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Application of the Neumann Boundary Conditions to One and Two Dimensional Analytical Solution of Wave Equation

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XXVII Brazilian Congress on Biomedical Engineering (CBEB 2020)

Part of the book series: IFMBE Proceedings ((IFMBE,volume 83))

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Abstract

This project aims the implementation of an approximate analytical solution for the wave equation in one and two dimensional domains for Neumann Boundary Conditions (NBC), which the gradient of the primary variable is known within the boundary domain and, for the proposed implementation, is defined as a periodic function of time. Fourier series was used to determine the approximated solutions for the wave equations and it was implemented in Python 3.7 programming language. The Object-Oriented Paradigm (OOP) approach was used to provide flexibility for the implementation, resulting in an Application Programming Interface (API) that provides functionalities such as increasing the number of approximation terms and several visualization tools. The results are presented considering two different frequencies and compared to the Finite Difference Method (FDM) solution, leading to root-mean-squared-errors of order \(10^{-6}\) (Pa).

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Acknowledgements

We would like to acknowledge the Federal University of ABC, and Technological Research Institute of the State of São Paulo (IPT).

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Authors and Affiliations

  1. Center for Engineering, Modeling and Applied Social Sciences, Biomedical Engineering, Federal University of ABC, Alameda da Universidade s/n, São Bernardo do Campo, Brazil

    S. G. Mello, C. Benetti & A. G. Santiago

Authors
  1. S. G. Mello
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  2. C. Benetti
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  3. A. G. Santiago
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Corresponding author

Correspondence to A. G. Santiago .

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Editors and Affiliations

  1. Department of Electrical Engineering, Universidade Federal do Espírito Santo, Vitória, Brazil

    Teodiano Freire Bastos-Filho

  2. Department of Electrical Engineering, Universidade Federal do Espírito Santo, Vitória, Brazil

    Eliete Maria de Oliveira Caldeira

  3. Department of Electrical Engineering, Universidade Federal do Espírito Santo, Vitória, Brazil

    Anselmo Frizera-Neto

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The authors declare that they have no conflict of interest.

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Mello, S.G., Benetti, C., Santiago, A.G. (2022). Application of the Neumann Boundary Conditions to One and Two Dimensional Analytical Solution of Wave Equation. In: Bastos-Filho, T.F., de Oliveira Caldeira, E.M., Frizera-Neto, A. (eds) XXVII Brazilian Congress on Biomedical Engineering. CBEB 2020. IFMBE Proceedings, vol 83. Springer, Cham. https://doi.org/10.1007/978-3-030-70601-2_256

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  • DOI: https://doi.org/10.1007/978-3-030-70601-2_256

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-70600-5

  • Online ISBN: 978-3-030-70601-2

  • eBook Packages: EngineeringEngineering (R0)

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