Finite-element time-domain modelling of cylindrical structures with a modal non-reflecting boundary condition
Bavelis, Konstantinos (2010) Finite-element time-domain modelling of cylindrical structures with a modal non-reflecting boundary condition. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2521717~S15
This dissertation presents Galerkin weighted residual Finite-Element Time-Domain
(FETD) formulations using a 2D cylindrical modal non-reflecting boundary condition
(MNRBC) for the modelling of plane wave scattering from cylindrical structures of
arbitrary cross-section surrounded by free space.
Chapter 1 begins by presenting the motivation for this work. Key concepts regarding
cylindrical geometries are introduced at this stage. The Galerkin weighted residual
Finite-Element method is briefly outlined.
Chapter 2 presents a novel scattered field FETD-MNRBC formulation for the
transverse electric polarisation of a modal non-reflecting boundary condition for plane
wave scattering from perfectly electrically conductive (PEC) cylindrical structures of
arbitrary cross-section. The boundary condition is based on a Vector-Fitting (VF)
approximation of the boundary kernel appearing in the time-domain formulation. The
convolution integral appearing in the time-domain formulation of the boundary
condition is calculated recursively using the Vector-Fitting coefficients. Accurate
numerical results are shown for the bistatic scattering width (BSW) that validate the
Chapter 3 focuses on the VF approximation of the cylindrical boundary kernel. Two
approaches are investigated; the so called Vector-Fitting G function approximation
(VFG) and the Vector-Fitting U function approximation (VFU). Both approaches
produce satisfactory finite-element results with the VFU being more versatile.
Chapter 4 presents, for the first time, the total field FETD-MNRBC formulation for
both transverse electric and transverse magnetic polarisations. The VFU approach is employed. The structures considered in this chapter are not only PEC cylinders but
also dielectric ones of various cross-sections and various values of relative
permittivity and permeability. The numerical results demonstrate the good accuracy
of this formulation.
Chapter 5 combines the cylindrical modal non-reflecting boundary condition with the
Floquet theorem and extends this formulation, for the first time, to azimuthally
periodic cylinders using scattered and total field time-domain formulations. The
advantages and disadvantages of the periodic modal non-reflecting boundary
condition approach are discussed and numerical results for the BSW are shown.
Chapter 6 presents a novel sparse-matrix scattered field FETD-MNRBC formulation
in which the fully dense submatrices associated with the boundary integral are
avoided. Through numerical results the accuracy of the proposed formulation is
Chapter 7 concludes the work by summarizing the main achievements and discussing
its impact in electromagnetics.
|Item Type:||Thesis or Dissertation (PhD)|
|Subjects:||Q Science > QA Mathematics|
|Library of Congress Subject Headings (LCSH):||Galerkin methods, Finite element method, Time-domain analysis, Scattering (Physics)|
|Official Date:||December 2010|
|Institution:||University of Warwick|
|Theses Department:||School of Engineering|
|Sponsors:||University of Warwick|
|Extent:||xvi, 172 leaves : ill., charts|
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