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 |
Keywords:
Green’s function; survival probability; random walk; cathodoluminescence; EBIC imaging; mesh free method; boundary value problems; semi-infinite domains; diffusion processes; algorithm; electron beam-induced current techniquesReferences:
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