Vorträge

The plasma in a fusion reactor is heated by neutral beam injection: injecting high energy neutrons which quickly ionize and swirl around in the reactor's magnetic fiel. Modelling this process requires solving the Lorentz equations numerically over long times (up to a second) with very small time steps (order of nanoseconds), which means very many time steps and thus long simulation times (from days up to a week). The talk will introduce GMRES-Boris-SDC (GBSDC), a new time stepping algorithm that can reduce computational cost compared to the currently used Boris method. The method is a potpourri of various numerical techniques, including the GMRES linear solver, spectral deferred corrections, the velocity Verlet scheme and the Boris trick. I will describe the algorithm and show examples of its performance for benchmarks with varying degree of realism.

This is joint work with Dr Krasymyr Tretiak, School of Mathematics, University of Leeds.

During their work-term at TUHH the two Canadian students worked on projects relating to current research in the institute.
As their term comes to an end they will present their ongoing work in short talks.

In this talk we study sufficient conditions for obserability of systems in Banach spaces. In an abstract Banach space setting we show that an uncertainty relation together with a dissipation estimate implies an observability estimate with explicit dependence on the model parameters. Our approach unifies and generalizes the respective advantages from earlier results obtained in the context of Hilbert spaces. As an application we consider elliptic operators on Lp spaces. Combined with the well-known relation between observability and controllability we derive sufficient conditions for null-controllability and bounds on the control cost.
The talk is based on joint work with Christian Seifert and Martin Tautenhahn.

We give a unified approach to handle the problem of extending functions with values in a locally convex Hausdorff space $E$ over the field $\mathbb{K}=\mathbb{R}$ or $\mathbb{C}$, which have weak extensions in a space $\mathcal{F}(\Omega,\mathbb{K})$ of scalar-valued functions on a set $\Omega$, to functions in a vector-valued counterpart $\mathcal{F}(\Omega,E)$ of $\mathcal{F}(\Omega,\mathbb{K})$. The main tool is the representation of vector-valued functions as linear continuous operators.