gstinoco / gfd

Generalized Finite Differences Methods for numerically solve different Partial Differential Equations

GFD Code pack

Generalized Finite Differences Methods for numerically solve different Partial Differential Equations.

All the codes are distributed under MIT License on GitHub and are free to use, modify, and distribute giving the proper copyright notice.

Description 📝

Researchers 🧑‍🔬

All the codes presented were developed by:

• Dr. Gerardo Tinoco Guerrero
  Universidad Michoacana de San Nicolás de Hidalgo
  Aula CIMNE-Morelia
  [email protected]
  https://orcid.org/0000-0003-3119-770X

• Dr. Francisco Javier Domínguez Mota
  Universidad Michoacana de San Nicolás de Hidalgo
  Aula CIMNE-Morelia
  [email protected]
  https://orcid.org/0000-0001-6837-172X

• Dr. José Gerardo Tinoco Ruiz
  Universidad Michoacana de San Nicolás de Hidalgo
  [email protected]
  https://orcid.org/0000-0002-0866-4798

• Dr. José Alberto Guzmán Torres
  Universidad Michoacana de San Nicolás de Hidalgo
  Aula CIMNE-Morelia
  [email protected]
  https://orcid.org/0000-0002-9309-9390

References 📚

More details on the Methods presented in these codes can be found in the following publications:

• Numerical solution of density-driven groundwater flows using a generalized finite difference method defined by an unweighted least-squares problem
  R. Román-Gutiérrez, C. Chávez-Negrete, F. J. Domínguez-Mota, J. A. Guzmán-Torres, and G. Tinoco-Guerrero
  Frontiers in Applied Mathematics and Statistics, 8:976958, 2022.
  https://doi.org/10.3389/fams.2022.976958

• Numerical Solution of Diffusion Equation using a Method of Lines and Generalized Finite Differences
  G. Tinoco-Guerrero, F. J. Domínguez-Mota, J. A. Guzmán-Torres, and J. G. Tinoco-Ruiz
  Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol. 38 (2), 2022.
  http://dx.doi.org/10.23967/j.rimni.2022.06.003

• A Generalized Finite-Differences Scheme used in Modeling of a Direct and a Inverse Problem of Advection-Diffusion
  F. J. Domínguez-Mota, J. S. Lucas-Martínez, and G. Tinoco-Guerrero
  International Journal of Applied Mathematics. Vol 33 (4), 2020.
  http://dx.doi.org/10.12732/ijam.v33i4.5

• Métodos Híbridos Aplicados a Modelos de Contaminantes Gobernados por Ecuaciones Diferenciales Parciales no Lineales (thesis)
  G. Tinoco-Guerrero
  Universidad Michoacana de San Nicolás de Hidalgo
  http://dx.doi.org/10.13140/RG.2.2.26334.46404

• A Generalized Finite Difference-Volume Hybrid Method Applied to Shallow-Water Equations
  G. Tinoco-Guerrero, F. J. Domínguez-Mota, J. G. Tinoco-Ruiz, J. S. Lucas-Martínez, N. S. Tinoco-Guerrero, Matti Leppäranta, and Ivan Mammarella
  Revista Mexicana de Métodos Numéricos. Vol. 4 (2). 2020.
  https://www.scipedia.com/public/Tinoco_Guerrero_et_al_2020a

• A study of the stability for a generalized finite-difference scheme applied to the advection-diffusion equation
  G. Tinoco-Guerrero, F. J. Domínguez-Mota, and J. G. Tinoco-Ruiz
  Mathematics and Computers in Simulation. Vol 176, 2020, 301-311.
  https://doi.org/10.1016/j.matcom.2020.01.020

• Aproximación de la ecuación de advección en regiones irregulares utilizando un Método de Líneas y Diferencias Finitas Generalizadas
  G. Tinoco-Guerrero, F. J Domínguez-Mota, J. G. Tinoco-Ruiz, and J. S. Lucas-Martínez
  Revista Mexicana de Métodos Numéricos. Vol. 2 (3). 2018.
  https://www.scipedia.com/public/Tinoco_Guerrero_et_al_2018b

• A stability analysis for a generalized finite-difference scheme applied to the pure advection equation
  G. Tinoco-Guerrero, F. J. Domínguez-Mota, A. Gaona-Arias, M. L. Ruiz-Zavala, and J. G. Tinoco-Ruiz
  Mathematics and Computers in Simulation. Vol. 147, 2018, 293-300.
  https://doi.org/10.1016/j.matcom.2017.06.001

• Modelado de Problemas de Aguas Someras en Regiones Irregulares Utilizando un Esquema de Diferencias Finitas Generalizadas (thesis)
  G. Tinoco-Guerrero
  Universidad Michoacana de San Nicolás de Hidalgo
  http://dx.doi.org/10.13140/RG.2.2.22676.30082

• An application of generalized differences to unsteady heat problems subject to mixed boundary conditions
  F. J. Domínguez-Mota, J. G. Tinoco-Ruiz, F. O. Guillén-Reyes, G. Tinoco-Guerrero, and A. Valencia-Ramírez
  Pan-American Congress on Computational Mechanics At Barcelona, Spain. Vol 1. 2015.
  http://dx.doi.org/10.13140/RG.2.1.2395.5922

• Solución numérica de la ecuación de advección empleando mallas estructuradas sobre regiones planas irregulares utilizando un esquema de diferencias finitas (thesis)
  G. Tinoco-Guerrero
  Universidad Michoacana de San Nicolás de Hidalgo, 2014.
  http://dx.doi.org/10.13140/RG.2.1.5070.4722

• Finite difference schemes satisfying an optimality condition for the unsteady heat equation
  F. J. Domínguez-Mota, S. Mendoza-Armenta, G. Tinoco-Guerrero, J. G. Tinoco-Ruiz
  Mathematics and Computers in Simulation, Vol 106, 2014, 76-83.
  https://doi.org/10.1016/j.matcom.2014.02.007

• An heuristic finite difference scheme on irregular plane regions
  F. J. Domínguez-Mota, P. M. Fernández-Valdez, E. Ruiz-Díaz, G. Tinoco-Guerrero, and J. G. Tinoco-Ruiz
  Applied Mathematical Sciences, Vol. 8 (14), 2014, 671-683.
  http://dx.doi.org/10.12988/ams.2014.312684

• Un esquema modificado de Lax-Wendroff de 6 puntos para la solución de la ecuación de advección en regiones planas irregulares
  J. G. Tinoco-Ruiz, F. J. Domínguez-Mota, E. Ruiz-Díaz, and G. Tinoco-Guerrero
  VI Congreso Internacional de Métodos Numéricos At Morelia, México. Vol. 4, 2013.
  http://dx.doi.org/10.13140/2.1.3770.8165

• Un esquema simplificado de primer orden para la solución de la ecuación de Poisson en regiones irregulares del plano.
  F. J. Domínguez-Mota, P. M. Fernandez-Valdez, G. Tinoco-Guerrero, and J. G. Tinoco-Ruiz
  II Encuentro Cuba-México de Métodos Numéricos y Optimización At: La Habana, Cuba. Vol. 2, 2013.
  https://www.researchgate.net/publication/265467094_Un_esquema_simplificado_de_primer_orden_para_la_solucion_de_la_ecuacion_de_Poisson_en_regiones_irregulares_del_plano

• An implicit modified Lax-Wendroff scheme for irregular 2D space regions
  G. Tinoco-Guerrero, F. J. Domínguez-Mota, and J. G. Tinoco-Ruiz
  Meeting on Applied Scientific Computing and Tools At: El Escorial, Spain. Vol. 13, 2013.
  http://dx.doi.org/10.13140/RG.2.1.1400.4567

• Numerical Solution of Differential Equations in Irregular Plane Regions Using Quality Structured Convex Grids
  F. J. Domínguez-Mota, P. Fernández-Valdez, S. Mendoza-Armenta, G. Tinoco-Guerrero, and J. G. Tinoco-Ruiz
  International Journal of Modeling, Simulation, and Scientific Computing, Vol. 4 (2), 2013.
  http://dx.doi.org/10.1142/S1793962313500049

Funding 💵

With the financing of:

• National Council of Science and Technology, CONACyT (Consejo Nacional de Ciencia y Tecnología, CONACyT), México.

• Coordination of Scientific Research, CIC-UMSNH (Coordinación de la Investigación Científica de la Universidad Michoacana de San Nicolás de Hidalgo, CIC-UMSNH), México.

• Aula CIMNE-Morelia, México.