Within the field of simulation this thesis focused on numerical issues emerging from the practical application of numerical algorithms to realistic examples from TCAD. Specialized mathematical publications often tend to ignore the full complexity of engineering problems. Often they abstract too much or only deal with unrealistically simple problems which have a nice mathematical structure. Then they leave the generic ``dirty'' problem with less structure to the engineer specialized on the field who is supposed to solve it by adapting methods mostly developed for the ``nice'' case. To deal with complex problems good software engineering skills are required. It is the required combination of both software engineering and mathematical skills together with the requirement of basic knowledge from the field of application which makes programming for TCAD a difficult task.

Coming from a theoretical research community (i.e., mathematics), the main conclusion I draw from writing this thesis is not at all related to any details about this or that problem in device simulation, although a whole branch of software industry and a part of academia make their living from this. The more important experience was the personal excursion out of the ``ivory tower'' of mathematics and doing some industry-related research on a research institute of international reputation.

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R. Kosik: Numerical Challenges on the Road to NanoTCAD