Amirreza Khodadadian

Amirreza Khodadadian, Benjamin Stadlbauer, Clemens Heitzinger

Nanowire field-effect sensors have recently been developed for label-free detection of biomolecules. In this work, we introduce a computational technique based on Bayesian estimation to determine the physical parameters of the sensor and, more importantly, the properties of the analyte molecules. To that end, we first propose a PDE based model to simulate the device charge transport and electrochemical behavior. Then, the adaptive Metropolis algorithm with delayed rejection (DRAM) is applied to estimate the posterior distribution of unknown parameters, namely molecule charge density, molecule density, doping concentration, and electron and hole mobilities. We determine the device and molecules properties simultaneously, and we also calculate the molecule density as the only parameter after having determined the device parameters. This approach makes it possible not only to determine unknown parameters, but it also shows how well each parameter can be determined by yielding the probability density function (pdf).

Mostafa Abbaszadeh, Amirreza Khodadadian, Mehdi Dehghan et al.

In this work, we develop a Legendre spectral element method (LSEM) for solving the stochastic nonlinear system of advection-reaction-diffusion models. The used basis functions are based on a class of Legendre functions such that their mass and diffuse matrices are tridiagonal and diagonal, respectively. The temporal variable is discretized by a Crank--Nicolson finite difference formulation. In the stochastic direction, we also employ a random variable $W$ based on the $Q-$Wiener process. We inspect the rate of convergence and the unconditional stability for the achieved semi-discrete formulation. Then, the Legendre spectral element technique is used to obtain a full-discrete scheme. The error estimation of the proposed numerical scheme is substantiated based upon the energy method. The numerical results confirm the theoretical analysis.

Vahid Mohammadi, Mehdi Dehghan, Amirreza Khodadadian et al.

In this work, we apply two meshless methods for the numerical solution of the time-dependent transport equation defined on the sphere in spherical coordinates. The first technique, which was introduced by Mirzaei (BIT Numerical Mathematics, 54 (4) 1041-1063, 2017) in Cartesian coordinates is a generalized moving least squares approximation, and the second one, which is developed here, is moving kriging least squares interpolation on the sphere. These methods do not depend on the background mesh or triangulation, and they can be implemented on the transport equation in spherical coordinates easily using different distribution points. Furthermore, the time variable is approximated by a second-order backward differential formula. The obtained fully discrete scheme is solved via the biconjugate gradient stabilized algorithm with zero-fill incomplete lower-upper (ILU) preconditioner at each time step. Three well-known test problems namely solid body rotation, vortex roll-up, and deformational flow are solved to demonstrate our developments.