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Numerical Solutions to Wave Propagation and Heat Transfer Non-Linear PDEs by Using a Meshless Method

Author

Listed:
  • Jesús Flores

    (Escuela Técnica Superior de Ingernieros Industriales, Universidad Nacional de Educación a Distancia (UNED), 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Ángel García

    (Escuela Técnica Superior de Ingernieros Industriales, Universidad Nacional de Educación a Distancia (UNED), 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Mihaela Negreanu

    (Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid (UCM), 28040 Madrid, Spain
    Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid (UCM), 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Eduardo Salete

    (Escuela Técnica Superior de Ingernieros Industriales, Universidad Nacional de Educación a Distancia (UNED), 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Francisco Ureña

    (Escuela Técnica Superior de Ingernieros Industriales, Universidad Nacional de Educación a Distancia (UNED), 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Antonio M. Vargas

    (Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid (UCM), 28040 Madrid, Spain
    Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid (UCM), 28040 Madrid, Spain
    These authors contributed equally to this work.)

Abstract

The applications of the Eikonal and stationary heat transfer equations in broad fields of science and engineering are the motivation to present an implementation, not only valid for structured domains but also for completely irregular domains, of the meshless Generalized Finite Difference Method (GFDM). In this paper, the fully non-linear Eikonal equation and the stationary heat transfer equation with variable thermal conductivity and source term are solved in 2D. The explicit formulae for derivatives are developed and applied to the equations in order to obtain the numerical schemes to be used. Moreover, the numerical values that approximate the functions for the considered domain are obtained. Numerous examples for both equations on irregular 2D domains are exposed to underline the effectiveness and practicality of the method.

Suggested Citation

  • Jesús Flores & Ángel García & Mihaela Negreanu & Eduardo Salete & Francisco Ureña & Antonio M. Vargas, 2022. "Numerical Solutions to Wave Propagation and Heat Transfer Non-Linear PDEs by Using a Meshless Method," Mathematics, MDPI, vol. 10(3), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:332-:d:730658
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    Cited by:

    1. Yongou Zhang & Zhongjian Ling & Hao Du & Qifan Zhang, 2023. "Finite-Difference Frequency-Domain Scheme for Sound Scattering by a Vortex with Perfectly Matched Layers," Mathematics, MDPI, vol. 11(18), pages 1-11, September.

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