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- Elastic BVP (3)
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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.
In this paper we address the improvement of transfer quality in public mass transit networks. Generally there are several transit operators offering service and our work is motivated by the question how their timetables can be altered to yield optimized transfer possibilities in the overall network. To achieve this, only small changes to the timetables are allowed. The set-up makes it possible to use a quadratic semi-assignment model to solve the optimization problem. We apply this model, equipped with a new way to assess transfer quality, to the solution of four real-world examples. It turns out that improvements in overall transfer quality can be determined by such optimization-based techniques. Therefore they can serve as a first step towards a decision support tool for planners of regional transit networks.
On a multigrid solver for the threedimensional Biot poroelasticity system in multilayered domains
(2006)
In this paper, we present problem–dependent prolongation and problem–dependent restriction for a multigrid solver for the three-dimensional Biot poroelasticity system, which is solved in a multilayered domain. The system is discretized on a staggered grid using the finite volume method. During the discretization, special care is taken of the discontinuous coefficients. For the efficient multigrid solver, a need in operator-dependent restriction and/or prolongation arises. We derive these operators so that they are consistent with the discretization. They account for the discontinuities of the coefficients, as well as for the coupling of the unknowns within the Biot system. A set of numerical experiments shows necessity of use of the operator-dependent restriction and prolongation in the multigrid solver for the considered class of problems.
The paper at hand presents a slender body theory for the dynamics of a curved inertial viscous Newtonian ber. Neglecting surface tension and temperature dependence, the ber ow is modeled as a three-dimensional free boundary value problem via instationary incompressible Navier-Stokes equations. From regular asymptotic expansions in powers of the slenderness parameter leading-order balance laws for mass (cross-section) and momentum are derived that combine the unrestricted motion of the ber center-line with the inner viscous transport. The physically reasonable form of the one-dimensional ber model results thereby from the introduction of the intrinsic velocity that characterizes the convective terms.
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.
Katja is a tool generating order-sorted recursive data types as well as position types for Java, from specifications using an enhanced ML like notation. Katja’s main features are its conciseness of specifications, the rich interface provided by the generated code and the Java atypical immutability of types. After several stages of extending and maintaining the Katja project, it became apparent many changes had to be done. The original design of Katja wasn’t prepared for the introduction of several backends, the introduction of position sorts and constant feature enhancements and bug fixes. By supplying this report Katja reaches release status for the first time.
In this paper we propose a finite volume discretization for the threedimensional Biot poroelasticity system in multilayered domains. For the stability reasons, staggered grids are used. The discretization accounts for discontinuity of the coefficients across the interfaces between layers with different physical properties. Numerical experiments, based on the proposed discretization showed second order convergence in the maximum norm for the primary as well as flux unknowns of the system. A certain application example is presented as well.
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
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.
Die Simulation von Prüfständen und insbesondere von Baugruppen und Gesamtfahrzeugen auf Prüfständen durch Kopplung von Mehrkörpersimulation mit Modellen für Regelung und Aktuatorik leistet einen wesentlichen Beitrag zur Entwicklungszeitverkürzung. In diesem Beitrag wird ein Kooperationsprojekt vorgestellt, in dem ein Co- Simulationsmodell für die beweglichen Massen sowie die Regelung und Hydraulik eines Gesamtfahrzeugprüfstands erstellt wurde. Es wird sowohl auf die Validierung des Fahrzeugmodells durch Straßenmessungen als auch auf die Identifikation und Validierung des Prüfstandsmodells einschließlich Servohydraulik und Regelung eingegangen.