Multilevel substructuring preconditioners for anisotropic diffusion problems on rectangular meshes

2012 ◽  
Vol 27 (6) ◽  
Author(s):  
Yu.A. Kuznetsov ◽  
A. Prokopenko ◽  
N. Yavich
Keyword(s):  
Anisotropic Diffusion ◽  
Diffusion Problems

scholarly journals Robust numerical schemes for anisotropic diffusion problems, a first step for turbulence modeling in Lagrangian hydrodynamics

2009 ◽  
Vol 28 ◽  
pp. 80-99
Author(s):  
Julien Dambrine ◽  
Philippe Hoch ◽  
Raphaël Kuate ◽  
Jérôme Lohéac ◽  
Jérôme Métral ◽  
...  
Keyword(s):  
Anisotropic Diffusion ◽  
Turbulence Modeling ◽  
Numerical Schemes ◽  
Lagrangian Hydrodynamics ◽  
Diffusion Problems

A random walk on small spheres method for solving transient anisotropic diffusion problems

2019 ◽  
Vol 25 (3) ◽  
pp. 271-282
Author(s):  
Irina Shalimova ◽  
Karl K. Sabelfeld
Keyword(s):  
Random Walk ◽  
Anisotropic Diffusion ◽  
First Passage Time ◽  
Three Dimensional ◽  
Passage Time ◽  
Exit Point ◽  
Stochastic Algorithm ◽  
Probability Densities ◽  
Spatially Varying ◽  
Diffusion Problems

Abstract A meshless stochastic algorithm for solving anisotropic transient diffusion problems based on an extension of the classical Random Walk on Spheres method is developed. Direct generalization of the Random Walk on Spheres method to anisotropic diffusion equations is not possible, therefore, we have derived approximations of the probability densities for the first passage time and the exit point on a small sphere. The method can be conveniently applied to solve diffusion problems with spatially varying diffusion coefficients and is simply implemented for complicated three-dimensional domains. Particle tracking algorithm is highly efficient for calculation of fluxes to boundaries. We present some simulation results in the case of cathodoluminescence and electron beam induced current in the vicinity of a dislocation in a semiconductor material.

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