Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
FEM APPROXIMATION OF MAXWELL EQUATIONS: THE SOURCE PROBLEM, EIGENPROBLEM, AND ELECTROMAGNETIC WAVES
Download
MscThesis_TugayDagli.pdf
Date
2023-1-25
Author
Dağlı, Tugay
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
606
views
421
downloads
Cite This
In this thesis, edge-based finite element method (FEM) approximations of Maxwell's equations describing the relationship between the space variables and sources along the electromagnetic field are considered. In particular, the lowest-order Nédélec basis functions are implemented to construct the FEM model of the Maxwell source problem, Maxwell eigenvalue problem (EVP), and electromagnetic wave propagation problem. A computational model is constructed to conduct all these problems in the same framework of an approximation formalism. The convergence properties of the Maxwell EVP formulation are analyzed by applying the spectral theory with those of the associated boundary value source problem. Therefore, the analyses for both of these problems are given together with the corresponding numerical results validating the theoretical features. Moreover, a comparison between the two convergent FEM approximations of the Maxwell EVP that utilizes the lowest-order Nédélec and the linear Lagrange basis functions is performed. This comparison is done by using a special triangulation, namely, a Powell-Sabin type, of the domain that contains a strong singularity. The electromagnetic wave propagation problem is also considered using two different approaches, namely, a direct time-domain approximation method and a modal analysis technique. For both approaches, a FEM model of the wave propagation problem is obtained by discretizing the spatial domain using the lowest-order Nédélec basis functions. The time domain approximation of this problem is obtained by employing a finite difference (FD) scheme to approximate the second-order temporal derivative in the obtained FEM model. On the other hand, the frequency domain approximation is acquired by truncating the modal expansion solution. Here, it is set forth that the solution to the electromagnetic wave propagation problem can be represented by an expansion of the approximate eigenmodes that are obtained from the associated Maxwell EVP. As a consequence, it is shown by exploiting the numerical test case of the inhomogeneous wave propagation problem that both methodologies lead to accurate approximations which agree well with each other.
Subject Keywords
Maxwell’s equations
,
Maxwell source problem
,
Maxwell eigenvalue problem
,
Electromagnetic wave propagation problem
,
Finite elements
,
Edge elements
,
Modal analysis
URI
https://hdl.handle.net/11511/102105
Collections
Graduate School of Applied Mathematics, Thesis
Suggestions
OpenMETU
Core
Boundary value problems for higher order linear impulsive differential equations
Uğur, Ömür; Akhmet, Marat (2006-07-01)
In this paper higher order linear impulsive differential equations with fixed moments of impulses subject to linear boundary conditions are studied. Green's formula is defined for piecewise differentiable functions. Properties of Green's functions for higher order impulsive boundary value problems are introduced. An appropriate example of the Green's function for a boundary value problem is provided. Furthermore, eigenvalue problems and basic properties of eigensolutions are considered. (c) 2006 Elsevier In...
Multiscale Modeling of Thin-Wire Coupling Problems Using Hybridization of Finite Element and Dipole Moment Methods and GPU Acceleration
ÖZGÜN, ÖZLEM; Mittra, Raj; Kuzuoğlu, Mustafa (2020-01-01)
In this article, a hybrid numerical method, called finite element method (FEM) + dipole moment (DM), is presented for efficient solution of multiscale electromagnetic radiation and scattering problems that involve structures with fine features, such as thin-wire antennas or objects. In this method, the FEM is hybridized with the DM approach to help ease certain computational burdens, such as mesh refinement, ill-conditioning, memory overload, and long computation times, when solving multiscale problems with...
Regular Polygonal and Regular Spherical Polyhedral Linkages Comprising Bennett Loops
Kiper, Goekhan; Söylemez, Eres (2009-05-08)
In this study, assemblies of Bennett loops constructing regular polygonal linkages and regular polyhedral linkages are presented. The regular polyhedral linkages, necessarily, depend on spherical polyhedral shapes. Most of the resulting linkages have single degree of freedom, but there are exceptions such as a cubic linkage.
Questioning Degree of Accuracy Offered by the Spectral Element Method in Computational Electromagnetics
Mahariq, I.; KURT, HAMZA; Kuzuoğlu, Mustafa (2015-07-01)
In this paper, a comparison amongst the spectral element method (SEM), the finite difference method (FDM), and the first-order finite element method (FEM) is presented. For the sake of consistency, the comparison is carried out on one-dimensional and two-dimensional boundary value problems based on the same measure of error in order to emphasize on the high accuracy gained by the SEM. Then, the deterioration in the accuracy of the SEM due to the elemental deformation is demonstrated. Following this, we try ...
MUTUAL COUPLING EFFECTS OF FINITE RECTANGULAR PHASED-ARRAYS
YAVUZ, H; BUYUKDURA, OM (1994-04-14)
A rigorous integral equation formulation for the analysis of a phased array of flangemounted waveguide apertures is given for a finite number of elements and nonuniform spacings. The resulting set of ihtegrd equations is reduced to a matrix equation called the coupling matrix which relates the coefficients of all the modes in all the waveguides to one another. The solution then yields the dominant mode reflection coefficient, coefficients of scattered modes and hence the field in each waveguide. The blockTo...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
T. Dağlı, “FEM APPROXIMATION OF MAXWELL EQUATIONS: THE SOURCE PROBLEM, EIGENPROBLEM, AND ELECTROMAGNETIC WAVES,” M.S. - Master of Science, Middle East Technical University, 2023.