## Berichte der Arbeitsgruppe Technomathematik (AGTM Report)

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#### Keywords

- Boltzmann Equation (7)
- Numerical Simulation (5)
- Elastoplastizität (4)
- Elastoplasticity (3)
- Hysterese (3)
- lattice Boltzmann method (3)
- low Mach number limit (3)
- Elastic BVP (2)
- Elastisches RWP (2)
- Elastoplastisches RWP (2)

- 275
- Identification of Temperature Dependent Parameters in Radiative Heat Transfer (2010)
- 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.

- 273
- Optimal Control of Film Casting Processes (2008)
- We present an optimal control approach for the isothermal film casting process with free surfaces described by averaged Navier-Stokes equations. We control the thickness of the film at the take-up point using the shape of the nozzle. The control goal consists in finding an even thickness profile. To achieve this goal, we minimize an appropriate cost functional. The resulting minimization problem is solved numerically by a steepest descent method. The gradient of the cost functional is approximated using the adjoint variables of the problem with fixed film width. Numerical simulations show the applicability of the proposed method.

- 274
- Optimal Control of Melt Spinning Processes (2008)
- An optimal control problem for a mathematical model of a melt spinning process is considered. Newtonian and non--Newtonian models are used to describe the rheology of the polymeric material, the fiber is made of. The extrusion velocity of the polymer at the spinneret as well as the velocity and temperature of the quench air serve as control variables. A constrained optimization problem is derived and the first--order optimality system is set up to obtain the adjoint equations. Numerical solutions are carried out using a steepest descent algorithm.

- 270
- Convergent Finite Element Discretizations of the Density Gradient Equation for Quantum Semiconductors (2007)
- 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.

- 271
- A condition that a continuously deformed, simply connected body does not penetrate itself (2007)
- In this article we give a sufficient condition that a simply connected flexible body does not penetrate itself, if it is subjected to a continuous deformation. It is shown that the deformation map is automatically injective, if it is just locally injective and injective on the boundary of the body. Thereby, it is very remarkable that no higher regularity assumption than continuity for the deformation map is required. The proof exclusively relies on homotopy methods and the Jordan-Brouwer separation theorem.

- 272
- A piecewise analytical solution for Jiangs model of elastoplasticity (2007)
- 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.

- 265
- Model Reduction Techniques for Frequency Averaging in Radiative Heat Transfer (2006)
- 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.

- 266
- Lipschitz estimates for the stop and the play operator (2006)
- 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.

- 267
- 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.

- 268
- A homotopy between the solutions of the elastic and elastoplastic boundary value problem (2006)
- 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.