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A mesh free floating random walk method for solving diffusion imaging problems. (English) Zbl 1354.65015

Summary: 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.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
60G50 Sums of independent random variables; random walks
60J60 Diffusion processes
78A35 Motion of charged particles
78M31 Monte Carlo methods applied to problems in optics and electromagnetic theory
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References:

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