A mixed high-order vector finite element method for waveguides

Convergence and spurious mode studies

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this article we construct and analyse the performance of various combinations of high order edge elements for the transverse field component with high order node elements for the longitudinal field component. The overall efficiency and mode resolution improve dramatically with high order elements. For example, quadratic/cubic elements provide accuracy of 10-4 in eigenvalue 1000 times faster and resolve the discontinuities in the field very accurately. In the mixed FEM for waveguides we observed that edge elements may produce spurious modes. When the order of the edge elements is equal or larger than the order of the node elements, spurious and degenerate modes are present. Any other combination of the orders did not produce spurious modes. We study the spurious modes from the divergence point of view. We also study the convergence properties of high order elements and compare the results with the theory.

Original languageEnglish (US)
Pages (from-to)351-364
Number of pages14
JournalInternational Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Volume18
Issue number5
DOIs
StatePublished - Sep 2005

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Edge Elements
Higher-order Elements
Waveguide
Waveguides
Finite Element Method
Higher Order
Finite element method
Vertex of a graph
Convergence Properties
Discontinuity
Resolve
Divergence
Transverse
Eigenvalue

Keywords

  • High order FEM
  • Spurious modes
  • Waveguide

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

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abstract = "In this article we construct and analyse the performance of various combinations of high order edge elements for the transverse field component with high order node elements for the longitudinal field component. The overall efficiency and mode resolution improve dramatically with high order elements. For example, quadratic/cubic elements provide accuracy of 10-4 in eigenvalue 1000 times faster and resolve the discontinuities in the field very accurately. In the mixed FEM for waveguides we observed that edge elements may produce spurious modes. When the order of the edge elements is equal or larger than the order of the node elements, spurious and degenerate modes are present. Any other combination of the orders did not produce spurious modes. We study the spurious modes from the divergence point of view. We also study the convergence properties of high order elements and compare the results with the theory.",
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AB - In this article we construct and analyse the performance of various combinations of high order edge elements for the transverse field component with high order node elements for the longitudinal field component. The overall efficiency and mode resolution improve dramatically with high order elements. For example, quadratic/cubic elements provide accuracy of 10-4 in eigenvalue 1000 times faster and resolve the discontinuities in the field very accurately. In the mixed FEM for waveguides we observed that edge elements may produce spurious modes. When the order of the edge elements is equal or larger than the order of the node elements, spurious and degenerate modes are present. Any other combination of the orders did not produce spurious modes. We study the spurious modes from the divergence point of view. We also study the convergence properties of high order elements and compare the results with the theory.

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