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Wed, 21 Jul 2010 14:10:41 +0200Wed, 21 Jul 2010 14:10:41 +0200Identification of Temperature Dependent Parameters in Radiative Heat Transfer
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2216
Laser-induced thermotherapy (LITT) is an established minimally invasive percutaneous technique of tumor ablation. Nevertheless, there is a need to predict the effect of laser applications and optimizing irradiation planning in LITT. Optical attributes (absorption, scattering) change due to thermal denaturation. The work presents the possibility to identify these temperature dependent parameters from given temperature measurements via an optimal control problem. The solvability of the optimal control problem is analyzed and results of successful implementations are shown.Oliver Tse; René Pinnau; Norbert Siedowpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2216Wed, 21 Jul 2010 14:10:41 +0200A piecewise analytical solution for Jiangs model of elastoplasticity
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1898
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.Holger Lang; Klaus Dressler; Rene Pinnaureporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1898Tue, 02 Oct 2007 12:27:59 +0200Convergent Finite Element Discretizations of the Density Gradient Equation for Quantum Semiconductors
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1864
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.Rene Pinnau; Jorge Mauricio Ruizpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1864Fri, 11 May 2007 20:46:05 +0200The Semiconductor Model Hierarchy in Optimal Dopant Profiling
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1781
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.Concetta Drago; Rene Pinnaupreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1781Tue, 26 Sep 2006 19:06:17 +0200A homotopy between the solutions of the elastic and elastoplastic boundary value problem
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1776
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.Holger Lang; Klaus Dressler; Rene Pinnau; Gerd Bitschreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1776Fri, 22 Sep 2006 16:05:14 +0200Error estimates for quasistatic global elastic correction and linear kinematic hardening material
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1775
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.Holger Lang; Klaus Dressler; Rene Pinnau; Michael Speckertreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1775Thu, 21 Sep 2006 20:54:30 +0200Lipschitz estimates for the stop and the play operator
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1773
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.Holger Lang; Klaus Dressler; Rene Pinnaureporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1773Thu, 21 Sep 2006 12:05:33 +0200Model Reduction Techniques for Frequency Averaging in Radiative Heat
Transfer
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1738
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 \(\mathrm{SP}_n\) model. We present several numerical results underlining the feasibility of our approach.Rene Pinnau; Alexander Schulzepreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1738Tue, 16 May 2006 14:12:20 +0200Parameter optimization for a stress-strain correction scheme
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1702
A gradient based algorithm for parameter identification (least-squares) is applied to a multiaxial correction method for elastic stresses and strains at notches. The correction scheme, which is numerically cheap, is based on Jiang's model of elastoplasticity. Both mathematical stress-strain computations (nonlinear PDE with Jiang's constitutive material law) and physical strain measurements have been approximized. The gradient evaluation with respect to the parameters, which is large-scale, is realized by the automatic forward differentiation technique.Holger Lang; Rene Pinnau; Klaus Dreßlerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1702Sat, 21 Jan 2006 15:51:35 +0100A multiaxial stress-strain correction scheme
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1701
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.Holger Lang; Rene Pinnau; Klaus Dreßlerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1701Sat, 21 Jan 2006 15:51:16 +0100Initial Temperature Reconstruction for a Nonlinear Heat Equation: Application to Radiative Heat Transfer
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1607
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.Sergiy Pereverzyev; Rene Pinnau; Norbert Siedowpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1607Fri, 04 Feb 2005 10:33:11 +0100