Working group of Prof. Dr. G. Dziuk

An overview of the field of research, tools and methods

Members of the working group

Projects and fields of activity:

(By clicking the headings you arrive at the respective project pages)

Simulation and Optimization of the Liquid Phase Epitaxy for the Production of Infrared Detectors O. Kriessl, K.G. Siebert, A. Schmidt (ZeTeM, Universität Bremen), K.-M. Lin (KI Freiburg), P. Dold (KI Freiburg)

Numerical Simulation of Heat and Mass Transport during the Industrial Production of (Cd,Zn)Te by the Vertical Bridgman Method A. Schmidt (ZeTeM, Universität Bremen), K.G. Siebert

BMBF project, joint with working group of Prof. K.W. Benz, Kristallographisches Institut und Industriepartner AIM Halbleitersysteme, Heilbronn Temperature gradients, concentration and convection in the melt play an important role for the quality of (Cd,Zn)Te single crystals during industrial production. The simulation of the whole growth process is split into two steps: A simulation of the heat transport in the growth furnace (KI) and a simulation of the phase transition including the influence of the convection and changes of concentration in the growth ampoule (IAM). Aim of the project is an increase of the usable amount of single crystals during the industrial production. Former members: E. Bänsch (IAM, now WIAS), S. Boschert (KI), B. Höhn (IAM)

Numerik für 3D-Marangonikonvektion bei der Kristallzüchtung in Halbleiterschmelzen mit freier Oberfläche A. Schmidt (ZeTeM, Universität Bremen), E. Bänsch (WIAS), S. Boschert, T. Kaiser (KI Freiburg) Ehemalige Mitarbeiter: B. Höhn

DFG-Projekt, gemeinsam mit Arbeitsgruppe Prof. K.W. Benz, Kristallographisches Institut Simulation der Halbleiterschmelzzone beim Floating-Zone Verfahren zur Züchtung von Silizium-Kristallen: Temperaturverteilung und Strömung mit freier kapillarer Oberfläche.

Efficient simulation and numerical analysis of the dynamics of dendrites M. Fried, A. Schmidt (ZeTeM, Universität Bremen), A. Veeser (Università di Milano)

This project is part of the DFG-Schwerpunkt "Ergodentheorie, Analysis und effiziente Simulation dynamischer Systeme" During the solidification of an undercooled melt treelike patterns, so-called dendrites develop. Error estimates for Finite Element discretisations as well as a Finite Element algorithm based on a level set formulation for the evolution of the phase boundary are developed.

ALBERT: An Adaptive Finite Element Toolbox A. Schmidt (ZeTeM, Universität Bremen), K.G. Siebert

ALBERT is a program library for adaptive finite element discretizations of elliptic and parabolic problems in one, two, or three space dimensions. ALBERT is used worldwide in more than 20 institutes for teachings and research.

Numerical Analysis and Numerical Methods for Incompressible Viscous Flows J. Mehnert, K.G. Siebert

The Navier Stokes equations play a central role in the modelling of many processes in nature. They describe the flow of an incompressible and viscous fluid in a container, which is driven by an external force, e.g. We examine and implement methods for the numerical treatment of the incompressible Navier-Stokes equations. Former members: E. Bänsch (jetzt WIAS), B. Höhn

Numerical methods and error estimators for Stefan problems A. Schmidt (ZeTeM, Universität Bremen), Z. Chen, R.H. Nochetto, C. Verdi

Phase transitions (liquid-solid, e.g.) can be modelled by degenerate parabolic equations. The classical Stefan problem is one example. In our work group, we develope error estimators and adaptive finite element methods for such equations.

Simulation of two and three-dimensional dendrites M. Fried, A. Schmidt (ZeTeM, Universität Bremen), E. Bänsch (WIAS)

Dendritic growth is a nonlinear process, which falls into the category of self-organizing pattern formation phenomena. It is of great practical importance, since it appears frequently and, in case of alloys, affects the engineering properties of the resulting solid. Finite Element discretizations based on parametric as well as level set representations of the phase boundary are investigated.

Mean Curvature Flow: Numerical analysis and computation of viscosity solutions M. Fried, R. Rusu, A. Veeser (Università di Milano), K. Deckelnick (Sussex, U.K.) Former coworker: C. Brandes

Different formulations of the curvature driven motion of hypersurfaces are investigated. Convergence results for space discretizations and time discretizations as well as numerical algorithms to the (adaptive) computation of discrete solutions based on a regularized version of the underlying partial differential equation.

Numerik und Fehlerschätzer für Flächen vorgeschriebener mittlerer Krümmung W. Dörfler (Universität Kaisrslautern), K.G. Siebert, P. Tchakoutio

Plateau-Problem: Flächen minimalen Inhalts bei vorgegebener Randkurve, ...

Allgemeine Fehlerschätzer und Adaptive Finite Elemente Methoden A. Schmidt (ZeTeM, Universität Bremen), K.G. Siebert

Entwicklung von Fehlerschätzern und adaptiven Methoden für: nichtlineare Probleme mittels dualer Problme, 1D h-p FEM für lineare Probleme, Anisotrope Fehlerschätzer und Gitterverfeinerungen ...

Visualization of data on general grids (GRAPE Mesh Concept) A. Schmidt (ZeTeM, Universität Bremen), K.G. Siebert M. Ohlberger, M. Rumpf (Bonn)

Design of an interface for the visualization of general data from numerical simulation.