A simple preconditioned domain decomposition method for electromagnetic scattering problems

We present a domain decomposition method (DDM) devoted to the iterative solution of time-harmonic electromagnetic scattering problems, involving large and resonant cavities. This DDM uses the electric field integral equation (EFIE) for the solution of Maxwell problems in both interior and exterior subdomains, and we propose a simple preconditioner for the global method, based on the single layer operator restricted to the fictitious interface between the two subdomains.Comment: 23 page

Numerical simulation of electromagnetic fields in complex multi-cavity superconducting radio frequency resonators

This thesis deals with the computation of electromagnetic fields in complex, superconducting resonators, as well as the efficient calculation of the losses of such resonances by the couplers and beampipes. A perturbation approach is used to efficiently assemble the resulting nonlinear eigenvalue problem, which is then solved by using the Newton method. Using the proposed methods, current research questions for the Third Harmonic Module of the FLASH accelerator, the bERLinPro mainlinear accelerator and the BESSY VSR cavity-design are be answered.Diese Arbeit beschäftigt sich mit der Berechnung elektromagnetischer Felder in komplexen, supraleitenden Resonatoren sowie der effizienten Berechnung der Verluste solcher Resonanzen durch die Koppler und Strahlrohre. Ein Störungsansatz wird verwendet, um das resultierende nichtlineare Eigenwertproblem effizient zusammenzusetzen, das dann mit der Newton-Methode gelöst wird. Mit den vorgeschlagenen Methoden werden aktuelle Forschungsfragen für das Third Harmonic Modul des FLASH-Beschleunigers, des bERLinPro Haupt-Linearbeschleunigers und des BESSY VSR Resonator-Designs beantwortet

A finite element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures

A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is employed to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms

Electromagnetic scattering and radiation from microstrip patch antennas and spirals residing in a cavity

A new hybrid method is presented for the analysis of the scattering and radiation by conformal antennas and arrays comprised of circular or rectangular elements. In addition, calculations for cavity-backed spiral antennas are given. The method employs a finite element formulation within the cavity and the boundary integral (exact boundary condition) for terminating the mesh. By virtue of the finite element discretization, the method has no restrictions on the geometry and composition of the cavity or its termination. Furthermore, because of the convolutional nature of the boundary integral and the inherent sparseness of the finite element matrix, the storage requirement is kept very low at O(n). These unique features of the method have already been exploited in other scattering applications and have permitted the analysis of large-size structures with remarkable efficiency. In this report, we describe the method's formulation and implementation for circular and rectangular patch antennas in different superstrate and substrate configurations which may also include the presence of lumped loads and resistive sheets/cards. Also, various modelling approaches are investigated and implemented for characterizing a variety of feed structures to permit the computation of the input impedance and radiation pattern. Many computational examples for rectangular and circular patch configurations are presented which demonstrate the method's versatility, modeling capability and accuracy

Essential spectrum of local multi-trace boundary integral operators

Considering pure transmission scattering problems in piecewise constant media, we derive an exact analytic formula for the spectrum of the corresponding local multi-trace boundary integral operators in the case where the geometrical configuration does not involve any junction point and all wave numbers equal. We deduce from this the essential spectrum in the case where wave numbers vary. Numerical evidences of these theoretical results are also presented