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Finite Element Method for Sensing Applications

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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 .

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Authors and Affiliations

  1. Centre for Photonics and Smart Materials, Zewail City of Science and Technology, October Gardens, 6th of October City, Giza, Egypt

    Khaled S. R. Atia, Ahmed M. Heikal & S. S. A. Obayya

  2. Advanced Research Complex, University of Ottawa, Ottawa, ON K1N 6N5, Canada

    Khaled S. R. Atia

  3. School of Mathematics, Computer Science and Engineering, City University of London, London, EC1V 0HB, England

    Souvik Ghosh & B. M. A. Rahman

  4. Faculty of Engineering, Department of Electronics and Communication Engineering, Mansoura University, Mansoura, Egypt

    Ahmed M. Heikal & S. S. A. Obayya

  5. Center for Photonics and Smart Materials and Nanotechnology Engineering Program, Zewail City of Science and Technology, October Gardens, 6th of October City, Giza, Egypt

    Mohamed Farhat O. Hameed

  6. Mathematics and Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura, Egypt

    Mohamed Farhat O. Hameed

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  1. Khaled S. R. Atia
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  2. Souvik Ghosh
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  3. Ahmed M. Heikal
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  4. Mohamed Farhat O. Hameed
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  5. B. M. A. Rahman
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  6. S. S. A. Obayya
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Correspondence to Mohamed Farhat O. Hameed .

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Editors and Affiliations

  1. Center for Photonics and Smart Materials and Nanotechnology Engineering Program, Zewail City of Science and Technology, Giza, Egypt

    Mohamed Farhat O. Hameed

  2. Center for Photonics and Smart Materials, Zewail City of Science and Technology, Giza, Egypt

    Salah Obayya

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Atia, K.S.R., Ghosh, S., Heikal, A.M., Hameed, M.F.O., Rahman, B.M.A., Obayya, S.S.A. (2019). Finite Element Method for Sensing Applications. In: Hameed, M., Obayya, S. (eds) Computational Photonic Sensors. Springer, Cham. https://doi.org/10.1007/978-3-319-76556-3_6

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  • DOI: https://doi.org/10.1007/978-3-319-76556-3_6

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