Colloquium Mathematics - Dr. David Martín de Diego (Instituto de Ciencias Matemáticas, Madrid)
|When:||Tu 24-09-2019 16:00 - 17:00|
Title: New developments on discrete mechanics and geometric integration
Abstract:The simulation, control and optimization of engineering systems pose serious challenges for the development of numerical methods. The increasing complexity of application problems requires the development of reliable and efficient numerical methods to approximate the analytical solution. To increase the efficiency of computational methods as well as the quality of an approximated solution, it is essential to account for characteristic properties of the system. Discrete Geometric Mechanics, in particular Discrete Variational Mechanics, provides such computational methods using techniques of differential geometry and numerical analysis.
Variational integrators comprise a special class of geometric integrators with the goal to capture the dynamical system's behavior in a realistic way. In particular, specific properties of the underlying system are inherited by the numerical solution. In recent years, much effort has been put into the analysis and the further development of variational integrators to make them applicable to a broad class of dynamical systems, in particular for applications in simulation and optimal control of engineering systems, multi-body dynamics, nonholonomic systems… In this talk we will discuss some new developments and applications of discrete mechanics.