Narrow Results

The design problem for semiconductor devices is studied via an optimal control approach for the standard drift–diffusion model. The solvability of the minimization problem is proved. The first-order optimality system is derived and the existence of Lagrange-multipliers is established. Further, estimates on the sensitivities are given. Numerical results concerning a symmetric n–p-diode are presented.

In this paper an optimal control problem for polymer crystallization is investigated. The crystallization is described by a non-isothermal Avrami–Kolmogorov model and the temperature at the boundary of the domain serves as control variable. The cost functional takes into account the spatial variation of the crystallinity and the final degree of crystallization. This results in a boundary control problem for a parabolic equation coupled with two ordinary differential equations, which is treated by an adjoint variable approach. We prove the existence and uniqueness of solutions to the state system as well as the existence of a minimizer for the cost functional under consideration. The adjoint system is derived and we use a steepest descent algorithm to solve the problem numerically. Numerical simulations illustrate the applicability and performance of the optimization algorithm.

We consider optimal design problems for semiconductor devices which are simulated using the energy transport model. We develop a descent algorithm based on the adjoint calculus and present numerical results for a ballistic diode. Furthermore, we compare the optimal doping profile with results computed based on the drift diffusion model. Finally, we exploit the model hierarchy and test the space mapping approach, especially the aggressive space mapping algorithm, for the design problem. This yields a significant reduction of numerical costs and programming effort.

In this work, we extend the one-dimensional Keller–Segel model for chemotaxis to general network topologies. We define appropriate coupling conditions ensuring the conservation of mass and show the existence and uniqueness of the solution. For our computational studies, we use a positive preserving first-order scheme satisfying a network CFL condition. Finally, we numerically validate the Keller–Segel network model and present results regarding special network geometries.

We present a numerical method to calculate resonances of Schottky surfaces based on Selberg theory, transfer operator techniques and Lagrange–Chebyshev approximation. This method is an alternative to the method based on periodic orbit expansion used previously in this context.

VisIVO is a package for supporting the visualization and analysis of astrophysical multidimensional data and has several built-in tools which allow the user an efficient manipulation and analysis of data. We are integrating VisIVO with VO services: connection to VO web services, retrieval and dealing with data in the VOTable format, interoperation with other VO compliant tools.