Displaying similar documents to “Nonlinear Tensor Diffusion in Image Processing”

An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems

Molati, Motlatsi, Murakawa, Hideki

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This paper deals with nonlinear diffusion problems which include the Stefan problem, the porous medium equation and cross-diffusion systems. We provide a linear scheme for these nonlinear diffusion problems. The proposed numerical scheme has many advantages. Namely, the implementation is very easy and the ensuing linear algebraic systems are symmetric, which show low computational cost. Moreover, this scheme has the accuracy comparable to that of the wellstudied nonlinear schemes and...

Implementation of the MR tractography visualization kit based on the anisotropic Allen-Cahn equation

Pavel Strachota (2009)

Kybernetika

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Magnetic Resonance Diffusion Tensor Imaging (MR–DTI) is a noninvasive in vivo method capable of examining the structure of human brain, providing information about the position and orientation of the neural tracts. After a short introduction to the principles of MR–DTI, this paper describes the steps of the proposed neural tract visualization technique based on the DTI data. The cornerstone of the algorithm is a texture diffusion procedure modeled mathematically by the problem for the...

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...

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

Similarity:

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...

A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations

Gabriel R. Barrenechea, Volker John, Petr Knobloch (2013)

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

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An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steady-state and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates...