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For the last decade, optimization of beam orientations in intensitymodulated radiation therapy (IMRT) has been shown to be successful in improving the treatment plan. Unfortunately, the quality of a set of beam orientations depends heavily on its corresponding beam intensity proles. Usually, a stochastic selector is used for optimizing beam orientation, and then a single objective inverse treatment planning algorithm is used for the optimization of beam intensity proles. The overall time needed to solve the inverse planning for every random selection of beam orientations becomes excessive. Recently, considerable improvement has been made in optimizing beam intensity proles by using multiple objective inverse treatment planning. Such an approach results in a variety of beam intensity proles for every selection of beam orientations, making the dependence between beam orientations and its intensity proles less important. We take advantage of this property to present a dynamic algorithm for beam orientation in IMRT which is based on multicriteria inverse planning. The algorithm approximates beam intensity proles iteratively instead of doing it for every selection of beam orientation, saving a considerable amount of calculation time. Every iteration goes from an N-beam plan to a plan with N + 1 beams. Beam selection criteria are based on a score function that minimizes the deviation from the prescribed dose, in addition to a reject-accept criterion. To illustrate the eciency of the algorithm it has been applied to an articial example where optimality is trivial and to three real clinical cases: a prostate carcinoma, a tumor in the head and neck region and a paraspinal tumor. In comparison to the standard equally spaced beam plans, improvements are reported in all of the three clinical examples, even, in some cases with a fewer number of beams.

In this article, we give an explicit homotopy between the solutions (i.e. stress, strain, displacement) of the quasistatic linear elastic and nonlinear elastoplastic boundary value problem, where we assume a linear kinematic hardening material law. We give error estimates with respect to the homotopy parameter.

We present the application of a meshfree method for simulations of interaction between fluids and flexible structures. As a flexible structure we consider a sheet of paper. In a two-dimensional framework this sheet can be modeled as curve by the dynamical Kirchhoff-Love theory. The external forces taken into account are gravitation and the pressure difference between upper and lower surface of the sheet. This pressure difference is computed using the Finite Pointset Method (FPM) for the incompressible Navier-Stokes equations. FPM is a meshfree, Lagrangian particle method. The dynamics of the sheet are computed by a finite difference method. We show the suitability of the meshfree method for simulations of fluid-structure interaction in several applications.

In this paper we present and investigate a stochastic model for the lay-down of fibers on a conveyor belt in the production process of nonwovens. The model is based on a stochastic differential equation taking into account the motion of the ber under the influence of turbulence. A reformulation as a stochastic Hamiltonian system and an application of the stochastic averaging theorem lead to further simplications of the model. Finally, the model is used to compute the distribution of functionals of the process that might be helpful for the quality assessment of industrial fabrics.

A unified approach to Credit Default Swaption and Constant Maturity Credit Default Swap valuation
(2006)

In this paper we examine the pricing of arbitrary credit derivatives with the Libor Market Model with Default Risk. We show, how to setup the Monte Carlo-Simulation efficiently and investigate the accuracy of closed-form solutions for Credit Default Swaps, Credit Default Swaptions and Constant Maturity Credit Default Swaps. In addition we derive a new closed-form solution for Credit Default Swaptions which allows for time-dependent volatility and abitrary correlation structure of default intensities.1

We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interiorpoint method developed by Stein. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on realworld data are also presented.

During the recent years, multiobjective evolutionary algorithms have matured as a flexible optimization tool which can be used in various areas of reallife applications. Practical experiences showed that typically the algorithms need an essential adaptation to the specific problem for a successful application. Considering these requirements, we discuss various issues of the design and application of multiobjective evolutionary algorithms to real-life optimization problems. In particular, questions on problem-specific data structures and evolutionary operators and the determination of method parameters are treated. As a major issue, the handling of infeasible intermediate solutions is pointed out. Three application examples in the areas of constrained global optimization (electronic circuit design), semi-infinite programming (design centering problems), and discrete optimization (project scheduling) are discussed.

It is commonly believed that not all degrees of freedom are needed to produce good solutions for the treatment planning problem in intensity modulated radiotherapy treatment (IMRT). However, typical methods to exploit this fact have either increased the complexity of the optimization problem or were heuristic in nature. In this work we introduce a technique based on adaptively refining variable clusters to successively attain better treatment plans. The approach creates approximate solutions based on smaller models that may get arbitrarily close to the optimal solution. Although the method is illustrated using a specific treatment planning model, the components constituting the variable clustering and the adaptive refinement are independent of the particular optimization problem.

In this article, we consider the quasistatic boundary value problems of linear elasticity and nonlinear elastoplasticity, with linear Hooke’s law in the elastic regime for both problems and with the linear kinematic hardening law for the plastic regime in the latter problem. We derive expressions and estimates for the difference of the solutions of both models, i.e. for the stresses, the strains and the displacements. To this end, we use the stop and play operators of nonlinear functional analysis. Further, we give an explicit example of a homotopy between the solutions of both problems.

The desire to simulate more and more geometrical and physical features of technical structures and the availability of parallel computers and parallel numerical solvers which can exploit the power of these machines have lead to a steady increase in the number of grid elements used. Memory requirements and computational time are too large for usual serial PCs. An a priori partitioning algorithm for the parallel generation of 3D nonoverlapping compatible unstructured meshes based on a CAD surface description is presented in this paper. Emphasis is given to practical issues and implementation rather than to theoretical complexity. To achieve robustness of the algorithm with respect to the geometrical shape of the structure authors propose to have several or many but relatively simple algorithmic steps. The geometrical domain decomposition approach has been applied. It allows us to use classic 2D and 3D high-quality Delaunay mesh generators for independent and simultaneous volume meshing. Different aspects of load balancing methods are also explored in the paper. The MPI library and SPMD model are used for parallel grid generator implementation. Several 3D examples are shown.

This paper analyzes and solves a patient transportation problem arising in several large hospitals. The aim is to provide an efficient and timely transport service to patients between several locations on a hospital campus. Transportation requests arrive in a dynamic fashion and the solution methodology must therefore be capable of quickly inserting new requests in the current vehicle routes. Contrary to standard dial-a-ride problems, the problem under study contains several complicating constraints which are specific to a hospital context. The paper provides a detailed description of the problem and proposes a two-phase heuristic procedure capable of handling its many features. In the first phase a simple insertion scheme is used to generate a feasible solution, which is improved in the second phase with a tabu search algorithm. The heuristic procedure was extensively tested on real data provided by a German hospital. Results show that the algorithm is capable of handling the dynamic aspect of the problem and of providing high quality solutions. In particular, it succeeded in reducing waiting times for patients while using fewer vehicles.

Selbstorganisation ist eine interessante und vielversprechende Möglichkeit, um die Komplexität verteilter Systeme beherrschbar zu machen. In diesem Beitrag schlagen wir ein leistungsfähiges Rechnersystem auf Basis von rekonfigurierbarer Hardware vor, welches aufgrund seiner Flexibilität in vielen Bereichen eingesetzt werden kann. Es wird die geplante Systemarchitektur und Systemsoftware beschrieben und ein intelligentes, verteiltes Kamerasystem vorgestellt, welches wir als Anwendung mit dem vorgeschlagenen System realisieren wollen, um Selbstorganisation in verteilten Systemen näher zu untersuchen.

The stationary heat equation is solved with periodic boundary conditions in geometrically complex composite materials with high contrast in the thermal conductivities of the individual phases. This is achieved by harmonic averaging and explicitly introducing the jumps across the material interfaces as additional variables. The continuity of the heat flux yields the needed extra equations for these variables. A Schur-complent formulation for the new variables is derived that is solved using the FFT and BiCGStab methods. The EJ-HEAT solver is given as a 3-page Matlab program in the Appendix. The C++ implementation is used for material design studies. It solves 3-dimensional problems with around 190 Mio variables on a 64-bit AMD Opteron desktop system in less than 6 GB memory and in minutes to hours, depending on the contrast and required accuracy. The approach may also be used to compute effective electric conductivities because they are governed by the stationary heat equation.

Error estimates for quasistatic global elastic correction and linear kinematic hardening material
(2006)

We consider in this paper the quasistatic boundary value problems of linear elasticity and nonlinear elastoplasticity with linear kinematic hardening material. We derive expressions and estimates for the difference of solutions (i.e. stress, strain and displacement) of both models. Further, we study the error between the elastoplastic solution and the solution of a postprocessing method, that corrects the solution of the linear elastic problem in order to approximate the elastoplastic model.

This report discusses two approaches for a posteriori error indication in the linear elasticity solver DDFEM: An indicator based on the Richardson extrapolation and Zienkiewicz-Zhu-type indicator. The solver handles 3D linear elasticity steady-state problems. It uses own input language to describe the mesh and the boundary conditions. Finite element discretization over tetrahedral meshes with first or second order shape functions (hierarchical basis) has been used to resolve the model. The parallelization of the numerical method is based on the domain decomposition approach. DDFEM is highly portable over a set of parallel computer architectures supporting the MPI-standard.

With the UML 2.0 standard, the Unified Modeling Language took a big step towards SDL, incorporating many features of the language. SDL is a mature and complete language with formal semantics. The Z.109 standard defines a UML Profile for SDL, mapping UML constructs to corresponding counterparts in SDL, giving them a precise semantics. In this report, we present a case study for the formalisation of the Z.109 standard. The formal definition makes the mapping precise and can be used to derive tool support.

In dem Forschungsvorhaben “Schubtragverhalten des Stahlbetongurtes von Verbundträgern im Bereich von großen Stegöffnungen“ wurden umfangreiche experimentelle und rechnerische Untersuchungen zum Querkrafttragverhalten und zur Querkrafttragfähigkeit des Betongurts im Bereich von großen Stegöffnungen durchgeführt. Anhand von 21 großmaßstäblichen Traglastversuchen, die erstmals so konzipiert waren, dass im Öffnungsbereich nahezu die gesamte Querkraft durch den Betongurt übertragen werden musste, konnte die Querkrafttragfähigkeit des Betongurts bestimmt werden. Neue Erkenntnisse über den Lastabtragungs- und Versagensmechanismus im Öffnungsbereich konnten durch die Auswertung der Dehnungen der Kopfbolzendübel im Öffnungsbereich und das nachträgliche Aufsägen des Betongurts der Versuchsträger gewonnen werden. Im rechnerischen Teil wurden ein dreidimensionales FE-Modell erstellt, das die Versuche in ihren wesentlichen Teilen abbildete, und Vergleichsberechnungen durchgeführt. Durch den Vergleich der rechnerischen mit den experimentell ermittelten Werten wurde das Modell überprüft. Auf dieser Grundlage wurden anschließend Parameteruntersuchungen durchgeführt. Schließlich wurde auf der Basis der experimentellen und rechnerischen Untersuchungen ein Ingenieurmodell zur Bestimmung der Querkrafttragfähigkeit im Öffnungsbereich entwickelt, mit dem sich die Querkrafttragfähigkeit des Betongurts im Öffnungsbereich nachweisen lässt. Ferner stellte sich heraus, dass die Querkrafttragfähigkeit des Betongurts im Öffnungsbereich durch Dübelleisten erheblich gesteigert werden kann, was wirtschaftliche Vorteile eröffnet.

Reliable methods for the analysis of tolerance-affected analog circuits are of great importance in nowadays microelectronics. It is impossible to produce circuits with exactly those parameter specifications proposed in the design process. Such component tolerances will always lead to small variations of a circuit’s properties, which may result in unexpected behaviour. If lower and upper bounds to parameter variations can be read off the manufacturing process, interval arithmetic naturally enters the circuit analysis area. This paper focuses on the frequency-response analysis of linear analog circuits, typically consisting of current and voltage sources as well as resistors, capacitances, inductances, and several variants of controlled sources. These kind of circuits are still widely used in analog circuit design as equivalent circuit diagrams for representing in certain application tasks Interval methods have been applied to analog circuits before. But yet this was restricted to circuit equations only, with no interdependencies between the matrix elements. But there also exist formulations of analog circuit equations containing dependent terms. Hence, for an efficient application of interval methods, it is crucial to regard possible dependencies in circuit equations. Part and parcel of this strategy is the handling of fill-in patterns for those parameters related to uncertain components. These patterns are used in linear circuit analysis for efficient equation setup. Such systems can efficiently be solved by successive application of the Sherman-Morrison formula. The approach can also be extended to complex-valued systems from frequency domain analysis of more general linear circuits. Complex values result here from a Laplace transform of frequency-dependent components like capacitances and inductances. In order to apply interval techniques, a real representation of the linear system of equations can be used for separate treatment of real and imaginary part of the variables. In this representation each parameter corresponds to the superposition of two fill-in patterns. Crude bounds – obtained by treating both patterns independently – can be improved by consideration of the correlations to tighter enclosures of the solution. The techniques described above have been implemented as an extension to the toolbox Analog Insydes, an add-on package to the computer algebra system Mathematica for modeling, analysis, and design of analog circuits.

In this article, we give some generalisations of existing Lipschitz estimates for the stop and the play operator with respect to an arbitrary convex and closed characteristic a separable Hilbert space. We are especially concerned with the dependency of their outputs with respect to different scalar products.

Testing a new suspension based on real load data is performed on elaborate multi channel test rigs. Usually wheel forces and moments measured during driving maneuvers are reproduced on the rig. Because of the complicated interaction between rig and suspension each new rig configuration has to prove its efficiency with respect to the requirements and the configuration might be subject to optimization. This paper deals with modeling a new rig concept based on two hexapods. The real physical rig has been designed and meanwhile built by MOOG-FCS for VOLKSWAGEN. The aim of the simulation project reported here was twofold: First the simulation of the rig together with real VOLKSWAGEN suspension models at a time where the design was not yet finalized was used to verify and optimize the desired properties of the rig. Second the simulation environment was set up in a way that it can be used to prepare real tests on the rig. The model contains the geometric configuration as well as the hydraulics and the controller. It is implemented as an ADAMS/Car template and can be combined with different suspension models to get a complete assembly representing the entire test rig. Using this model, all steps required for a real test run such as controller adaptation, drive file iteration and simulation can be performed. Geometric or hydraulic parameters can be modified easily to improve the setup and adapt the system to the suspension and the load data.