I³MS - Schöps Seminar
Prof. Dr. Sebastian Schöps - On Isogeometric Analysis in Frequency Domain and Finite Differences in Space-Time for Electromagnetics
Graduate School CE , Technische Universität Darmstadt
The numerical simulation of particle accelerator experiments, e.g. the electromagnetic field distributions in a cavity or in a bending magnet, is a challenging task because these devices have to operate at the physical limits, i.e., particles are accelerated almost up to the speed of light. A high numerical accuracy is inevitable since small errors can have serious consequences. In particular the description of the device's geometry is crucial for determining its performance. In the case of accelerator cavities, controlling the resonant frequency of the eigenmodes is important in order to guarantee the synchronization of the electromagnetic field and the particle beam which determines the accelerating efficiency of the device. Furthermore, mechanical deformations, either due to manufacturing imperfections or due to the electromagnetic pressure (Lorentz detuning) may cause a non-negligible frequency shift. The first part of this talk will discuss the application of (high order) Isogeometric Analysis to the coupled electromagnetic-mechanic problem and show that this approach is particularly well suited for numerical shape optimization. The second part of the talk will deal with a (lowest order) discretization of Maxwell’s equations in integral form in space-time. The approach is based on the Geometric Algebra associated with Minkowski space-time and is closely related to Discrete Exterior Calculus and the Finite Integration Technique. The motion of the system, e.g., up to the speed of light, is encoded in the geometry of the space-time mesh. As a research example, a rotating ring resonator with electric boundary conditions is investigated.