A. Khodadadian, L. Taghizadeh, C. Heitzinger:

"Optimal multilevel randomized quasi-Monte-Carlo method for the stochastic drift-diffusion-Poisson system";

Computer Methods in Applied Mechanics and Engineering,329(2018), 480 - 497.

In this paper, an optimal multilevel randomized quasi-Monte-Carlo method to solve the stationary stochastic drift-diffusion-Poisson system is developed. We calculate the optimal values of the parameters of the numerical method such as the mesh sizes of the spatial discretization and the numbers of quasi-points in order to minimize the overall computational cost for solving this system of stochastic partial differential equations. This system has a number of applications in various fields, wherever charged particles move in a random environment. It is shown that the computational cost of the optimal multilevel randomized quasi-Monte-Carlo method, which uses randomly shifted low-discrepancy sequences, is one order of magnitude smaller than that of the optimal multilevel Monte-Carlo method and five orders of magnitude smaller than that of the standard Monte-Carlo method. The method developed here is applied to a realistic transport problem, namely the calculation of random-dopant effects in nanoscale field-effect transistors.

Multilevel randomized quasi-Monte-Carlo, Multilevel Monte-Carlo, Randomized quasi-Monte-Carlo, Optimal numerical method, Stochastic partial differential equation, Field-effect transistor

http://dx.doi.org/10.1016/j.cma.2017.10.015

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