Random walk on spheres method for solving anisotropic transient diffusion problems and flux calculations

IF 0.8 Q3 STATISTICS & PROBABILITY Monte Carlo Methods and Applications Pub Date : 2023-11-15 DOI:10.1515/mcma-2023-2022
Irina Shalimova, Karl Sabelfeld
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Abstract

Abstract The Random Walk on Spheres (RWS) algorithm for solving anisotropic transient diffusion problems based on a stochastic learning procedure for calculation of the exit position of the anisotropic diffusion process on a sphere is developed. Direct generalization of the Random Walk on Spheres method to anisotropic diffusion equations is not possible, therefore, we have numerically calculated the probability density for the exit position on a sphere. The first passage time is then represented explicitly. The method can easily be implemented to solve diffusion problems with spatially varying diffusion coefficients for complicated three-dimensional domains. Particle tracking algorithm is highly efficient for calculation of fluxes to boundaries. We apply the developed algorithm for solving an exciton transport in a semiconductor material with a threading dislocation where the measured functions are the exciton fluxes to the semiconductor’s substrate and on the dislocation surface.
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球上随机游走法求解各向异性瞬态扩散问题及通量计算
提出了一种求解各向异性瞬态扩散问题的随机学习算法(RWS),该算法用于计算各向异性扩散过程在球体上的出口位置。将球上随机游走法直接推广到各向异性扩散方程是不可能的,因此,我们数值计算了球上出口位置的概率密度。然后显式地表示第一个通过时间。该方法可方便地求解复杂三维区域中具有空间变化扩散系数的扩散问题。粒子跟踪算法对于边界通量的计算具有很高的效率。我们将开发的算法应用于解决具有螺纹位错的半导体材料中的激子输运,其中测量的函数是半导体衬底和位错表面上的激子通量。
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来源期刊
Monte Carlo Methods and Applications
Monte Carlo Methods and Applications STATISTICS & PROBABILITY-
CiteScore
1.20
自引率
22.20%
发文量
31
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