arXiv subjects

Thomas Weiland

Publications and source records attributed to Thomas Weiland.

12 recordsLinked to original sources

arXiv2026

Eta-Virginids: another asteroidal meteoroid stream

Eta-Virginids is a less-known meteor shower active in March. We investigated the meteoroids of this shower using fireball data from the European Fireball Network supplemented by video data of faint meteors. We first derived the criteria for assigning meteors to this shower. A fragmentation model was then applied to selected shower fireballs with good deceleration data and light curves. Meteoroid fragmentation strengths and bulk densities were derived and compared with three other showers. We have confirmed the four year periodicity in the activity of eta-Virginids and their presence in the 3:1 mean motion resonance with Jupiter. The orbital period of four years was directly measured for the fireballs. Fainter meteors showed somewhat longer periods but the shower is poor in faint meteors. No member fainter than magnitude +1 was observed instrumentally. The physical properties of meteoroids are different from cometary streams and are similar to the Geminids. The limiting fragmentation strength of 0.5 MPa and typical bulk density of cm-sized meteoroids of 1500 kg/m3 suggest that the parent body is a carbonaceous asteroid. Besides Geminids, eta-Virginids is another stream of asteroidal origin. Some small meteoroids have densities around 2500 kg/m3. Three asteroids of the sizes between 40 - 120 meters have been found to have similar orbits but their relation to eta-Virginids remains uncertain.

astro-ph.EP↗

arXiv2023

Reformulation and generalisation of the air-gap element

The air-gap macro element is reformulated such that rotation, rotor or stator skewing and rotor eccentricity can be incorporated easily. The air-gap element is evaluated using Fast Fourier Transforms which in combination with the Conjugate Gradient algorithm leads to highly efficient and memory inexpensive iterative solution scheme. The improved air-gap element features beneficial approximation properties and is competitive to moving-band and sliding-surface technique.

cs.CE↗

arXiv2017

A Space-Time Approach for the Time-Domain Simulation in a Rotating Reference Frame

We approach the discretisation of Maxwell's equations directly in space-time without making any non-relativistic assumptions with the particular focus on simulations in rotating reference frames. As a research example we study Sagnac's effect in a rotating ring resonator. After the discretisation, we express the numerical scheme in a form resembling 3D FIT with leapfrog. We compare the stability and convergence properties of two 4D approaches, namely FIT and FEM, both using Whitney interpolation.

physics.comp-ph↗

arXiv2016

Discretization of Maxwell's Equations for Non-inertial Observers Using Space-Time Algebra

We employ Maxwell's equations formulated in Space-Time Algebra to perform discretization of moving geometries directly in space-time. All the derivations are carried out without any non-relativistic assumptions, thus the application area of the scheme is not restricted to low velocities. The 4D mesh construction is based on a 3D mesh stemming from a conventional 3D mesh generator. The movement of the system is encoded in the 4D mesh geometry, enabling an easy extension of well-known 3D approaches to the space-time setting. As a research example, we study a manifestation of Sagnac's effect in a rotating ring resonator. In case of constant rotation, the space-time approach enhances the efficiency of the scheme, as the material matrices are constant for every time step, without abandoning the relativistic framework.

cs.CE↗

arXiv2016

Stochastic Modeling and Regularity of the Nonlinear Elliptic Curl-Curl Equation

This paper addresses the nonlinear elliptic curl-curl equation with uncertainties in the material law. It is frequently employed in the numerical evaluation of magnetostatic fields, where the uncertainty is ascribed to the so-called B-H curve. A truncated Karhunen-Loève approximation of the stochastic B-H curve is presented and analyzed with regard to monotonicity constraints. A stochastic non-linear curl-curl formulation is introduced and numerically approximated by a finite element and collocation method in the deterministic and stochastic variable, respectively. The stochastic regularity is analyzed by a higher order sensitivity analysis. It is shown that, unlike to linear and several nonlinear elliptic problems, the solution is not analytic with respect to the random variables and an algebraic decay of the stochastic error is obtained. Numerical results for both the Karhunen-Loève expansion and the stochastic curl-curl equation are given for illustration.

math.NA↗

arXiv2014

A Space-Time Discontinuous Galerkin Trefftz Method for time dependent Maxwell's equations

We consider the discretization of electromagnetic wave propagation problems by a discontinuous Galerkin Method based on Trefftz polynomials. This method fits into an abstract framework for space-time discontinuous Galerkin methods for which we can prove consistency, stability, and energy dissipation without the need to completely specify the approximation spaces in detail. Any method of such a general form results in an implicit time-stepping scheme with some basic stability properties. For the local approximation on each space-time element, we then consider Trefftz polynomials, i.e., the subspace of polynomials that satisfy Maxwell's equations exactly on the respective element. We present an explicit construction of a basis for the local Trefftz spaces in two and three dimensions and summarize some of their basic properties. Using local properties of the Trefftz polynomials, we can establish the well-posedness of the resulting discontinuous Galerkin Trefftz method. Consistency, stability, and energy dissipation then follow immediately from the results about the abstract framework. The method proposed in this paper therefore shares many of the advantages of more standard discontinuous Galerkin methods, while at the same time, it yields a substantial reduction in the number of degrees of freedom and the cost for assembling. These benefits and the spectral convergence of the scheme are demonstrated in numerical tests.

math.NA↗

arXiv2014

Transparent boundary conditions in a Discontinuous Galerkin Trefftz method

The modeling and simulation of electromagnetic wave propagation is often accompanied by a restriction to bounded domains which requires the introduction of artificial boundaries. The corresponding boundary conditions should be chosen in order to minimize parasitic reflections. In this paper, we investigate a new type of transparent boundary condition for a discontinuous Galerkin Trefftz finite element method. The choice of a particular basis consisting of polynomial plane waves allows us to split the electromagnetic field into components with a well 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 by numerical tests. A comparison with first order absorbing boundary conditions, that are frequently used in practice, is made. For a proper choice of basis functions, we observe spectral convergence in our numerical test and an overall dissipative behavior for which we also give some theoretical explanation.

math.NA↗

arXiv2013

Non-dissipative space-time $hp$-discontinuous Galerkin method for the time-dependent Maxwell Equations

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 \cite{vegt_space_2002} test and trial space do not coincide. This allows for obtaining a non-dissipative method. In order to obtain an efficient implementation, a hierarchical tensor product basis in space and time is proposed. In particular it 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.

math.NA↗

arXiv2013

Discontinuous Galerkin Methods with Trefftz Approximation

We present a novel Discontinuous Galerkin Finite Element Method for wave propagation problems. The method employs space-time Trefftz-type basis functions that satisfy the underlying partial differential equations and the respective interface boundary conditions exactly in an element-wise fashion. The basis functions can be of arbitrary high order, and we demonstrate spectral convergence in the $\Lebesgue_2$-norm. In this context, spectral convergence is obtained with respect to the approximation error in the entire space-time domain of interest, i.e. in space and time simultaneously. Formulating the approximation in terms of a space-time Trefftz basis makes high order time integration an inherent property of the method and clearly sets it apart from methods, that employ a high order approximation in space only.

physics.comp-ph↗

arXiv2012

High Bandwidth Pickup Design for Bunch Arrival-time Monitors for Free-Electron Laser

In this paper, we present the design and realization of high bandwidth pickup electrodes with a cutoff frequency above 40 GHz. The proposed cone-shaped pickups are part of a bunch arrival-time monitor (BAM) designed for high (> 500 pC) and low (20 pC) bunch charge operation mode providing for a time resolution of less than 10 fs for both operation modes. The proposed design has a fast voltage response, low ringing, and a resonance-free spectrum. For assessing the influence of manufacturing tolerances on the performance of the pickups, an extensive tolerance study has been performed via numerical simulations. A non-hermetic model of the pickups was built for measurement and validation purposes. The measurement and simulation results are in good agreement and demonstrate the capability of the proposed pickup system to meet the given specifications.

physics.acc-ph↗

arXiv2011

Efficient Large Scale Electromagnetics Simulations Using Dynamically Adapted Meshes with the Discontinuous Galerkin Method

A framework for performing dynamic mesh adaptation with the discontinuous Galerkin method (DGM) is presented. Adaptations include modifications of the local mesh step size (h-adaptation) and the local degree of the approximating polynomials (p-adaptation) as well as their combination. The computation of the approximation within locally adapted elements is based on projections between finite element spaces (FES), which are shown to preserve an upper limit of the electromagnetic energy. The formulation supports high level hanging nodes and applies precomputation of surface integrals for increasing computational efficiency. Error and smoothness estimates based on interface jumps are presented and applied to the fully hp-adaptive simulation of two examples in one-dimensional space. A full wave simulation of electromagnetic scattering form a radar reflector demonstrates the applicability to large scale problems in three-dimensional space.

physics.comp-ph↗

arXiv2011

Extension of the Finite Integration Technique including dynamic mesh refinement and its application to self-consistent beam dynamics simulations

An extension of the framework of the Finite Integration Technique (FIT) including dynamic and adaptive mesh refinement is presented. After recalling the standard formulation of the FIT, the proposed mesh adaptation procedure is described. Besides the linear interpolation approach, a novel interpolation technique based on specialized spline functions for approximating the discrete electromagnetic field solution during mesh adaptation is introduced. The standard FIT on a fixed mesh and the new adaptive approach are applied to a simulation test case with known analytical solution. The numerical accuracy of the two methods are shown to be comparable. The dynamic mesh approach is, however, much more efficient. This is also demonstrated for the full scale modeling of the complete RF gun at the Photo Injector Test Facility DESY Zeuthen (PITZ) on a single computer. Results of a detailed design study addressing the effects of individual components of the gun onto the beam emittance using a fully self-consistent approach are presented.

physics.comp-ph↗