## Fraunhofer (ITWM)

### Filtern

#### Erscheinungsjahr

- 2010 (20) (entfernen)

#### Schlagworte

- optimal control (2)
- portfolio choice (2)
- work effort (2)
- Brinkman equations (1)
- Darcy’s law (1)
- Filtering (1)
- Fokker-Planck equations (1)
- Hedge funds (1)
- Kalman Filter (1)
- Lagrange formalism (1)

- Variational multiscale Finite Element Method for flows in highly porous media (2010)
- We present a two-scale finite element method for solving Brinkman’s and Darcy’s equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes’ equations byWang and Ye and the concept of subgrid approximation developed by Arbogast for Darcy’s equations. In order to reduce the “resonance error” and to ensure convergence to the global fine solution the algorithm is put in the framework of alternating Schwarz iterations using subdomains around the coarse-grid boundaries. The discussed algorithms are implemented using the Deal.II finite element library and are tested on a number of model problems.

- Comparison of quaternionic and rotationfree null space formalisms for multibody dynamics (2010)
- In this article, we summarise the rotation-free and quaternionic parametrisation of a rigid body. We derive and explain the close interrelations between both parametrisations. The internal constraints due to the redundancies in the parametrisations, which lead to DAEs, are handled with the null space technique. We treat both single rigid bodies and general multibody systems with joints, which lead to external joint constraints. Several numerical examples compare both formalisms to the index reduced versions of the corresponding standard formulations.

- A 3d model for fiber lay-down in nonwoven production processes (2010)
- In this paper a three dimensional stochastic model for the lay-down of fibers on a moving conveyor belt in the production process of nonwoven materials is derived. The model is based on stochastic diferential equations describing the resulting position of the fiber on the belt under the influence of turbulent air ows. The model presented here is an extension of an existing surrogate model, see [6, 3].

- Fluid-fiber-interactions in rotational spinning process of glass wool production (2010)
- The optimal design of rotational production processes for glass wool manufacturing poses severe computational challenges to mathematicians, natural scientists and engineers. In this paper we focus exclusively on the spinning regime where thousands of viscous thermal glass jets are formed by fast air streams. Homogeneity and slenderness of the spun fibers are the quality features of the final fabric. Their prediction requires the computation of the fuidber-interactions which involves the solving of a complex three-dimensional multiphase problem with appropriate interface conditions. But this is practically impossible due to the needed high resolution and adaptive grid refinement. Therefore, we propose an asymptotic coupling concept. Treating the glass jets as viscous thermal Cosserat rods, we tackle the multiscale problem by help of momentum (drag) and heat exchange models that are derived on basis of slender-body theory and homogenization. A weak iterative coupling algorithm that is based on the combination of commercial software and self-implemented code for ow and rod solvers, respectively, makes then the simulation of the industrial process possible. For the boundary value problem of the rod we particularly suggest an adapted collocation-continuation method. Consequently, this work establishes a promising basis for future optimization strategies.

- Asymptotic transition from Cosserat rod to string models for curved viscous inertial jets (2010)
- This work deals with the modeling and simulation of slender viscous jets exposed to gravity and rotation, as they occur in rotational spinning processes. In terms of slender-body theory we show the asymptotic reduction of a viscous Cosserat rod to a string system for vanishing slenderness parameter. We propose two string models, i.e. inertial and viscous-inertial string models, that differ in the closure conditions and hence yield a boundary value problem and an interface problem, respectively. We investigate the existence regimes of the string models in the four-parametric space of Froude, Rossby, Reynolds numbers and jet length. The convergence regimes where the respective string solution is the asymptotic limit to the rod turn out to be disjoint and to cover nearly the whole parameter space. We explore the transition hyperplane and derive analytically low and high Reynolds number limits. Numerical studies of the stationary jet behavior for different parameter ranges complete the work.

- On a numerical subgrid upscaling algorithm for Stokes-Brinkman equations (2010)
- This paper discusses a numerical subgrid resolution approach for solving the Stokes-Brinkman system of equations, which is describing coupled ow in plain and in highly porous media. Various scientic and industrial problems are described by this system, and often the geometry and/or the permeability vary on several scales. A particular target is the process of oil ltration. In many complicated lters, the lter medium or the lter element geometry are too ne to be resolved by a feasible computational grid. The subgrid approach presented in the paper is aimed at describing how these ne details are accounted for by solving auxiliary problems in appropriately chosen grid cells on a relatively coarse computational grid. This is done via a systematic and a careful procedure of modifying and updating the coecients of the Stokes-Brinkman system in chosen cells. This numerical subgrid approach is motivated from one side from homogenization theory, from which we borrow the formulations for the so called cell problem, and from the other side from the numerical upscaling approaches, such as Multiscale Finite Volume, Multiscale Finite Element, etc. Results on the algorithm's eciency, both in terms of computational time and memory usage, are presented. Comparison with solutions on full ne grid (when possible) are presented in order to evaluate the accuracy. Advantages and limitations of the considered subgrid approach are discussed.

- A regime-switching regression model for hedge funds (2010)
- The modelling of hedge funds poses a difficult problem since the available reported data sets are often small and incomplete. We propose a switching regression model for hedge funds, in which the coefficients are able to switch between different regimes. The coefficients are governed by a Markov chain in discrete time. The different states of the Markov chain represent different states of the economy, which influence the performance of the independent variables. Hedge fund indices are chosen as regressors. The parameter estimation for the switching parameter as well as for the switching error term is done through a filtering technique for hidden Markov models developed by Elliott (1994). Recursive parameter estimates are calculated through a filter-based EM-algorithm, which uses the hidden information of the underlying Markov chain. Our switching regression model is applied on hedge fund series and hedge fund indices from the HFR database.

- Optimal investment for executive stockholders with exponential utility (2010)
- The scope of this paper is to enhance the model for the own-company stockholder (given in Desmettre, Gould and Szimayer (2010)), who can voluntarily performance-link his personal wealth to his management success by acquiring stocks in the own-company whose value he can directly influence via spending work effort. The executive is thereby characterized by a parameter of risk aversion and the two work effectiveness parameters inverse work productivity and disutility stress. We extend the model to a constant absolute risk aversion framework using an exponential utility/disutility set-up. A closed-form solution is given for the optimal work effort an executive will apply and we derive the optimal investment strategies of the executive. Furthermore, we determine an up-front fair cash compensation applying an indifference utility rationale. Our study shows to a large extent that the results previously obtained are robust under the choice of the utility/disutility set-up.

- Thermodynamic consistent transport theory of Li-Ion batteries (2010)
- We will present a rigorous derivation of the equations and interface conditions for ion, charge and heat transport in Li-ion insertion batteries. The derivation is based exclusively on universally accepted principles of nonequilibrium thermodynamics and the assumption of a one step intercalation reaction at the interface of electrolyte and active particles. Without loss of generality the transport in the active particle is assumed to be isotropic. The electrolyte is described as a fully dissociated salt in a neutral solvent. The presented theory is valid for transport on a spatial scale for which local charge neutrality holds i.e. beyond the scale of the diffuse double layer. Charge neutrality is explicitely used to determine the correct set of thermodynamically independent variables. The theory guarantees strictly positive entropy production. The various contributions to the Peltier coeficients for the interface between the active particles and the electrolyte as well as the contributions to the heat of mixing are obtained as a result of the theory.

- Real-time simulation of multibodysystems for on-board applications (2010)
- Simulation of multibody systems (mbs) is an inherent part in developing and design of complex mechanical systems. Moreover, simulation during operation gained in importance in the recent years, e.g. for HIL-, MIL- or monitoring applications. In this paper we discuss the numerical simulation of multibody systems on different platforms. The main section of this paper deals with the simulation of an established truck model [9] on different platforms, one microcontroller and two real-time processor boards. Additional to numerical C-code the latter platforms provide the possibility to build the model with a commercial mbs tool, which is also investigated. A survey of different ways of generating code and equations of mbs models is given and discussed concerning handling, possible limitations as well as performance. The presented benchmarks are processed under terms of on-board real time applications. A further important restriction, caused by the real-time requirement, is a fixed integration step size. Whence, carefully chosen numerical integration algorithms are necessary, especially in the case of closed loops in the model. We investigate linearly-implicit time integration methods with fixed step size, so-called Rosenbrock methods, and compare them with respect to their accuracy and performance on the tested processors.