## Berichte der Arbeitsgruppe Technomathematik (AGTM Report)

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#### Document Type

- Preprint (4) (remove)

#### Keywords

- numerics (2)
- Frequency Averaging (1)
- Optimal semiconductor design (1)
- Order of printed copy (1)
- Radiative Heat Trasfer (1)
- adjoints (1)
- aggressive space mapping (1)
- consistency (1)
- convergence (1)
- density gradient equation (1)

- 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.

- 269
- The Semiconductor Model Hierarchy in Optimal Dopant Profiling (2006)
- 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.

- 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.

- 261
- Initial Temperature Reconstruction for a Nonlinear Heat Equation: Application to Radiative Heat Transfer (2005)
- 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.