Basis adaptation for the stochastic nonlinear Poisson–Boltzmann equation

Abstract

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.