School of Mathematics and Natural Sciences

Welcome at the

Chair of Applied Mathematics / Numerical Analysis

The progress in data processing over the last forty years has opened all new application areas to mathematics and demands its continuous development as a modern science. A close, natural interaction of mathematics, engineering, and computer science emerged and has settled in a new discipline, scientific computing. Today, the traditional engineering and natural sciences problems are supplemented by an increasing number of tasks from economy and social sciences.

The economic impact of scientific computing is briefly highlighted by slogans such as "high-tech equals math-tech" or "high technology equals mathematical technology".

Besides the classical dichotomy, theory and experiment, here simulation offers a third access to knowledge, and is already indispensable for technological progress. So, the specification of this task is precisely defined by the Association of Engineers (VDI) in Norm 3633. It can be concisely stated as: Simulation is the reproduction of a system and its dynamic processes in an experimental model to achieve knowledge which carries over to reality.

Real objects and their interrelations are replaced by mathematical models. These are tested and experienced: simulation is experimentation with models. In an industrial environment, simulation replaces the time and cost consuming real, physical experiments by computer tasks.

Our research group represents and considers numerical analysis as the core part of scientific computing. The main objective of numerical analysis is the development, analysis and implementation of efficient and robust numerical algorithms to simulate mathematical models. The analytical properties of mathematical models affect this task as well as the hard- and software implications of underlying computer environments; both have to be included to the method's development. In the context of scientific computing, numerical analysis is per se interdisciplinary.

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