Numerical analysis and scientific computing

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Accurate numerical models are the backbone of our modern society. Of particular relevance are numerical methods that can be used for solving physical problems over time periods ranging from a few milliseconds to several thousands of years and longer. Such methods are required in astronomy, geophysics, mathematical biology and climate science. Traditional numerical methods generally do not satisfy the accuracy needs imposed by these fields. The numerical methods I will develop as a Chair will preserve geometric properties such as symmetries and conservation laws of physical models, which is a main requirement for obtaining precise long time numerical solutions.