TY - JOUR
T1 - MULTISCALE MODELING OF FLUCTUATIONS IN STOCHASTIC ELLIPTIC PDE MODELS OF NANOSENSORS
AU - Heitzinger, Clemens
AU - Ringhofer, Christian
N1 - KAUST Repository Item: Exported on 2021-09-21
Acknowledged KAUST grant number(s): KUK-I1007-43
Acknowledgements: This work was supported by the FWF (Austrian Science Fund) project No. P20871-N13 and by the WWTF (Viennese Science and Technology Fund) project No. MA09-028. This publication is based on work supported by Award No. KUK-I1007-43, funded by the King Abdullah University of Science and Technology (KAUST). This work was supported by the NSF under grants DMS-0604986 and DMS-0757309.
PY - 2014
Y1 - 2014
N2 - In this work, the multiscale problem of modeling fluctuations in boundary layers in stochastic elliptic partial differential equations is solved by homogenization. A homogenized equation for the covariance of the solution of stochastic elliptic PDEs is derived. In addition to the homogenized equation, a rate for the covariance and variance as the cell size tends to zero is given. For the homogenized problem, an existence and uniqueness result and further properties are shown. The multiscale problem stems from the modeling of the electrostatics in nanoscale field-effect sensors, where the fluctuations arise from random charge concentrations in the cells of a boundary layer. Finally, numerical results and a numerical verification are presented. © 2014 International Press.
AB - In this work, the multiscale problem of modeling fluctuations in boundary layers in stochastic elliptic partial differential equations is solved by homogenization. A homogenized equation for the covariance of the solution of stochastic elliptic PDEs is derived. In addition to the homogenized equation, a rate for the covariance and variance as the cell size tends to zero is given. For the homogenized problem, an existence and uniqueness result and further properties are shown. The multiscale problem stems from the modeling of the electrostatics in nanoscale field-effect sensors, where the fluctuations arise from random charge concentrations in the cells of a boundary layer. Finally, numerical results and a numerical verification are presented. © 2014 International Press.
UR - http://hdl.handle.net/10754/671356
UR - http://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0012/0003/a001/
UR - http://www.scopus.com/inward/record.url?scp=84891374906&partnerID=8YFLogxK
U2 - 10.4310/cms.2014.v12.n3.a1
DO - 10.4310/cms.2014.v12.n3.a1
M3 - Article
SN - 1539-6746
VL - 12
SP - 401
EP - 421
JO - COMMUNICATIONS IN MATHEMATICAL SCIENCES
JF - COMMUNICATIONS IN MATHEMATICAL SCIENCES
IS - 3
ER -