displaying similar documents to “Parareal operator splitting techniques for multi-scale reaction waves: Numerical analysis and strategies”

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

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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...

A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems

Hideki Murakawa (2009)

Kybernetika

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This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems....

Solution of contaminant transport with adsorption in porous media by the method of characteristics

Jozef Kacur, Roger Van Keer (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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A new approximation scheme is presented for the mathematical model of convection-diffusion and adsorption. The method is based on the relaxation method and the method of characteristics. We prove the convergence of the method and present some numerical experiments in 1D. The results can be applied to the model of contaminant transport in porous media with multi-site, equilibrium and non-equilibrium type of adsorption.

Fast optical tracking of diffusion in time-dependent environment of brain extracellular space

Hrabě, Jan

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An improved version of the Integrative Optical Imaging (IOI) method for diffusion measurements in a geometrically complex environment of the brain extracellular space has been developed. We present a theory for this Fast Optical Tracking Of Diffusion (FOTOD) which incorporates a time-dependent effective diffusion coefficient in homogeneous anisotropic media with time-dependent nonspecific linear clearance. FOTOD can be used to measure rapid changes in extracellular diffusion permeability...