TY - JOUR

T1 - An adaptive multilevel Monte Carlo algorithm for the stochastic drift–diffusion–Poisson system

AU - Khodadadian, Amirreza

AU - Parvizi, Maryam

AU - Heitzinger, Clemens

N1 - Funding Information: The first and the last authors acknowledge support by FWF (Austrian Science Fund) START project no. Y660 PDE Models for Nanotechnology. The second author also acknowledges support by FWF project no. P28367-N35 . The authors appreciate useful comments by Markus Melenk (TU Wien). The authors also acknowledge the helpful comments by three anonymous reviewers.

PY - 2020/8/15

Y1 - 2020/8/15

N2 - We present an adaptive multilevel Monte Carlo algorithm for solving the stochastic drift–diffusion–Poisson system with non-zero recombination rate. The a-posteriori error is estimated to enable goal-oriented adaptive mesh refinement for the spatial dimensions, while the a-priori error is estimated to guarantee linear convergence of the H1 error. In the adaptive mesh refinement, efficient estimation of the error indicator gives rise to better error control. For the stochastic dimensions, we use the multilevel Monte Carlo method to solve this system of stochastic partial differential equations. Finally, the advantage of the technique developed here compared to uniform mesh refinement is discussed using a realistic numerical example.

AB - We present an adaptive multilevel Monte Carlo algorithm for solving the stochastic drift–diffusion–Poisson system with non-zero recombination rate. The a-posteriori error is estimated to enable goal-oriented adaptive mesh refinement for the spatial dimensions, while the a-priori error is estimated to guarantee linear convergence of the H1 error. In the adaptive mesh refinement, efficient estimation of the error indicator gives rise to better error control. For the stochastic dimensions, we use the multilevel Monte Carlo method to solve this system of stochastic partial differential equations. Finally, the advantage of the technique developed here compared to uniform mesh refinement is discussed using a realistic numerical example.

KW - A-posteriori error estimation

KW - A-priori error estimation

KW - Adaptive mesh refinement

KW - Multilevel Monte Carlo

KW - Stochastic drift–diffusion–Poisson system

KW - Stochastic partial differential equation (SPDEs)

UR - http://www.scopus.com/inward/record.url?scp=85085841358&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1904.05851

DO - 10.48550/arXiv.1904.05851

M3 - Article

AN - SCOPUS:85085841358

VL - 368

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 113163

ER -