29 research outputs found
Instantaneous control of interacting particle systems in the mean-field limit
Controlling large particle systems in collective dynamics by a few agents is
a subject of high practical importance, e.g., in evacuation dynamics. In this
paper we study an instantaneous control approach to steer an interacting
particle system into a certain spatial region by repulsive forces from a few
external agents, which might be interpreted as shepherd dogs leading sheep to
their home. We introduce an appropriate mathematical model and the
corresponding optimization problem. In particular, we are interested in the
interaction of numerous particles, which can be approximated by a mean-field
equation. Due to the high-dimensional phase space this will require a tailored
optimization strategy. The arising control problems are solved using adjoint
information to compute the descent directions. Numerical results on the
microscopic and the macroscopic level indicate the convergence of optimal
controls and optimal states in the mean-field limit,i.e., for an increasing
number of particles.Comment: arXiv admin note: substantial text overlap with arXiv:1610.0132
Model Reduction Techniques for Frequency Averaging in Radiative Heat Transfer
We study model reduction techniques for frequency averaging in radiative heat transfer. Especially, we employ proper orthogonal decomposition in combination with the method of snapshots to devise an automated a posteriori algorithm, which helps to reduce significantly the dimensionality for further simulations. The reliability of the surrogate models is tested and we compare the results with two other reduced models, which are given by the approximation using the weighted sum of gray gases and by an frequency averaged version of the so-called model. We present several numerical results underlining the feasibility of our approach
The Semiconductor Model Hierarchy in Optimal Dopant Profiling
We consider optimal design problems for semiconductor devices which are simulated using the energy transport model. We develop a descent algorithm based on the adjoint calculus and present numerical results for a ballistic diode. Further, we compare the optimal doping profile with results computed on basis of the drift diffusion model. Finally, we exploit the model hierarchy and test the space mapping approach, especially the aggressive space mapping algorithm, for the design problem. This yields a significant reduction of numerical costs and programming effort
Convergent Finite Element Discretizations of the Density Gradient Equation for Quantum Semiconductors
We study nonlinear finite element discretizations for the density gradient equation in the quantum drift diffusion model. Especially, we give a finite element description of the so--called nonlinear scheme introduced by {it Ancona}. We prove the existence of discrete solutions and provide a consistency and convergence analysis, which yields the optimal order of convergence for both discretizations. The performance of both schemes is compared numerically, especially with respect to the influence of approximate vacuum boundary conditions
A piecewise analytical solution for Jiangs model of elastoplasticity
In this article, we present an analytic solution for Jiang's constitutive model of elastoplasticity. It is considered in its stress controlled form for proportional stress loading under the assumptions that the one-to-one coupling of the yield surface radius and the memory surface radius is switched off, that the transient hardening is neglected and that the ratchetting exponents are constant.In diesem Artikel stellen wir eine analytische Lösung fĂŒr das Jiangsche ElastoplastizitĂ€tsmodell vor. Wir betrachten es in seiner spannungskontrollierten Version unter proportionaler Belastung und unter den Annahmen, dass die Eins-zu-Eins-Kopplung zwischen dem FliessflĂ€chenradius und dem GedĂ€chtnisflĂ€chenradius ausgeschaltet ist, dass transiente Verfestigung vernachlĂ€ssigt wird und dass die Ratchettingexponenten konstant sind
Initial Temperature Reconstruction for a Nonlinear Heat Equation: Application to Radiative Heat Transfer
Consider a cooling process described by a nonlinear heat equation. We are interested to recover the initial temperature from temperature measurements which are available on a part of the boundary for some time. Up to now even for the linear heat equation such a problem has been usually studied as a nonlinear ill-posed operator equation, and regularization methods involving Frechet derivatives have been applied. We propose a fast derivative-free iterative method. Numerical results are presented for the glass cooling process, where nonlinearity appears due to radiation
A multiaxial stress-strain correction scheme
A method to correct the elastic stress tensor at a fixed point of an elastoplastic body, which is subject to exterior loads, is presented and analysed. In contrast to uniaxial corrections (Neuber or ESED), our method takes multiaxial phenomena like ratchetting or cyclic hardening/softening into account by use of Jiang's model. Our numerical algorithm is designed for the case that the scalar load functions are piecewise linear and can be used in connection with critical plane/multiaxial rainflow methods in high cycle fatigue analysis. In addition, a local existence and uniqueness result of Jiang's equations is given.Es wird eine Methode vorgestellt, den elastischen Spannungstensor an einem festen Punkt eines elastoplastischen Körpers, der Ă€uĂeren Lasten ausgesetzt ist, zu korrigieren. Im Gegensatz zu einachsigen Korrekturen (Neuber oder ESED) berĂŒcksichtigt unsere Methode durch die Benutzung des Jiang-Modells mehrachsige MaterialphĂ€nomene wie Ratchetting oder zyklische Ver-/Entfestigung. Unser Algorithmus ist fĂŒr den Fall stĂŒckweiser linearer skalarer Lastfunktionen zurechtgeschnitten und kann zur Betriebsfestigkeitsberechnung (kritische Schnittebenen, mehrachsiges Rainflow) bei hoher Schwingspielzahl verwendet werden. ZusĂ€tzlich wird ein lokaler Existenz- und Eindeutigkeitssatz fĂŒr die Jiang'schen Gleichungen bewiesen
Lipschitz estimates for the stop and the play operator
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.In diesem Artikel geben wir einige Verallgemeinerungen bestehender LipschitzabschĂ€tzungen fĂŒr den Stop- und Play-Operator bezĂŒglich einer beliebigen konvexen, abgeschlossenen Charakteristik in einem separablen Hilbertraum. Wir sind vor allem an der AbhĂ€ngigkeit ihrer Outputs bezĂŒglich verschiedener Skalarprodukte interessiert