# Paper on Optimal Control of the Inhomogeneous Relativistic Maxwell Newton Lorentz Equations

Oliver Thoma and Christian Meyer of the Chair of Scientific Computing at TU Dortmund and I submitted a paper on the optimal control of the inhomogeneous relativistic Maxwell Newton Lorentz equations. The abstract reads

This note is concerned with an optimal control problem governed by the relativistic Maxwell-Newton-Lorentz equations, which describes the motion of charges particles in electro-magnetic fields and consists of a hyperbolic PDE system coupled with a nonlinear ODE. An external magnetic field acts as control variable. Additional control constraints are incorporated by introducing a scalar magnetic potential which leads to an additional state equation in form of a very weak elliptic PDE. Existence and uniqueness for the state equation is shown and the existence of a global optimal control is established. Moreover, first-order necessary optimality conditions in form of Karush-Kuhn-Tucker conditions are derived. A numerical test illustrates the theoretical findings.

Please find the preprint on arXiv.

On Friday, Nov 7 Alexander Kuhl successfully defended his thesis entitled

Entwicklung und Realisierung eines 40 GHz Ankunftszeitmonitors für Elektronenpakete für FLASH und den European XFEL

(Development and Realization of a 40 GHz Bunch Arrival Time Monitor for FLASH and European XFEL)

Congratulations!

# Paper on Transparent Boundary Conditions in a Discontinuous Galerkin Trefftz method

Fritz Kretzschmar, Herbert Egger, Igor Tsukerman, Thomas Weiland and I submitted a paper on transparent boundary conditions in the Discontinuous Galerkin Trefftz method.

EDIT: The paper was published in Applied Mathematics and Computation
Volume 267, Pages 42–55

The modeling and simulation of electromagnetic wave propagations is often accompanied by a restriction to bounded domains and the introduction of artificial boundary conditions which should be chosen in order to minimize parasitic reflections. In this paper, we investigate a new type of transparent boundary condition and its implementation in a Discontinuous Galerkin Trefftz Finite Element Method. The choice of a particular set of basis functions allows us to split the electromagnetic field into components with a specified direction of propagation. The reflections at the artificial boundaries are then reduced by penalizing components of the field incoming into the space-time domain of interest. We formally introduce this concept, discuss its realization within the discontinuous Galerkin framework, and demonstrate the performance of the resulting approximations in comparison with commonly used absorbing boundary conditions. In our numerical tests, we observe spectral convergence in the L2 norm and a dissipative behavior for which we provide a theoretical explanation.

# Paper on a Non-dissipative space–time hp-discontinuous Galerkin method for the time-dependent Maxwell equations published in JCP

Our paper dealing with the PhD project of Martin Lilienthal has been published in JCP: Non-dissipative space–time hp-discontinuous Galerkin method for the time-dependent Maxwell equations. The abstract reads:

A finite element method for the solution of the time-dependent Maxwell equations in mixed form is presented. The method allows for local hp-refinement in space and in time. To this end, a space–time Galerkin approach is employed. In contrast to the space–time DG method introduced in [Van der Vegt, JCP(182) 2002] test and trial spaces do not coincide. This allows for obtaining a non-dissipative method. To obtain an efficient implementation, a hierarchical tensor product basis in space and time is proposed. This allows to evaluate the local residual with a complexity of $$\mathcal{O}(p^4)$$ and $$\mathcal{O}(p^5)$$ for affine and non-affine elements, respectively.

# New Job from August 2014

I am starting a new position tomorrow — and will convert into a geophysicist (watch this for some background info). These are my new utensils:

Ok, seriously:
I wish to thank the Alexander von Humboldt-Foundation for supporting me over the last two years.
Particularly, I wish to thank Prof. Christian Hafner and the Institute of Electromagnetic Fields at ETH Zurich. Prof. Hafner was as welcoming as anyone can possibly be. Experiencing how he still enjoys his research after more than 35 years made a strong impression on me. Thank you!

Starting from August I am with the Geophysical Fluid Dynamics group of Prof. Tackley at ETH. They give me the opportunity to join the GeoPC project, which deals with infrastructure development for hybrid parallel smoothers for multigrid preconditioners. GeoPC is part of the larger PASC (Platform for Advanced Scientific Computing) initiative. The abstract of the project proposal reads:

The GeoPC project is developing computational infrastructure to enable massively parallel, scalable smoothers and coarse grid solvers to be used within multigrid preconditioners. This infrastructure is intended to (i) facilitate the execution of high resolution, 3D geodynamic models of the planetary evolution; (ii) provide the Earth Science community (and others) with a suite of continually maintained and re-usable HPC components to build robust multi-level preconditioners (iii) position Swiss computational geosciences in the emerging exa-scale era.

GeoPC is a PASC co-design project involving the University of Lugano (USI), the Swiss Federal Institute of Technology (ETH), University of Chicago (UC), Vienna University of Technology (TU Wien), as well as other stakeholders.

Our developments will become part of PETSc, the Portable, Extensible Toolkit for
Scientific Computation. I am very much looking forward to contributing to a library as renowned as PETSc!

My new coordinates are:
ETH Zurich
Institute of Geophysics – Geophysical Fluid Dynamics
NO H23, Sonneggstrasse 5, 8092 Zurich, Switzerland
Phone: +41 44 632 0244

# Student Paper Competition Award for Fritz Kretzschmar

Fritz Kretzschmar received a Student Paper Competition Award for his contribution entitled

The Discontinuous Galerkin Trefftz Method

at the 12th International Workshop on Finite Elements for Microwave Engineering (FEM2014). Coauthors are Igor Tsukerman, Thomas Weiland and myself. Congratulations!

If you are interested in more information on the time-domain DG Trefftz method have a look at our recent paper in JCAM and/or contact Fritz or me.