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A mesh free floating random walk method for solving diffusion imaging problems

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  • Sabelfeld, Karl K.

Abstract

We suggest a new mesh free random walk method for solving boundary value problems in semi-infinite domains with mixed boundary conditions. The method is based on a probabilistic interpretation of the diffusion processes. Our simulations show that the suggested algorithm is extremely efficient for solving diffusion imaging problems, in particular, for calculating the defect contrast in cathodoluminescence (CL) and electron beam-induced current (EBIC) techniques. The method avoids to simulate the long diffusion trajectories. Instead, it exploits exact probability distributions of the first passage and survival probabilities.

Suggested Citation

  • Sabelfeld, Karl K., 2017. "A mesh free floating random walk method for solving diffusion imaging problems," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 6-11.
    • Handle: RePEc:eee:stapro:v:121:y:2017:i:c:p:6-11
    DOI: 10.1016/j.spl.2016.10.006
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    Cited by:

    1. Karl K. Sabelfeld & Anastasia E. Kireeva, 2022. "Stochastic Simulation Algorithms for Solving Transient Anisotropic Diffusion-recombination Equations and Application to Cathodoluminescence Imaging," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3029-3048, December.
    2. Sabelfeld, Karl K. & Kireeva, Anastasya, 2020. "Stochastic simulation algorithms for solving a nonlinear system of drift–diffusion-Poisson equations of semiconductors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    3. Sabelfeld Karl K., 2016. "Random walk on spheres method for solving drift-diffusion problems," Monte Carlo Methods and Applications, De Gruyter, vol. 22(4), pages 265-275, December.

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