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05.01.2025 | Original Article

A waveguide port boundary condition based on approximation space restriction for finite element analysis

verfasst von: Francisco T. Orlandini, Philippe R. B. Devloo, Hugo E. Hernández-Figueroa

Erschienen in: Engineering with Computers

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Abstract

A waveguide port boundary condition (WPBC) based on the restriction of the approximation space is presented in the context of Finite Element Analysis. As well as efficiently truncating the computational domain in the same manner as the traditional WPBC, the proposed scheme significantly reduces the degrees of freedom at the waveguide ports, simplifies the implementation and seamlessly provides post-processing results such as the reflected power in each waveguide mode. The boundary condition is thoroughly derived, and numerical examples are used as a support for the discussion on topics such as the needed number of modes to be employed at a waveguide port. Finally, a nanograting-based plasmonic sensor is analysed to illustrate further possibilities of the scheme.

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Fußnoten
1
The precise definition of the fractional Sobolev spaces is out of the scope of this paper, and they have been mentioned in the equations above for correctness. For the present discussion, it suffices that they are seen as a subspace of (possibly vector-valued) \(\text {L}^{2}(\Omega )\) corresponding to the range of the trace operator for the associated space.
 
2
The scope of this work does not contemplate waveguides with periodicity in the propagation direction.
 
3
The z-component of Eqs. 20 and 21 are ignored due to the cross product with \(\hat{\varvec{z}}\)
 
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Metadaten
Titel
A waveguide port boundary condition based on approximation space restriction for finite element analysis
verfasst von
Francisco T. Orlandini
Philippe R. B. Devloo
Hugo E. Hernández-Figueroa
Publikationsdatum
05.01.2025
Verlag
Springer London
Erschienen in
Engineering with Computers
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-024-02101-z