A hybrid finite element method for electromagnetics with applications in time-domain
Doctoral thesis, 2007

In this thesis, a new hybrid method that combines the Finite Element Method (FEM) with the Finite-Difference in Time-Domain (FDTD) method is presented. Tetrahedrons in the unstructured FEM region are connected directly to the hexahedrons in the structured FDTD region. The discontinuity in the tangential electric field inherent to this type of discretization is treated rigorously by means of Nitsche's method. It is possible to prove that the hybrid is stable for time steps that satisfy the Courant criterion for the FDTD region. The hybridization combines the efficiency of the FDTD scheme with the flexibility of the FEM that efficiently models curved boundaries and fine details to high accuracy. This allows the hybrid to treat a wide range of problems and here it is applied to resonant cavities, scattering and antenna problems. For scattering analysis of periodic structures at oblique incidence, a new technique is proposed that constructs the broad-band incident wave as a spectrum of plane waves, such that simple periodic boundary conditions may be used. Furthermore, we consider shape and material optimization by means of continuum design sensitivity analysis and the adjoint problem.

Nitsche's method

antenna arrays

NASA almond

edge elements

scattering

explicit-implicit time-stepping

Maxwell's equations

Finite Element Method

mass lumping

stability analysis

Finite-Differences Time-Domain

periodic structures

shape and material optimization

EE-salen, Hörsalsvägen 11, Chalmers
Opponent: Prof. Romanus Dyczij-Edlinger, Universität des Saarlandes, Sarbrücken, Germany

Author

DAVID DEGERFELDT

Chalmers, Signals and Systems, Signal Processing and Biomedical Engineering

Other publications Research

Gradient Optimization of Microwave Devices Using Continuum Design Sensitivities from the Adjoint Problem

IEEE Transactions on Magnetics,; Vol. 2005(2005)p. 1780-1783

Journal article

Calculating the Scattering from Periodic Surfaces in Time Domain Using a FEM-FDTD Hybrid Code

EMB04, Computational Electromagnetics - Methods and Applications, Conference Proceedings,; (2004)p. 74-79

Paper in proceeding

Optimization of Frequency Selective Surfaces

RVK05 - Radiovetenskap och Kommunikation,; (2005)

Paper in proceeding

A higher-order finite element method with an explicit higher-order time integration scheme

EMB07 Computational Electromagnetics Methods and Applications, Lund, Sweden, Oct 18-19, 2007,; (2007)p. 91-98

Paper in proceeding

Shape and material optimization using gradient methods and the adjoint problem in time and frequency domain

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering,; Vol. 24(2005)p. 882-892

Journal article

A broad frequency band analysis of conformal array antennas

The Nordic antenna symposium -- Antenn06,; (2006)

Paper in proceeding

A quasi-planar incident wave excitation for time-domain scattering analysis of periodic structures

International Journal of Numerical Modelling: Electronic Networks, Devices, and Fields,; Vol. 19(2006)p. 409-419

Journal article

Subject Categories

Other Electrical Engineering, Electronic Engineering, Information Engineering

ISBN

978-91-7385-032-2

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 2713

EE-salen, Hörsalsvägen 11, Chalmers

Opponent: Prof. Romanus Dyczij-Edlinger, Universität des Saarlandes, Sarbrücken, Germany

More information

Created

10/8/2017

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