Maximally Orthogonalized Higher Order Basis Functions in Large-Domain Finite Element Modeling in Electromagnetics

Curl-conforming max-ortho basis functions (MOBFs) are coupled with higher order large-domain curved finite elements (FEs). The performance of the functions is compared with that of the classical and near-ortho basis functions. Through numerical experiments, it is shown that max-ortho FEs yield highl...

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Published inIEEE transactions on antennas and propagation Vol. 68; no. 8; pp. 6455 - 6460
Main Authors Savic, Slobodan V., Ilic, Milan M., Kolundzija, Branko M.
Format Journal Article
LanguageEnglish
Published New York IEEE 01.08.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Antennas
Basis functions
Condition number
differential equations
Domains
Electric fields
Finite element analysis
Finite element method
finite element method (FEM)
higher order basis functions
higher order modeling
Integral equations
Iterative methods
Mathematical analysis
Mathematical model
Method of moments
numerical analysis
orthogonal functions
Polynomials
Silicon
Solvers
Online AccessGet full text
ISSN0018-926X
1558-2221
DOI10.1109/TAP.2020.2970038

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Abstract Curl-conforming max-ortho basis functions (MOBFs) are coupled with higher order large-domain curved finite elements (FEs). The performance of the functions is compared with that of the classical and near-ortho basis functions. Through numerical experiments, it is shown that max-ortho FEs yield highly orthogonal mass matrices, for practically arbitrarily high orders of polynomial field approximations. This facilitates the usage of iterative solvers and it significantly increases their efficiency. Accurate and fast computation of MOBFs, of arbitrarily high orders, is enabled by the proposed two-term recurrent formula.
AbstractList Curl-conforming max-ortho basis functions (MOBFs) are coupled with higher order large-domain curved finite elements (FEs). The performance of the functions is compared with that of the classical and near-ortho basis functions. Through numerical experiments, it is shown that max-ortho FEs yield highly orthogonal mass matrices, for practically arbitrarily high orders of polynomial field approximations. This facilitates the usage of iterative solvers and it significantly increases their efficiency. Accurate and fast computation of MOBFs, of arbitrarily high orders, is enabled by the proposed two-term recurrent formula.
Author Savic, Slobodan V.
Kolundzija, Branko M.
Ilic, Milan M.
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10.1109/APS.2005.1552645
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10.1080/02726340600872914
10.1109/9780470544631
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10.1109/TAP.2013.2249036
10.1109/TAP.2004.835279
10.1109/TAP.2012.2194669
10.1109/TAP.2018.2835499
10.1109/8.791939
10.1109/9780470546710
10.1109/TAP.2010.2103012
10.1109/22.775434
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References ref13
ref12
ref15
ref14
ref20
ref11
ref10
ref1
ref17
ref16
jin (ref2) 2014
ref19
ref7
ref9
ref3
ref6
ref5
kolundžija (ref8) 2001
mitrinovic (ref18) 2016
kolundzija (ref4) 2002
References_xml – year: 2002
  ident: ref4
  publication-title: Electromagnetic modeling of composite metallic and dielectric structures
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  doi: 10.1017/CBO9781139170611
– ident: ref12
  doi: 10.1109/APS.2005.1552645
– ident: ref16
  doi: 10.1109/TAP.2014.2323081
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  doi: 10.1080/02726340600872914
– ident: ref3
  doi: 10.1109/9780470544631
– year: 2016
  ident: ref18
  publication-title: Introduction to Special Functions (in Serbian)
– ident: ref6
  doi: 10.1109/TMTT.2003.808680
– ident: ref15
  doi: 10.1109/TAP.2013.2249036
– ident: ref10
  doi: 10.1109/TAP.2004.835279
– ident: ref7
  doi: 10.1109/TAP.2012.2194669
– start-page: 588
  year: 2001
  ident: ref8
  article-title: Iterative solvers in frequency analysis of complex structures based on mom solution of surface integral equations
  publication-title: Proc IEEE Antennas Propag Soc Int Symp (APS)
– ident: ref17
  doi: 10.1109/TAP.2018.2835499
– ident: ref9
  doi: 10.1109/8.791939
– ident: ref19
  doi: 10.1109/9780470546710
– year: 2014
  ident: ref2
  publication-title: The Finite Element Method in Electromagnetics
– ident: ref13
  doi: 10.1109/TAP.2010.2103012
– ident: ref5
  doi: 10.1109/22.775434
– ident: ref20
  doi: 10.1016/0165-2125(88)90011-X
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  doi: 10.1109/TAP.2011.2158789
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SubjectTerms Antennas
Basis functions
Condition number
differential equations
Domains
Electric fields
Finite element analysis
Finite element method
finite element method (FEM)
higher order basis functions
higher order modeling
Integral equations
Iterative methods
Mathematical analysis
Mathematical model
Method of moments
numerical analysis
orthogonal functions
Polynomials
Silicon
Solvers
Title Maximally Orthogonalized Higher Order Basis Functions in Large-Domain Finite Element Modeling in Electromagnetics
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