Data and methods for numerically solving the wave equation using a meshless Generalized Finite Differences Scheme.
All the codes are distributed under MIT License on GitHub and are free to use, modify, and distribute giving the proper copyright notice.
This repository proposes a way to achieve approximations to Wave Equation in two dimensions over regions that can range from regular (CUA) to highly irregular (ENG).
For this, the proposed solution uses a Generalized Finite Differences Method for the numerical solution over all the regions on unstructured clouds of points.
| England Cloud of Points With Holes | England Cloud of Points |
|---|---|
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It is possible to find all test data in the "Data" folder and some sample results in the "Results" folder. Numerical results were not saved in the repository due to file-size limitations, nevertheless, they can be computed and saved by executing the Example files.
The implemented methods are discussed in detail in the following publications:
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Tinoco-Guerrero G., Arias-Rojas H., Guzmán-Torres J.A., Román-Gutiérrez R., and Tinoco-Ruiz J.G., A meshless finite difference scheme applied to the numerical solution of wave equation in highly irregular space regions. Computers & Mathematics with Applications. 136 (2023) 25-33. 10.1016/j.camwa.2023.01.035
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Tinoco-Guerrero G., Domínguez-Mota F.J., Guzmán-Torres J.A., Román-Gutiérrez R., and Tinoco-Ruiz J.G., Study of the stability of a meshless generalized finite difference scheme applied to the wave equation. Frontiers in Applied Mathematics and Statistics 9:1214022 (2023) 10.3389/fams.2023.1214022
All the codes presented were developed by:
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Dr. Gerardo Tinoco Guerrero
Universidad Michoacana de San Nicolás de Hidalgo
Aula CIMNE-Morelia
gerardo.tinoco@umich.mx
https://orcid.org/0000-0003-3119-770X -
Dr. Francisco Javier Domínguez Mota
Universidad Michoacana de San Nicolás de Hidalgo
Aula CIMNE-Morelia
francisco.mota@umich.mx
https://orcid.org/0000-0001-6837-172X -
Dr. José Gerardo Tinoco Ruiz
Universidad Michoacana de San Nicolás de Hidalgo
jose.gerardo.tinoco@umich.mx
https://orcid.org/0000-0002-0866-4798 -
Dr. José Alberto Guzmán Torres
Universidad Michoacana de San Nicolás de Hidalgo
Aula CIMNE-Morelia
jose.alberto.guzman@umich.mx
https://orcid.org/0000-0002-9309-9390
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Heriberto Arias Rojas
Universidad Michoacana de San Nicolás de Hidalgo
heriberto.arias@umich.mx
https://orcid.org/0000-0002-7641-8310 -
Gabriela Pedraza Jiménez
Universidad Michoacana de San Nicolás de Hidalgo
2220157h@umich.mx
https://orcid.org/0009-0002-8118-0260 -
Miguel Ángel Rodríguez Velázquez
Universidad Michoacana de San Nicolás de Hidalgo
miguel.rodriguez@umich.mx
https://orcid.org/0009-0009-7245-1517 -
Ricardo Román Gutiérrez
Universidad Michoacana de San Nicolás de Hidalgo
ricardo.roman@umich.mx
https://orcid.org/0000-0001-8521-9391
With the financing of:
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National Council of Humanities, Sciences and Technologies, CONAHCyT (Consejo Nacional de Humanidades, Ciencias y Tecnologías, CONAHCyT), México.
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Coordination of Scientific Research, CIC-UMSNH (Coordinación de la Investigación Científica de la Universidad Michoacana de San Nicolás de Hidalgo, CIC-UMSNH), México.
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Aula CIMNE-Morelia, México.