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Finite Element Method for Sensing Applications

  • Khaled S. R. Atia
  • Souvik Ghosh
  • Ahmed M. Heikal
  • Mohamed Farhat O. Hameed
  • B. M. A. Rahman
  • S. S. A. Obayya
Chapter

Abstract

In this chapter, the fundamentals of the nodal finite element method (FEM) are presented, including the first-order element and second-order element. The nodal FEM is introduced for the scalar concept of the propagation constant of 2D waveguide cross section. Then, it is extended to include the time domain analysis under perfectly matched layer absorbing boundary conditions. A simple sensor based on optical grating is thereafter simulated using the time domain FEM. Also, the full vectorial analysis is discussed through the application of the penalty function method on the nodal FEM and the vector finite element method (VFEM). For the penalty function method, a global weighting factor is used to incorporate the effect of the divergence-free equation. In the VFEM, nodes are used to represent the orthogonal component of the field while the edges are used to represent the tangential component for accurate application of the boundary conditions. Finally, surface plasmon resonance photonic crystal fiber biosensor is introduced as an example of the full vectorial analysis using the VFEM.

Keywords

Finite element method Finite element time domain Penalty function method Full-vector finite element method Edge finite element method 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Khaled S. R. Atia
    • 1
    • 2
  • Souvik Ghosh
    • 3
  • Ahmed M. Heikal
    • 1
    • 4
  • Mohamed Farhat O. Hameed
    • 5
    • 6
  • B. M. A. Rahman
    • 3
  • S. S. A. Obayya
    • 1
    • 4
  1. 1.Centre for Photonics and Smart MaterialsZewail City of Science and TechnologyGizaEgypt
  2. 2.Advanced Research ComplexUniversity of OttawaOttawaCanada
  3. 3.School of Mathematics, Computer Science and EngineeringCity University of LondonLondonEngland
  4. 4.Faculty of Engineering, Department of Electronics and Communication EngineeringMansoura UniversityMansouraEgypt
  5. 5.Center for Photonics and Smart Materials and Nanotechnology Engineering ProgramZewail City of Science and TechnologyGizaEgypt
  6. 6.Mathematics and Engineering Physics Department, Faculty of EngineeringMansoura UniversityMansouraEgypt

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