Doctoral Program: Partial Differential Equations - Modelling, Analysis, Numerical Methods and Optimization

Many application problems coming from physics, chemistry, biology, or engineering sciences are described by mathematical models involving Partial Differential Equations (PDEs). Often such problems involve different kinds of nonsmooth structures (singularities, interfaces, inequality constraints, etc.). The mathematical treatment of the corresponding PDE-based models is crucial for the efficient solution of practical problems. There is a significant demand for highly qualified junior scientists with postgraduate education and experience in this area, in academia as well as in industry and commerce. The international research training group (IGDK) "Optimization and Numerical Analysis for Partial Differential Equations with Nonsmooth Structures" intends to meet this demand. The major goals of the proposed international research training group are: Transfer of cutting-edge research topics to the education of doctoral students. Development and investigation of novel methods in numerical treatment and optimization for problems involving PDEs and possessing nonsmooth structures. The involved institutions in Munich and Graz contribute to the joint research program through their internationally visible scientific strengths: The Technische Universität München has long range experience in the analytical and numerical treatment of nonlinear phenomena, where the institutes in Graz contribute their expertise in optimization, variational calculus, and numerical analysis. The combination of these expertise will result in high synergy effects which shall be highlighted and exploited by this international research training group: Methodological approaches ranging from adaptivity and nonsmooth optimization to the treatment of interfaces and shapes will enter in the research and study program of the proposed international research training group. Our concept for a successful education of doctoral students will be based upon bilateral supervision, mentoring, and performance control. Simultaneously we shall encourage doctoral students to early scientific independence. The study program consisting of lectures, compact courses, and summer schools will provide the knowledge of state-of-the art methods for numerical analysis and optimization of problems governed by PDEs.