Journal of Computational Electronics

, Volume 15, Issue 4, pp 1393–1406 | Cite as

Basis adaptation for the stochastic nonlinear Poisson–Boltzmann equation

  • Amirreza Khodadadian
  • Clemens Heitzinger


A basis-adaptation method based on polynomial chaos expansion is used for the stochastic nonlinear Poisson–Boltzmann equation. The uncertainty in this numerical approach is motivated by the quantification of noise and fluctuations in nanoscale field-effect sensors. The method used here takes advantage of the properties of the nonlinear Poisson–Boltzmann equation and shows an exact and efficient approximation of the real solution. Numerical examples are motivated by the quantification of noise and fluctuations in nanowire field-effect sensors as a concrete example. Basis adaptation is validated by comparison with the full solution, and it is compared to optimized multi-level Monte-Carlo method, and the model equations are validated by comparison with experiments. Finally, various design parameters of the field-effect sensors are investigated in order to maximize the signal-to-noise ratio.


Poisson–Boltzmann equation Current Biological noise Polynomial chaos expansion Biosensor 



The authors acknowledge the support by FWF (Austrian Science Fund) START Project No. Y660 PDE Models for Nanotechnology. The authors also would like to appreciate Prof. Roger Ghanem (University of Southern California) for useful discussions about polynomial chaos expansion.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institute for Analysis and Scientific ComputingVienna University of Technology (TU Vienna)ViennaAustria
  2. 2.School of Mathematical and Statistical SciencesArizona State University (ASU)TempeUSA

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