Department of Mathematics colloquium - Sibe Mardešić presents a sequence of lectures given by leading experts in the fields of theoretical and applied mathematics. The lectures take place at the Department of Mathematics, Faculty of Science, Bijenička cesta 30, Zagreb.
Lecture announcement
About the lecturer: Volker Mehrmann received his Diploma in mathematics in 1979, his Ph.D. in 1982, and his habilitation in 1987 from the University of Bielefeld, Germany. He spent research years at Kent State University in 1979-1980, at the University of Wisconsin in 1984-1985, and at IBM Research Center in Heidelberg in 1988--1989. After spending the years 1990-1992 as a visiting full professor at the RWTH Aachen, he was a full professor at TU Chemnitz from 1993 to 2000. He was full professor for Mathematics at TU Berlin until his retirement in October 2023. He is a member of acatech (the German academy of engineering), academia europaea and the European Academy of Scienes, he was president of GAMM the (International association of Applied Mathematics and Mechanics), and until the end of 2022 president of the European Mathematical Society (EMS). He was chair of MATHEON, the Research Center `Mathematics for key technologies´ and the Einstein Center ECMath in Berlin. Volker Mehrmann is SIAM and AMS Fellow, has held an ERC Advanced Grant and also was member of the ERC Mathematics Panel. He is editor of several journals in numerical analysis and editor-in-chief of Linear Algebra and its Applications. His research interests are in the areas of numerical mathematics/scientific computing, applied and numerical linear algebra, control theory, the theory and numerical solution of differential-algebraic equations, and in energy based mathematical modeling.
Lecture abstract: Mathematical models in form of differential equations are used in all areas of science and engineering for the simulation, control and optimization of physical systems. Ideally such models are close to the real physical system in the sense that the physical properties are encoded in the mathematical structure of the equations. The model equations should be easy to analyze and allow for good numerical methods that reflect the physical properties as well. A modern modeling paradigm is that of port-Hamiltonian systems, which originates from Hamilton dynamics enriched with inputs, outputs and constraints. We will describe this mathematical framework and analyze its properties from an algebraic, analytic and geometric point of view. We will illustrate the successful use of the model class at the hand of the control of district heating networks modelled by the energy based formulation of the incompressible Euler equations.