Leila Taghizadeh

TU Wien | TU Wien

Optimal design of electronic devices such as sensors is essential since it results in more accurate output at the shortest possible time. In this work, we develop optimal Bayesian inversion for electrical impedance tomography (EIT) technology in order to improve the quality of medical images generated by EIT and to put this promising imaging techno...

Mathematical modeling of epidemiological diseases using differential equations are of great importance in order to recognize the characteristics of the diseases and their outbreak. The procedure of modeling consists of two essential components: the first component is to solve the mathematical model numerically, the so-called forward modeling. The s...

The main goal of this paper is to develop the forward and inverse modeling of the Coronavirus (COVID-19) pandemic using novel computational methodologies in order to accurately estimate and predict the pandemic. This leads to governmental decisions support in implementing effective protective measures and prevention of new outbreaks. To this end, w...

We develop an electrical-impedance tomography (EIT) inverse model problem in an infinite-dimensional setting by introducing a nonlinear elliptic PDE as a new EIT forward model. The new model completes the standard linear model by taking the transport of ionic charge into account, which was ignored in the standard equation. We propose Bayesian inver...

We propose a mathematical model based on a system of partial differential equations (PDEs) for biofilms. This model describes the time evolution of growth and degradation of biofilms which depend on environmental factors. The proposed model also includes quorum sensing (QS) and describes the cooperation among bacteria when they need to resist again...

We investigate possible connections between two different implementations of the Poisson-Nernst-Planck (PNP) anomalous models used to analyze the electrical response of electrolytic cells. One of them is built in the framework of the fractional calculus, and considers integro-differential boundary conditions also formulated by using fractional deri...

Massively parallel nanosensor arrays fabricated with low-cost CMOS technology represent powerful platforms for biosensing in the Internet-of-Things (IoT) and Internet-of-Health (IoH) era. They can efficiently acquire “big data” sets of dependable calibrated measurements, representing a solid basis for statistical analysis and parameter estimation....

We consider the fully adaptive space–time discretization of a class of nonlinear heat equations by Rothe’s method. Space discretization is based on adaptive polynomial collocation which relies on equidistribution of the defect of the numerical solution, and the time propagation is realized by an adaptive backward Euler scheme. From the known scalin...

https://www.siam.org/meetings/uq18/uq18_abstracts.pdf

https://www.siam.org/meetings/uq18/uq18_abstracts.pdf

The three-dimensional stochastic drift–diffusion–Poisson system is used to model charge transport through nanoscale devices in a random environment. Applications include nanoscale transistors and sensors such as nanowire field-effect bio- and gas sensors. Variations between the devices and uncertainty in the response of the devices arise from the r...

In this paper, an optimal multilevel randomized quasi-Monte-Carlo method to solve the stationary stochastic drift–diffusion-Poisson system is developed. We calculate the optimal values of the parameters of the numerical method such as the mesh sizes of the spatial discretization and the numbers of quasi-points in order to minimize the overall compu...

The basic analytical properties of the drift-diffusion-Poisson-Boltzmann system in the alternating-current (AC) regime are shown. The analysis of the AC case differs from the direct-current (DC) case and is based on extending the transport model to the frequency domain and writing the variables as periodic functions of the frequency in a small-sign...

Existence and local-uniqueness theorems for weak solutions of a system consisting of the drift-diffusion-Poisson equations and the Poisson-Boltzmann equation, all with stochastic coefficients, are presented. For the numerical approximation of the expected value of the solution of the system, we develop a multi-level Monte-Carlo (MLMC) finite-elemen...