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Über dieses Buch

Efficient transfer between science and society is crucial for their future development. The rapid progress of information technology and computer systems offers a large potential and new perspectives for solving complex problems. Mathematical modelling and simulation have become important tools not only in scientific investigations but also in analysing, planning and controlling technological and economic processes. Mathematics, imbedded in an interdisciplinary concept, has become a key technology.

The book covers the results of a variety of major projects in industrial mathematics following an initiative of the German Federal Ministry of Education and Research. All projects are collaborations of industrial companies and university-based researchers, and range from automotive industry to computer technology and medical visualisation. In general, the projects presented in this volume prove that new mathematical ideas and methods can be decisive for the solution of industrial and economic problems.



Motors, Vehicles


Synthesis of Automotive Cams Using Multiple Shooting-SQP Methods for Constrained Optimization

Cam design is an old field of mechanical engineering. Because of the complexity of the problem, design procedures have emphasized the use of standardized approaches and rules-of-thumb, which produce reasonable designs without attempting to obtain a truly optimized performance. Increased competition among manufacturers puts pressure on designers to find new ways to deal with the complexity of the problem In recent years progress in the mathematics of numerical solution of optimal control problems has made it possible to obtain numerical solutions for these problems using realistic models and the needed highly nonlinear state inequality constraints. The work reported here develops a high level user interface for cam system designers as well as researchers in the field. It makes available sophisticated numerical integration that handles the necessary discontinuities, and numerical optimization with SQP methods to handle the complex optimization criteria and side conditions. This forms a tool for interactively designing cam systems to create optimal trade offs between the multiple performance characteristics of importance.

Hans Georg Bock, Richard W. Longman, Johannes P. Schlöder, Michael J. Winckler

Numerical Optimization of Scavenging in Two-Stroke Engines with Transfer Ducts, an Exhaust Port and a Moving Piston

For the benefit of the environment, the HC-emission of two-stroke engines has to be reduced. This can be done by reducing the losses of scavenging by improving the geometry of the transfer ducts and the exhaust port. Numerical simulations of the flow through the two-stroke engine should be performed for different geometries in order to reveal the geometry with an optimal scavenge process. The simulations can help to accelerate the development of new two-stroke engines. The underlying mathematical model consists of the compressible Navier-Stokes equations in the cylinder with a moving piston. For the discretization we use a stabilized finite volume scheme on a hexahedral mesh. Up to now we have developed a numerical code for computing the flow in the cylinder and the most important integral quantities such as trapping efficiency and the percentage of exhaust gas at the exhaust port. Now we are able to analyze quantitatively the scavenge process and to estimate the quality of different drafts for the geometrical design.

D. Kröner, L. Klassen, A. Klimmek, D. Trescher

A Numerical Tool for Flow Simulation in a Wankel Motor

We describe the main steps in the development of a new numerical tool for simulating gas flow and heat transfer in a rotary engine (“Wankel motor”). Our approach comprises a 2D/3D grid generator for the Wankel motor geometry, an implicit finite element discretization for coping with the stiff pressure-velocity coupling and robust multigrid solvers on strongly distorded meshes. These components are implemented within a new FE-software package named Hi-Flow++ which is presently under development.

Rolf Rannacher, Vincent Heuveline

An Efficient Navier-Stokes Solver for Automotive Aerodynamics

The aim of this project is the development of efficient and robust numerical methods for the simulation of industrial flows, particularly for incompressible flows in and around vehicles. Since the corresponding flow configurations lead to very huge systems of nonlinear equations with fully nonstationary behavior, the CPU requirements are so high such that special data and matrix structures and hardware-oriented implementation techniques have to be realized. These must be able to exploit a significant percentage of the potentially available computing power of almost 1 GFLOP/s on modern hardware in combination with the powerful FEM discretization and parallel multigrid solution techniques on the mathematical software side. This project is carried out in cooperation with DaimlerChrysler AG at Stuttgart (Dr. M. Wessels, Research and Technology FT1/FB, E222).

R. Rannacher, Chr. Becker, S. Turek

Numerical Simulation of Exhaust Systems in Car Industry — Efficient Calculation of Radiation Heat Transfer

The aim of this project is a complete yet simple numerical model for the heat transfer in a system of exhaust pipes of an automobile. The industrial partner Tenneco Automotive, H. Gillet GmbH at Edenkoben, uses this simulation for optimising the construction of the exhaust system in order to improve the efficiency of the catalytic converters. In this model forced convection of the exhaust gas, the heat conduction and the heat transfer due to radiation are taken into account. For the effective numerical solution of the boundary integral equation for the radiation heat transfer a method that is based on matrix compression is developed. Some numerical examples for the matrix compression and calculations using a developed software package are presented.

S. Rjasanow, M. Bebendorf

Combinatorial Optimization Techniques for Three-Dimensional Arrangement Problems

This paper presents two approaches for the automated layout of threedimensional objects in space. The goal is to achieve high packing densities and fitting of objects in predefined design spaces while satisfying technological side constraints. The focus is on small-sized problem instances (up to 20 objects) with complex, possibly non-convex shapes. Linear programming methods form the common ground of our approaches.The first approach is a global optimization algorithm based on the branch-and- bound paradigm. We introduce a discretization of the configuration space of all possible arrangements which facilitates a complete enumeration of solutions. The bounding procedure then allows for a drastic reduction of the search space. We use a limited number of discrete object orientations within this method.The second approach is a local optimization scheme which starts out from a given initial arrangement and is capable to perform continuous object rotations. It is based on a linearization of orthonormal rotation matrices. We also present a perspective for combining global optimization and continuous object rotations. Examples in this paper are taken from the automobile industry but applications are not limited to this area. Various objective functions may be optimized, including the volume and the location of the center of gravity. We also show how to integrate a wiring area estimation into the global optimization procedure.

Thomas Lengauer, Mike Schäfer

Simulation of Test-drives of Automobiles at Driving Limit

This project has been carried out in cooperation with the Volkswagen AG at Wolfsburg/Germany. The scope of the project is the computer-aided simulation of test-drives of an automobile at driving limit. Today the development of a new automotive model is a very expensive process. A large amount of the development costs is consumed by the building of prototypes. Therefore comparatively cheap computer based simulation methods are used to win insights to the future dynamical behavior of the automobile as soon as possible during the development process. The use of powerful software tools allows the complete modelling of automobiles by differential-algebraic equation systems of possibly higher index, e.g., as mechanical multi-body systems. An optimal test-driver is modeled by formulating an optimal control problem subject to the equations of motion of the automobile and additional constraints given by the test-course. The mathematical challenge is to solve large scale optimal control problems with differential-algebraic equation systems of higher index. The benefit for the industrial partner may be described by the slogan “test- drives without prototypes”.

H. J. Pesch, M. Gerdts

An Optimal Control Approach To Real-Time Vehicle Guidance

A newly developed two-level driver model is presented. On the anticipation level, optimal control problems for a reduced vehicle dynamics model are solved repeatedly on a moving prediction horizon to yield near optimal setpoint trajectories for the full model. On the stabilization level, a nonlinear position controller is developed to accurately track the setpoint trajectories with a full motor vehicle dynamics model in real-time. The formulation of the optimal control problems on the anticipation level is based on a nonlinear single track model which is extended by a complex tire model and further nonlinear model details such as to match the main properties of the full vehicle dynamics model. The optimal control problems are solved efficiently by a recently developed sparse direct collocation method. Numerical results for various vehicle maneuvers are presented, including a time-optimal double lane change at high speed.

Roland Bulirsch, Martin Vögel, Oskar von Stryk, Cornelius Chucholowski, Thieß-Magnus Wolter

Theoretical and Experimental Studies of an S-Catamaran

Using a nonlinear shallow-water solitary-wave theory it was demonstrated that for a ship moving at supercritical speed along the centerline of a rectangular channel, if the hull sectional-area curve is of a special form determined by the solution of an oblique double-soliton interaction and the channel width is chosen to ensure complete wave cancelation through sidewall reflection, the ship waves can be made to form a purely localized pattern around the ship so that its wave resistance, which results only from far-field free waves, theoretically vanishes. To get rid of the crucial dependence on impractical sidewall reflection, this mechanism was developed further to obtain a novel catamaran comprising twin hulls with curved centerlines, yaw and skegs; it has theoretically zero wave-resistance at a chosen supercritical design speed in laterally unrestricted shallow water. Despite certain deviations from the ideal form for practical reasons, the wave-resistance of the new curved-yawed-hull catamaran with and without skeg was numerically found to be less than that of an equivalent straight-unyawed-hull catamaran by 50 and 30%, respectively. Now, the new design, albeit without skeg, has been validated by model experiment and comparison with a state-of-the-art reference catamaran of equal main dimensions that was developed and tested earlier in the VBD. Up to 28% wave-resistance reduction was achieved in the experiment, although not in the originally designed configuration but at a reduced yaw angle found by trial and error.

Klaus Kirchgässner, Som Deo Sharma, Xue-Nong Chen, Norbert Stuntz

Environmental Technology


Robust Error Estimators for Interface Problems Occuring in Transport Processes in Porous Media

The aim of the project is the adptive numerical simulation of transport processes in porous media within the groundwater simulation code FEFLOW [4]. These processes can be very complex and take place in highly heterogeneous media. The nature of the describing equations is such that error estimators for the full nonlinear model can be defined only heuristically based on considerations on known model problems and numerical experiments. Here one could only proceed with heuristical error indicators, which give a criterion where to refine the grid to become probably more accurate. As adaptivity and error control suggest to the engineer that we really give him a measure of the error — i.e. an error estimate, in consensus with the industry partner, we disregarded the heuristical approach as much as we could and rather tried to verify both theoretically and experimentally estimators for a relevant problem class where we still are able to proceed with mathematical theory.

Jürgen Fuhrmann, Martin Petzoldt

Modelling and Simulation of a Planned Bio-Chemical in situ Remediation

In this paper, the simulation of a bio-chemical in situ remediation approach is discussed. We consider a field case of a contaminant plume consisting of dissolved chloroethenes. A regional flow model shows, that the contaminants may reach a water works located 2 km downstream of the spill area. Thus, an in situ remediation is anticipated, where the dechlorination and mineralization of the chloroethenes is stimulated by a sequence of aerobic and anaerobic treatments. The equations of the reactive transport model are discretized using implicit time schemes and locally refined meshes. The resulting discrete equations are solved simultaneously with a Newton method and a point-block multigrid method, which turned out to be an efficient solver for the considered systems. Simulation results for several remediation configurations show a fast bio-chemical degradation of the chloroethenes which is however limited to the vicinity of the injection wells. After two years about 60% of the initial contaminant mass is removed, while a pure pump-and-treat scheme removes only 40% of the initial mass in the same time. The simulations suggest that the remediation scheme could be optimized with respect to the in situ biodégradation efficiency.

Willi Jäger, Gabriel Wittum, Wolfgang Schäfer, Christian Wagner, Harald Willershausen

Influence of Surfactants on Spreading of Contaminants and Soil Remediation

Surfactants occur already in undisturbed biological processes in soils but within the development of remediation techniques these substances are of large interest because of their interaction with hydrophobic substances. The standard models for (un-)saturated water flow and solute transport are extended to include the influence of the surfactant transport on the flow of the water phase. Two effects of surfactants on (un-)saturated water flow are included: the modification of the interfacial tension between water and air and the swelling of clay minerals due to sorption of surfactants. Simulations are presented, which exhibit the feedback of surfactant transport on water flow and content. An identification algorithm for hydraulic soil properties has been developed that supplements the simulation tool.

P. Knabner, S. Bitterlich, R. Iza Teran, A. Prechtel, E. Schneid

Improvement of Environment Observing Remote Sensing Devices by Regularization Techniques

This project is carried out jointly with the support of the company Elight Laser Systems GmbH in Teltow. The goal is to improve the evaluation software of the measurements of so-called lidar (ligth detection and ranging) devices which are produced in the company. Such lidar devices are used for instance at Departments of Environment for air pollution control. To this end, we developed a capable and efficient regularization method for this inverse ill-posed problem by which future problems of this type may be treated routinely on PC’s.

P. Maaß, Christine Böckmann, Alexander Mekler

Flow, Transport and Reactions in Technological Processes


Stability Analysis for Reactors from Chemical Industry

We present, for a class of industrially relevant chemical reactions the dependence of stability on important chemical parameters, such as coolant, dilution and diffusion rates. Moreover, the influence of the order of reaction rates for stability is considered. Our analysis is based on a generalized upscaling balance condition for the equilibria concentrations.

B. Fiedler, M. A. Efendiev, L. Lerman, J. Rademacher, A. Schuppert

Heterogeneous Dynamic Process Flowsheet Simulation of Chemical Plants

For large-scale dynamic simulation problems in chemical process engineering, a heterogeneous simulation concept is described which allows to distribute the solution of the models of coupled dynamic subprocesses to a computer network. The main principle of such a technique is to solve the submodels of an overall model independently of each other on subsequent time intervals. This is done by estimating the vector of input variables of the submodels, calculating the corresponding time behaviour of the output variables concurrently, and matching the time profiles of the interconnecting variables of the process flowsheet iteratively. Therefore, accelerated waveform iteration methods are considered, using Broyden- and block-Broyden- type updates. The simulation concept is investigated especially in the case that the submodels do not provide input-output sensitivities.

Friedrich Grund, Klaus Ehrhardt, Jürgen Borchardt, Dietmar Horn

Numerical Simulation of Annular Chromatography

This project is carried out jointly with Prof. Seidel-Morgenstern from the Institute for Process Engineering of university of Magdeburg and with the support of Schering AG at Berlin. Preparative chromatography attains increasing importance for the isolation and purification of value added products in the pharmaceutical industry and in biotechnology. The goal of this project is the numerical simulation of the separation process in an annular Chromatograph to study the influence of the main design parameters on the efficiency of the multicomponent separation. Simulations to optimize the separation process with the aim of a high efficiency of pure products are of special interests. On the basis of the mass balance equations a mathematical model is proposed and an efficient solution strategy is developed using streamline diffusion method, adaptive refinement and multigrid solver.

Lutz Tobiska, Angela Thiele

Numerical Methods for Parameter Estimation in Bingham-Fluids

Bingham models are frequently used for describing the flow of pastes. In this project together with Braun GmbH at Friedrichshafen, we develop a parameter estimation method for the automatic determination of certain model parameters. The result of this project is a software tool for the simultaneous determination of all model parameters by using data from a single experiment sweep.

Gabriel Wittum, Volker Schulz, Bernd Maar, Dmitriy Logashenko

A Viscoelastic Turbulence Model Based on Renormalization Group Theory

The aim of this project, which is in cooperation with DaimlerChrysler AG, Rhodia Acetow AG, the Steinbeis transfer center HTCO and Prof. H.Kielhoefer at the University of Augsburg, is to improve the numerical simulation of turbulent separated flows. Flows of that type arise in a variety of technically important situations. An example from automotive industry is the flow behind a car. By means of the renormalization group theory (RNG), we have constructed a Reynolds stress model with model coefficients calculated from theory. A first version of our turbulence model has been tested with the aid of the finite element code FIDAP with encouraging results for the flow over a backward facing step. Within this project, we have also addressed some more theoretical aspects, ranging from questions regarding the “epsilon expansion” up to the question of existence and regularity of solutions of the stochastically forced Navier Stokes equation. The latter work, which will be essential for a mathematically rigorous foundation of our model, has been done by Dipl.-Math. Ch. Gugg at the University of Augsburg. The ultimate test case for our model shall be the flow behind a car with data from wind tunnel experiments provided by the DaimlerChrysler AG.

M. Niggemann, M. Holzmann, D. Schmidt, K. Söldner

Modelling and Simulation of Capacitor Impulse Welding

We present a numerical simulation of capacitor resistance welding. The model accounts for electrical, thermal and mechanical effects, which are nonlinearly coupled by the balance laws, constitutive equations and boundary conditions. Assuming only plane strains, we develop a two-dimensional FE approximation with simplicial elements, which is especially suited for the simulation of work- pieces with longitudinal projections or thin-walled rings with annular projection. In the melted zone the material is described as an isotropic, electrically conducting thermo-viscoelstic Maxwellian body. In the solid it is assumed to behave nonlinearly thermoelastic.

D. Hömberg, W. Dreyer, F. Duderstadt

Analysis of Transport Processes for Layered Porous Materials Used in Industrial Applications

This work was aimed at the development of mathematical models and corresponding numerical solution and parameter estimation procedures which are needed as a basis for the computer-aided design of layered porous materials for industrial applications (e.g., hygienic products, technical textiles). The applications lead to nonlinear partial differential equations which must be solved in complex 3D geometries in many cases. Additionally, they may involve saturated/unsaturated flow, coupled flow and deformation problems, swelling particles, large jumps of the material parameters at the interfaces, convection dominance and complex boundary conditions. We introduce a generic mathematical model for layered porous materials, discuss some of the numerical aspects with an emphasis on 3D geometry description and present example applications.

H. Neunzert, A. Zemitis, K. Velten, O. Iliev

Modelling and Numerical Simulation of District Heating Networks with Time-Saving Solution Methods

The main aim of the project is the thermo-hydraulic calculation of district heating networks with an incompressible feed medium by time-saving numerical methods. The modelling of the hydraulic and thermal relations of the various components of the heating network are based on earlier studies on this topic. Graph-theoretical methods are used to describe the topology of the heating system, in which spanning trees play a crucial role. The solution concept is based on sparse-matrix techniques with special data structures, which have been fitted to the particular problem. The main interest of the district heating supplier is a longtime simulation of the heating network combined with an optimization of the heat distribution and the producer’s service. They are important for the power station to plan things like fuel supply and intervals of maintenance more efficiently. In the already existing computer codes an arising problem was the need to accelerate the simulation in order to obtain results in an acceptable amount of time on common computers.The obtained simulation tool makes the calculation of the system states in acceptable short times possible. Furthermore, it approaches more realistically the behaviour of the heating system by considering a time-dependent consumer demand (heat load). Questions regarding the main operation and the flow time behaviour of the heat distribution of the system are also examined.This project was supported by a grant from the german BMBF ministery and carried out in collaboration with the Bewag company in Berlin.

Rolf Dieter Grigorieff, Ralf Köcher

Sensitivity and Robustness Analysis for Construction and Monitoring of Tubine-Generator Shafts

Sensitivity and robustness analysis are important tools in order to guarantee an efficient construction and error free running of a turbine generator shaft. It is very important to test different design parameters simultaneously before the machine is in use. Therefore, the knowledge of the characteristic frequencies of the system is crucial since they should be sufficiently different from the excitation frequency, e.g. the electrical main frequency. Often the important system parameters are inexactly or hardly known and so the resulting model, which describes the dynamical behaviour of a turbine generator shaft, differs significantly from reality. Therefore one has to analyze how large the permissible errors in the critical design parameters are, so that a smooth running of the system is still assured. Besides estimating the influence of parameter variations, one also requires a suitable model adaption based on real measured dynamical system parameters. Such a well-adapted shaft model then is the basis for the monitoring of the machine during its life-time.

D. Prätzel-Wolters, P. Lang, A. Wirsen, S. Kulig

Optics and Sensors


Adaptive Multigrid Methods for the Vectorial Maxwell Eigenvalue Problem for Optical Waveguide Design

This paper has been motivated by the need for a fast robust adaptive multigrid method to solve the vectorial Maxwell eigenvalue problem arising from the design of optical chips. Our nonlinear multigrid methods are based on a previous method for the scalar Helmholtz equation, which must be modified to cope with the null space of the Maxwell operator due to the divergence condition. We present two different approaches. First, we present a multigrid algorithm based on an edge element discretization of time-harmonic Maxwell’s equations, including the divergence condition. Second, an explicit elimination of longitudinal magnetic components leads to a nodal discretization known to avoid discrete spurious modes also and a vectorial eigenvalue problem, for which we present a multigrid solver. Numerical examples show that the edge element discretization clearly outperforms the nodal element approach.

Peter Deuflhard, Frank Schmidt, Tilmann Friese, Lin Zschiedrich

Direct and Inverse Problems for Diffractive Structures — Optimization of Binary Gratings

The goal of the project is to provide flexible analytical and numerical tools for the optimal design of binary and multilevel gratings occurring in many applications in micro-optics. The direct modelling of these diffractive elements has to rely on rigorous grating theory, which is based on Maxwell’s equations. We developed efficient and accurate direct solvers using a variational approach together with a generalized finite element method which appears to be well adapted to rather general diffractive structures as well as complex materials. The optimal design problem is solved by minimization algorithms based on gradient descent and the exact calculation of gradients with respect to the geometry parameters of the grating.

Johannes Elschner, Rainer Hinder, Günther Schmidt

Computation of Electromagnetic Fields for a Humidity Sensor

We simulate an electromagnetic humidity sensor in order to determine its eigenfrequencies. The underlying model is given by Maxwell’s field equations, they are transformed into two decoupled two-dimensional problems by eliminating the magnetic field and changing to cylinder coordinates.A time-harmonic approach leads to two generalized eigenproblems that are discretized using appropriate finite elements. The usual multigrid solvers are modified in order to cope with the anisotropic structure of the resulting matrices. These modifications can be used in order to build robust eigenproblem solvers of optimal asymptotic complexity.Numerical experiments show that the resulting method is able to capture those effects that are relevant for the sensor under investigation.

Wolfgang Hackbusch, Steffen Börm

Crystal Growth, Semiconductors


Simulation of Industrial Crystal Growth by the Vertical Bridgman Method

Single crystals of Cadmium-Zinc-Telluride are used as a substrate material for the production of infrared detectors and are usually grown by the vertical Bridgman method. We present a simulation of the whole growth process in two steps: In the first step, the (stationary) heat transport in the furnace is modeled and calculated for different positions of the ampoule. This provides information about the most important parameter during this process: the temperature distribution in furnace and ampoule. The obtained temperatures are then used in the second step as boundary conditions for the (time dependent) simulation of temperature and convection in the ampoule. Only the use of adaptive finite element methods allows an efficient numerical simulation of the moving phase boundary, the convection in the melt and the temperature distribution in melt and crystal. Numerical results are presented for both furnace and ampoule simulations.

Gerhard Dziuk, Stefan Boschert, Alfred Schmidt, Kunibert G. Siebert, Eberhard Bänsch, Klaus-Werner Benz, Thomas Kaiser

Numerical Simulation and Control of Industrial Crystal Growth Processes

This project is carried out jointly by the Crystal Growth Laboratory at the Chair of Material Science VI at the University of Erlangen (Prof. G. Müller) and the Chair of Applied Mathematics at the Technical University of Munich (Prof. K.-H. Hoffmann) with the support of the companies Korth Kristalle GmbH and Preiberger Compound Materials GmbH. The goal of the project is the development of proper numerical models for optimisation and control of industrial crystal growth processes. To this end the research group concentrates on the numerical treatment, simulation and optimal control of techniques for growing high quality single and compound semiconductor crystals. The result of this project is the flexible and efficient computer code CrysVUn that is today successfully used to optimise industrial growth processes.

Karl-Heinz Hoffmann, Axel Voigt, Michael Metzger

Optimal Control of Sublimation Growth of SiC Crystals

The project aims at providing numerical tools to control and optimize sublimation growth of SiC bulk single crystals via the Modified Lely Method. It is in cooperation with the experimental group of Dr. Dietmar Siche at the Institute of Crystal Growth in Berlin. In the course of the project the Modified Lely Method is mathematically modeled and numerically simulated. We present a transient model which for the gas phase consists of balance equations for mass, momentum and energy, and reaction-diffusion equations. The model for the solid components takes into account heat transfer via conduction inside the solid materials and via radiation between solid surfaces of cavities. Results of transient numerical simulations of the temperature evolution inside the growth apparatus are depicted, illustrating the paramount influence of radiation at growth temperature.

Jürgen Sprekels, Olaf Klein, Peter Philip, Krzysztof Wilmański

Mathematical Modelling and Numerical Simulation of Semiconductor Detectors

We report on a system of nonlinear partial differential equations describing signal conversion and amplification in semiconductor detectors. We explain the main ideas governing the numerical treatment of this system as they are implemented in our code WIAS-TeSCA. This software package has been used by the MPI Semiconductor Laboratory for numerical simulation of innovative radiation detectors. We present some simulation results focussing on three-dimensional effects in X-ray detectors for satellite missions.

H. Gajewski, H.-Chr. Kaiser, H. Langmach, R. Nürnberg, R. H. Richter

Optimal Design of High Power Electronic Devices by Topology Optimization

High power electronic devices such as converter modules are frequently used as electric drives for high power electromotors. The efficient and reliable operating behaviour of such devices requires an optimal design with regard to a minimization of power losses due to parasitic inductivities caused by eddy currents. The mathematical modelling gives rise to a topology optimization problem where the state variables are required to satisfy the quasistationary limit of Maxwell’s equations and the design variables are subject to both equality and inequality constraints. Based on appropriate finite element approximations involving domain decomposition techniques, the discretized optimization problem is solved by a primaldual Newton interior-point method.

Ronald H. W. Hoppe, Peter Böhm, George Mazurkevitch, Svetozara Petrova, Gerhard Wachutka, Eckhard Wolfgang

Modelling and Simulation of Strained Quantum Wells in Semiconductor Lasers

A model allowing for efficiently obtaining band structure information on semiconductor Quantum Well structures will be demonstrated which is based on matrix-valued kp-Schrödinger operators. Effects such as confinement, band mixing, spin-orbit interaction and strain can be treated consistently. The impact of prominent Coulomb effects can be calculated by including the Hartree interaction via the Poisson equation and the bandgap renormalization via exchange-correlation potentials, resulting in generalized (matrix-valued) Schrödinger-Poisson systems. Band structure information enters via densities and the optical response function into comprehensive simulations of Multi Quantum Well lasers. These device simulations yield valuable information on device characteristics, including effects of carrier transport, waveguiding and heating and can be used for optimization.

Hans-Christoph Kaiser, Uwe Bandelow, Thomas Koprucki, Joachim Rehberg

Electronic Circuits


Efficient Analysis of Oscillatory Circuits

Circuit simulation is a standard task in the computer-aided design of electronic circuits. The generation of the circuit equations leads to differentialalgebraic equations (DAE). With respect to the analysis of oscillatory circuits, periodic solutions are of major interest. For highly oscillatory circuits, direct methods must be used to obtain the limit cycle efficiently. A specialized shooting method for solving the associated boundary-value problem of the differential-algebraic network equations is presented.

Roland Bulirsch, Rolf Neubert, Angela Schwarz

Modelling and Simulation of Power Devices for High-Voltage Integrated Circuits

Process and device simulators turned out to be important tools in the design of high-voltage integrated circuits and in the development of their technology. The main goal of this project was the improvement of the device simulator WIAS-TeSCA in order to simulate different power devices in high-voltage integrated circuits developed by the industrial partner. Some simulation results are presented. Furthermore, we discuss some aspects of the mathematics of relevant model equations which device and process simulations are based on.

Rolf Hünlich, Günter Albinus, Herbert Gajewski, Annegret Glitzky, Wilfried Röpke, Jürgen Knopke

Finding Beneficial DAE Structures in Circuit Simulation

Circuit simulation is a standard task for the computer-aided design of electronic circuits. The transient analysis is well understood and realized in powerful simulation packages for conventional circuits. But further developments in the production engineering lead to new classes of circuits which may cause difficulties for the numerical integration. The dimension of circuit models can be quite large (105 equations). The complexity of the models demands a higher abstraction level. In this paper, we analyze electric circuits with respect to their structural properties. We discuss the relevant subspaces of the resulting differential algebraic equations (DAEs) and present algorithms for calculating the index as well as consistent initial values.

Roswitha März, Diana Estévez Schwarz, Uwe Feldmann, Sandra Sturtzel, Caren Tischendorf

CHORAL — a Charge-Oriented Algorithm for the Numerical Integration of Electrical Circuits

Circuit simulation packages generate the network equations automatically. In time domain analysis this results in a system of differential-algebraic equations that is solved numerically by BDF schemes and/or the trapezoidal rule. CHORAL, a charge-oriented Rosenbrock-Wanner method, has been developed as an alternative approach for digital circuits. By its successful implementation into TITAN, the circuit simulator of Infineon Technologies, a second integration scheme is available for the first time. Results for benchmarks and industrial circuits show that CHORAL is competitive with the standard ansatz and possesses advantages for oscillatory circuits.

P. Rentrop, M. Günther, M. Hoschek, U. Feldmann

Tomography, Image Analysis and Visualisation


Reconstructing Crystalline Structures from Few Images Under High Resolution Transmission Electron Microscopy

The present paper is motivated by the demand from material sciences to reconstruct crystalline structures given through their images under high resolution transmission electron microscopy (HRTEM) in a certain limited number of directions. In particular, [31] and [22] show how a quantitative analysis of images from high resolution transmission electron microscopy can be used to determine the number of atoms on atomic columns in certain directions; see Sects. 2 and 3. Mathematically, this leads to the problem of reconstructing finite lattice sets from certain of their marginal sums; see Sect. 4.

Peter Gritzmann, Sven de Vries

Measurement of Paint Layer Thickness with Photothermal Infrared Radiometry

Photothermal infrared radiometry has been used for the measurement of thermo-physical, optical and geometrical properties of multi-layered samples of paint on a metalic substrate. A special data-normalization is applied to reduce the number of sensitive parameters which makes the identification task for the remaining parameters easier. The normalization stabilizes the evaluation of the photothermal signal and makes the infrared radiometry more attractive for applications in the industrial environment. It is shown that modelling and multi-parameter- fitting can be applied successfully to the normalized data for the determination of layer thicknesses. A second approach is presented to verify the adaptability of reconstruction algorithms for thickness measurements. An algorithm which uses the affinity of the thermal waves to the acoustic waves and the inverse scattering problem demonstrates the applicability in general.

A. K. Louis, P. Dörr, C. Gruss, H. Petry

Spatio-Temporal Current Density Reconstruction from EEG-/MEG-Data

The determination of the sources of electric activity inside the brain from electric measurements on the surface of the head is known to be an ill-posed problem. In this paper a new algorithm which takes temporal a-priori information into account is described and compared to existing algorithms as Tikhonov-Phillips. There are further applications in medical and technical fields as the determination of electrical sources in the living heart and the determination of acoustic sources.

Alfred K. Louis, Uwe Schmitt, Felix Darvas, Helmut Büchner, Manfred Fuchs

Signal Correction in NMR Spectroscopy

The correction of baseline and phase distortions is an important problem in magnetic resonance spectroscopy. In this work, fast and automatic correction methods based on the adaptive construction of Wiener filters are presented. The proposed methods consist of estimating and classifying the model parameters of the measured spectrum and of approximating correlation operators for the measured and the corrected signal. Results of numerical simulations and applications to real data are given.

Heinz-Otto Peitgen, Tobias Boskamp, Peter Singer

On Scattering of Ultrasonic Waves

We report investigations regarding the possibility for improving ultrasonic imaging by an analysis of pulse deformations. Starting with a stochastic solution of the lossy wave equation, we present a general approach for perturbing stochastic processes on Lie groups by a Poisson process. Applications to radiation transport are indicated.

Peter Mathé, Johann Hinrich Zacharias-Langhans

Smoothing of Tomographic Data and Hybrid Volume-Surface Visualisation

Visualisation of higher dimensional data sets is an important tool for their analysis and most important in medical diagnosis and therapy. Starting from application in dental medicine and facial surgery, this project had as an aim to improve the methods of volumetric image processing.Here, high quality of the visual representation and speed in generating the images on standard hardware are challenging demands. Nonlinear filtering techniques were applied to smooth the data obtained from computer tomography. The paper presents some features and implementation details of an object oriented software specialized in volumetric image processing. It is a report of the results in hybrid visualisation of volumes and different surface types, where the most important progress could be achieved. The volume rendering techniques of this project were developed for medical applications, however, they are in the meantime applied to high dimensional data sets, e.g. to visualise reactive flow and transport.This BMBF supported project had in medical application the following partners: Klinik für Mund-, Kiefer- und Gesichtschirurgie, Universität Heidelberg (Priv. Doz. Dr. Dr. S. Haßfeld) Friatec AG, Mannheim-Friedrichsfeld

Willi Jäger, Cătălin Dârtu

Video Coding with Adaptive Vector Quantization and Rate Distortion Optimization

The goal of the research presented in this paper is the development and evaluation of adaptive image sequence coding. The method, based on adaptive vector quantization, has been combined with several video coding techniques like wavelet transform, quad-trees, and rate distortion optimization. In addition we provide a comparison with a state-of-the-art video codec (H.263) and describe experiments with motion compensation.

D. Saupe, M. Wagner

Statistical Methods in Medical Applications


The Application of Statistical Methods of Meta-Analysis for Heterogeneity Modelling in Medicine and Pharmacy, Psychology, Quality Control and Assurance

In the past few years meta-analysis has become increasingly popular in many areas of science such as medicine and pharmacy, psychology and other social sciences. In these areas of application meta-analyses have been performed in order to obtain a pooled estimate of various single studies. Obtaining a single summary measure implicitly assumes homogeneity of these studies, i.e. the results of individual studies differ only by chance. In this case a combined estimate of the individual studies provides a powerful and important result. However this pooled estimate may be seriously misleading if study conditions are heterogenous.Thus, increasingly an approach has been advocated which considers meta- analysis as a study over studies. This approach seeks to investigate heterogeneity between studies. An important feature of this type of meta-analysis lies in the fact that it tries to identify factors which cause heterogeneity.It has been the focus on this project (in corporation with the unit of quality assurance of ASTA Medica at location Künsebeck) to extend this approach appropriately to the area of quality control, where batches of the produced goods replace the role of studies in medicine or the social sciences. Clearly, in this setting an investigation of heterogeneity is equally attractive, since identification and modelling of heterogeneity helps to improve the production process.

Dankmar Böhning, Uwe Malzahn, Peter Schlattmannn, Uwe-Peter Dammann, Wolfgang Mehnert, Heinz Holling, Ralf Schulze

An Application for the Analysis of Human Tremor Time-Series

For many diseases various methods for the diagnosis and treatment monitoring are available. Presently, such methods are not established for an investigation of human tremor diseases, although the different forms of tremor are common neurological symptoms and occur frequently in various neurological diseases and also other conditions. Human tremor is defined as an involuntary oscillation of one or more parts of the body. The goal of this project was to develop new methods and to improve and automate already proposed methods for the diagnosis and treatment monitoring of human tremors. We built an easy-to-use application for tremor-analysis and recording, running on conventional personal computers, that allows to investigate different forms of human tremor by advanced mathematical methods of time series analysis. The software is also applicable for users who are not familiar with these kind of advanced data analysis methods. It provides tools for the diagnosis and treatment monitoring under laboratory conditions, mainly based on the cross-spectral and spectral analysis of tremor acceleration time-series and electromyographic time-series. The software is now available on the market.

Josef Honerkamp, Michael Lauk, Jens Timmer, Carl-Herrmann Lücking, Günther Deuschl

Optimization in Design and Production


Free Material Optimization

Free material design deals with the question of finding the stiffest structure with respect to one or more given loads which can be made when both the distribution of material as the material itself can be freely varied. We present the single and multiple-load situation (understood in the worst-case sense). We further introduce a software tool MOPED for free material optimization of general two- dimensional bodies. The graphical post-processor of MOPED is tailored for a design of fibre-reinforced composite materials used by our industrial partner DaimlerChrysler Aerospace. Finally, we generalize the above approach to the case of uncertain loads in order to design an optimal robust material.

Jochem Zowe, Michal Kocvara

Automatic Layout and Labelling of State Diagrams

We consider the problem of automatically generating readable layouts for state diagrams. Such diagrams appear in the field of automation engineering in the design process of control systems. Our industrial partner, the Siemens AG, realised that due to the complex nature of these diagrams, automatic layout tools lead to a better design and documentation of control systems.The layout problem turns out to be difficult, since not only a graph drawing problem has to be solved but also an additional labelling problem. In this article we study the combined graph layout and labelling problem and present new results for the two-dimensional compaction problem in graph drawing, the label number maximisation problem and the combined graph labelling problem.

Petra Mutzel, Gunnar W. Klau

Optimization Problems in a Semi-Automatic Device for Cutting Leather

Cutting large leather skins is a two step process, a “decision step” and a “cutting step”. In the decision step, it has to be decided which piece is cut from which part of the skin. This is called nesting. After the nesting process the actual cutting takes place. The cooperation company HUMANTEC GmbH in Wemding (Germany, Bavaria) has developed a machine where the nesting is done by a person and not by a computer. The machine just assists the worker and helps her to find a good nesting. Only the cutting process is basically fully automatic. In both parts, the nesting and the cutting process, mathematical problems related to the travelling salesman problem occur.

Alexander Pott, Holger Glaab

Stochastic Programming for Power Production and Trading Under Uncertainty

Optimization models under uncertainty for mid-term cost-optimal operation of a hydro-thermal power system and for simultaneous power production and day-ahead trading at a power exchange are presented. Algorithms for solving these models are sketched and initial numerical experience is reported.

Rüdiger Schultz, Matthias P. Nowak, Robert Nürnberg, Werner Römisch, Markus Westphalen

Scheduling Scarce Resources in Chemical Engineering

The efficient utilization of scarce resources, such as machines or manpower, is major challenge within production planning in the chemical industry. We describe solution methods for a resource-constrained scheduling problem which arises at a production facility at BASF AG in Ludwigshafen. We have developed and implemented two different algorithms to solve this problem, an approach which is based on Lagrangian relaxation, as well as a branch-and-bound procedure. Particularly the Lagrangian approach is applicable for a whole variety of resourceconstrained scheduling problems, hence it is of interest not only for the specific problem we describe, but also for many other industrial applications. In this paper, we describe both approaches, and also report on computational results, based upon practical problem instances as well as benchmark test sets.

Rolf H. Möhring, Marc Uetz

Optimization in Traffic and Communication


Duty Scheduling in Public Transit

This article is about adaptive column generation techniques for the solution of duty scheduling problems in public transit. The current optimization status is exploited in an adaptive approach to guide the subroutines for duty generation, LP resolution, and schedule construction toward relevant parts of a large problem. Computational results for three European scenarios are reported.

Martin Grötschel, Ralf Borndörfer, Andreas Löbel

Rotation Planning for the Continental Service of a European Airline

We consider a version of the aircraft rotation problem where the objective is to minimize delay risks. Given a set of flights to be flown by a subfleet the rotation problem is to find a specific route for each aircraft of the subfleet such that each flight is flown by exactly one aircraft. Additionally, the sequence of flights defining a route must satisfy certain requirements mainly to avoid delays. We present a mathematical model for the problem of minimizing the delay risk according to special requirements of a major airline. An efficient Lagrangian heuristic is proposed that uses subgradient optimization and linear assignments as subproblems. Computational results on real data are given and compared to actual aircraft rotations of that airline.

M. Jünger, M. Elf, V. Kaibel

Computer Aided Scheduling of Switching Engines

Scheduling the switching engines of an industrial railroad is a formidable and responsible task, closely related to the well-studied pickup and delivery problem with time windows. Aiming at an efficient usage of resources the need arose for a computer aided scheduling tool as support for the human dispatcher. We sketch a set partitioning formulation of this problem to be solved via column generation. The pricing subproblem is hard in the theoretical sense but can be solved by means of a combination of heuristics and exact algorithms. A trade-off between mathematical rigor and practicability becomes apparent and is extensively discussed. Our computational experience with an academic prototype implementation is encouraging. We succeed in obtaining practically acceptable solutions for instances of more than forty customers and six vehicles.

Uwe T. Zimmermann, Marco E. Lübbecke

Train Schedule Optimization in Public Rail Transport

Attractive train schedules are quite important for the success of public rail transport. We consider schedules which are repeated after some fixed time period. Periodicity is a well accepted, convenient attribute of all major railroad systems. Since trains share the public railroad network, we have to handle many conflicting demands. Increasing competition from transportation alternatives as well as the politically motivated process of deregulation forces railroad companies to reduce cost and resource utilization. In this situation, better decision tools are quite welcome. Here, we discuss models and corresponding methods for cost optimal train scheduling in real world railroad networks.

U. T. Zimmermann, T. Lindner

An Integrated Planning Approach for Cellular Radio Networks

Two major planning problems must be solved in the design phase of a cellular radio network. The initial question is where to locate the base transmitter stations such that full coverage is achieved at low interference. This is relevant for frequency division (FDMA) as well as code division multiple access (CDMA) technology. To tackle this problem, precise knowledge of the radio wave propagation from each candidate base station location is necessary, particularly in urban areas. A corresponding software tool has been developed in the present project. Its main advantages are high precision and fast computation times, which is achieved by a sophisticated preprocessing phase. Once the base station positions are fixed, for FDMA systems frequencies have to be assigned such that in each cell there is a sufficient number of channels available at a low overall interference in the network. Since cell site selection and frequency allocation have mutual influence on each other, the ultimate goal is to deal with both problems in a single design step. In this paper, the above planning issues are modelled as linear integer programs and approximate solution methods for the corresponding NP-hard problems are discussed. It turns out that optimal solutions can be found for realistic problem sizes, which makes the developed software a versatile tool for third generation radio network planning.

Rudolf Mathar, Michael Schmeink


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