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• An Implicit Modified Lax-Wendroff Scheme for Irregular 2D Space Regions

  G. Tinoco Guerrero, F. Domínguez Mota, J. Tinoco-Ruiz

  IMACS Series in Computational and Applied Mathematics (2013).

  
  

  Abstract

  Nowadays, there are many modelling problems which involve the shallow water equations for irregular domains. One of the most important blocks for solving these equations is the advection equation. In this paper, we present the implementation of an implicit modified Lax-Wendroff scheme in order to approximate the solution of the advection equation in some irregular domains in the plane, using a general finite difference method on structured convex grids.

  Abstract
  Nowadays, there are many modelling problems which involve the shallow water equations for irregular domains. One of the most important blocks for solving these equations is [...]

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• Numerical solution of diffusion equation using a method of lines and generalized finite differences

  G. Tinoco Guerrero, F. Domínguez Mota, J. Guzmán Torres, J. Tinoco-Ruiz

  Rev. int. métodos numér. cálc. diseño ing. (2022). Vol. 38, (2), 24

  
  

  Abstract

  One of the greatest challenges in the area of applied mathematics continues to be the design of numerical methods capable of approximating the solution of partial differential equations quickly and accurately. One of the most important equations, due to the hydraulic and transport applications it has, and the large number of difficulties that it usually presents when solving it numerically is the Diffusion Equation.   In the present work, a Method of Lines applied to the numerical solution of the said equation in irregular regions is presented using a scheme of Generalized Finite Differences. The second-order finite difference method uses a central node and 8 neighbor points in order to address the spatial approximation. A series of tests and numerical results are presented, which show the accuracy of the proposed method.

  Abstract
  One of the greatest challenges in the area of applied mathematics continues to be the design of numerical methods capable of approximating the solution of partial differential [...]

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• A numerical approximation for build the stress/strain diagram with just the maximum load obtained

  J. Guzmán Torres, F. Domínguez Mota, G. Tinoco Guerrero

  SMCCA (2020). 2

  
  

  Abstract

  One of the fundamental features in the design of rigid pavements is the rupture modulus, which value is obtained experimentally using a bending test and indicates the maximum load that a concrete beam can support. To determine this value is expensive and impractical since the tests require rather large stress values, there is always a risk of producing brittle fractures in the probes used. For this reason, it is proposed in this paper an implementation of a numerical estimation for the deformations due to the maximum load through a simple interpolation model that allows the generation of the stress/strain diagram using the only data available: the maximum load. The results show that it is possible to calculate the maximum deformation value in the beam previous to the failure. Also, it is possible to generate the stress/strain diagram and distinguish the elastic and elastoplastic areas of the concrete.

  Abstract
  One of the fundamental features in the design of rigid pavements is the rupture modulus, which value is obtained experimentally using a bending test and indicates the maximum [...]

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• Numerical Solution of Advection Equations Using Structured Grids on Plane Irregular Regions With a Finite Differences Scheme

  G. Tinoco Guerrero, F. Domínguez Mota, J. Tinoco-Ruiz

  SMCCA (2015). 20

  
  

  Abstract

  Today we faced the problem of solving equations for shallow bodies of water in irregular regions; These equations are very important to be able to model the behavior of liquids that have the characteristic that their extension is much greater than their depth. One of the important blocks to solve these equations is the advection equation. In this work, some schemes are proposed to approximate the solution of the advection equation in irregular regions in the plane, using a variation of the finite difference method in convex and structured meshes.

  Abstract
  Today we faced the problem of solving equations for shallow bodies of water in irregular regions; These equations are very important to be able to model the behavior of liquids [...]

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• Solución numérica de la ecuación vectorial de Saint-Venant utilizando métodos híbridos

  M. Zavala, F. Domínguez Mota

  SMCCA (2018). 14

  
  

  Abstract

  Las inundaciones y desbordamientos de canales son fenómenos que han venido afectando a la sociedad por muchos años; estos se han incrementado debido a lluvias atípicas provocadas por el cambio climático. Para prevenir las afectaciones es conveniente mejorar nuestra comprensión del fenómeno, el cual está descrito por ecuaciones como las de Saint-Venant. En este trabajo se muestra una alternativa a aproximar numéricamente la solución de tales ecuaciones en dominios como canales.

  Abstract
  Las inundaciones y desbordamientos de canales son fenómenos que han venido afectando a la sociedad por muchos años; estos se han incrementado debido a lluvias [...]

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• Generalized finite difference solution for the Motz Problem

  C. Chávez, F. Domínguez Mota, S. Lucas-Martinez, J. Tinoco-Ruiz, D. Santana Quinteros

  Rev. int. métodos numér. cálc. diseño ing. (2021). Vol. 37, (1), 13

  
  

  Abstract

  In this paper, it is presented a formulation of a generalized finite difference scheme to solve the Motz problem. It is based on a general difference scheme defined by an optimality condition, which has been developed to solve Poisson-like equations whose domains are approximated by a wide variety of grids over general regions. Numerical examples showing second-order accuracy of the calculated solutions are presented.

  Abstract
  In this paper, it is presented a formulation of a generalized finite difference scheme to solve the Motz problem. It is based on a general difference scheme defined by an [...]

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• A Generalized Finite Difference-Volume Hybrid Method Applied to Shallow-Water Equations

  G. Tinoco Guerrero, F. Domínguez Mota, J. Tinoco-Ruiz, J. Martínez, N. Tinoco-Guerrero, M. Leppäranta, I. Mammarella

  Revista Mexicana de Métodos Numéricos (2020). Vol. 4, 2

  
  

  Abstract

  Due to the importance of the shallow-water equations in models of real-life phenomena, in recent years the study and model of problems that involve them have been the object of interest of many people. By reason of this, it is imperative to have efficient numerical methods to obtain an approximation of the solutions of the shallow-water equations. Several authors have worked in approximations using the well-known finite volume and finite element methods, nevertheless, even when these methods compute good approximations to real-life behavior, the computational cost is usually high, which could be a limitation to the application of these methods. This paper presents an explicit Generalized Finite Difference-Volume Hybrid approximation to the solution of the shallow-water equations, solved on irregular regions meshed with logically rectangular grids; the numerical results show the accuracy obtained with a low-cost implementation. The proposed scheme is a hybridization of a generalized finite difference scheme with the finite volume method.

  Abstract
  Due to the importance of the shallow-water equations in models of real-life phenomena, in recent years the study and model of problems that involve them have been the object [...]

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• Cálculo de daño en pavimentos mediante un análisis hidro-mecánico de pavimentos flexibles

  C. Chávez, F. Domínguez Mota, M. Hernandez-Peña, E. Arreygue

  Revista Mexicana de Métodos Numéricos (2020). Vol. 4, 1

  
  

  Abstract

  A hydro-mechanical analysis of a pavement is presented in which the variation of the water content is considered for the estimation of modulus of elasticity of the layers of soil in the pavement. To do this, the Richards differential equation and equilibrium in the axi-symmetric condition are solved simultaneously, considering a non-linear elasticity that depends on the suction and stress state in the soil. With this type of analysis, it is possible to quantify the variation of the damage with respect to time and visualize the deterioration of the pavement structures. It is considered a practical case in which the increase in damage is quantified in function of the variation of environmental conditions and conclusions are obtained. 

  Abstract
  A hydro-mechanical analysis of a pavement is presented in which the variation of the water content is considered for the estimation of modulus of elasticity of the layers [...]

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• Approximation to advection equation in plane irregular regions using a Method of Lines and Generalized Finite Differences

  G. Tinoco Guerrero, F. Domínguez Mota, J. Martínez, J. Tinoco-Ruiz

  Revista Mexicana de Métodos Numéricos (2018). Vol. 2, 3

  
  

  Abstract

  One of the greatest challenges in our days continues being to design numerical methods capable of approaching the solution of partial differential equations in a fast and precise way. One of the most important equations, due to the hydraulic and transport applications that it has, and the great amount of difficulties that it usually presents when resolving it numerically is the Advection Equation. In the present work we present a Method of Lines applied to the numerical solution of said equation in irregular regions making use of a Generalized Finite Differences scheme. A series of numerical tests and results are presented, which show the accuracy of the proposed method.

  Abstract
  One of the greatest challenges in our days continues being to design numerical methods capable of approaching the solution of partial differential equations in a fast and [...]

  • 70
  •  read

Articles (Documents not available in Scipedia)

• Modeling Tensile Strength of Concrete Using Support Vector Regression

  J. A. Guzmán-Torres, E. M. Alonso-Guzmán, and W. Martínez-Molina

  ACI Materials Journal, V. 119, No. 3, May 2022, pág. 25-38.

• Effective medium crack classification on laboratory concrete specimens via competitive machine learning

  JA Guzmán-Torres, MZ Nase

  Structures 37, 858-870

• A review of concrete performance employing a starch as addition using several regression techniques

  JA Guzmán-Torres, EM Alonso-Guzmán,

  Advanced Materials Research 1160, 1-14

• Data Science and Machine Learning Technique for Predicting Electrical Resistivity in Recycled Concrete with Nopal as Addition

  José Alberto Guzmán-Torres, Arturo Zalapa-Damian, Elia Mercedes Alonso-Guzmán

  Advanced Engineering Forum 40, 43-62

• A Solution of Richards’ Equation by Generalized Finite Differences for Stationary Flow in a Dam

  C Chávez-Negrete, D Santana-Quinteros

  Mathematics 9 (14), 1604

• Estimating the flexural strength of concrete using compressive strength as input value in a deep learning model

  JA Guzmán-Torres, FJ Domínguez-Mota, EM Alonso-Guzmán

  IOP Conference Series: Materials Science and Engineering 1150 (1), 012019

• Estimation of the main conditions in (SARS-CoV-2) Covid-19 patients that increase the risk of death using Machine learning, the case of Mexico

  JA Guzmán-Torres, EM Alonso-Guzmán

  Results in Physics 27, 104483

• A multi-layer approach to classify the risk of corrosion in concrete specimens that contain different additives

  José A Guzmán-Torres, Elia M Alonso-Guzmán

  Case Studies in Construction Materials, Volume 15, 2021, e00719, ISSN 2214-5095.

• Prediction of the Tensile Strength and Electrical Resistivity of Concrete with Organic Polymer and their Influence on Carbonation Using Data Science and a Machine Learning Technique

  Guzmán Torres, José Alberto; Elia Mercedes Alonso-Guzmán; Martínez-Molina, Wilfrido; Tinoco Ruiz, José Gerardo;

  Key Engineering Materials; Zurich Tomo 862, (Sep 2020): 72-77.

• Numerical and Observational Analysis of the Hydro-Dynamical Variability in a Small Lake: The Case of Lake Zirahuén, México

  T Gasca-Ortiz, DA Pantoja, A Filonov, J Alcocer

  Water 12 (6), 1658 6 2020

• A study of the stability for a generalized finite-difference scheme applied to the advection–diffusion equation

  G Tinoco-Guerrero, JG Tinoco-Ruiz

  Mathematics and Computers in Simulation 176, 301-311

• Reconstruction Methodology of a Francis runner blade using numerical tools

  G Delgado, S Galván, JC García, E Valencia

  Journal of Mechanical Science and Technology 34 (3), 1237-1247

• A stability analysis for a generalized finite-difference scheme applied to the pure advection equation

  G Tinoco-Guerrero, FJ Domínguez-Mota, A Gaona-Arias, ML Ruiz-Zavala, ...

  Mathematics and Computers in Simulation 147, 293-300, 2018

• Numerical solution of Richards’ equation of water flow by generalized finite differences

  C Chávez-Negrete, FJ Domínguez-Mota, D Santana-Quinteros

  Computers and Geotechnics 101, 168-175, 2018

• Finite difference schemes satisfying an optimality condition for the unsteady heat equation

  FJ Domínguez-Mota, SM Armenta, G Tinoco-Guerrero, JG Tinoco-Ruiz

  Mathematics and Computers in Simulation 106, 76-83, 2014

• An Heuristic Finite Difference Scheme on Irregular Plane Regions

  FJ Domınguez-Mota, PM Fernández-Valdez, E Ruiz-Dıaz, ...

  Applied Mathematical Sciences 8 (14), 671-683, 2014

• Effects of the grid geometry on the convergence of the discrete Laplace operator defined by finite differences on structured convex grids

  FJ Domínguez-Mota, P Fernández-Valdez, E Ruíz-Díaz, JG Tinoco-Ruíz, ...

  19th IMACS World Congress, 2013

• An implicit modified Lax-Wendroff scheme for irregular 2D space regions

  FJ Domínguez-Mota, P Fernández-Valdez, E Ruíz-Díaz, JG Tinoco-Ruíz, ...

  19th IMACS World Congress, 2013

• Numerical Structured Grid Generation: some recents developments and the UNAMalla 5.0 system

  P Barrera-Sánchez, FJ Domínguez-Mota, G García-Cano, ...

  19th IMACS World Congress, 2013

• AN IMPLEMENTATION OF THE COLLOCATION METHOD FOR INITIAL VALUE PROBLEMS

  RG CAMPOS, FD MOTA

  International Journal of Modeling, Simulation, and Scientific Computing 4 …, 2013

• Numerical Solution of Differential Equations in Irregular Plane Regions Using Quality Structured Convex Grids

  F Domínguez-Mota, P FERNÁNDEZ-VALDEZ, S MENDOZA-ARMENTA, ...

  International Journal of Modeling, Simulation, and Scientific Computing 4 …, 2013

• Some experiences using ITC based course materials for teaching high school Physics at the Universidad Michoacana de San Nicolás de Hidalgo, México

  HG Cruz, FD Mota, JV Cabrera

  Lat. Am. J. Phys. Educ. Vol 1 (231), 6, 2012

• A modified Lax-Wendroff scheme for irregular space 2D regions

  FJ Domínguez-Mota, JG Tinoco-Ruiz, G Tinoco-Guerrero, ...

  MASCOT&ISGG 2012, 2012

• Quadrature formulas for integrals transforms generated by orthogonal polynomials

  RG Campos, FD Mota, E Coronado

  IMA journal of numerical analysis 31 (3), 1181-1193, 2011

• Smoothness and Convex Area Functionals—Revisited

  PB Sánchez, JJ Cortés, FJ Domínguez-Mota, GG Flores, JG Tinoco-Ruiz

  SIAM Journal on Scientific Computing 32 (4), 1913-1928, 2010

• Smoothness and Convex Area Functionals-revisited

  P Barrera Sanchez, JJ Cortés, FJ Dominguez-Mota, GG Flores, ...

  SIAM Journal on Scientific Computing 32 (4), 1913-1928, 2010

• A simple convergent solver for initial value problems

  RG Campos, FD Mota

  arXiv preprint arXiv:0907.0693, 2009

• Generating quality structured convex grids on irregular regions

  P Barrera-Sánchez, FJ Domínguez-Mota, GG ALEZ-FLORES, ...

  Electronic Transactions on Numerical Analysis 34, 76-89, 2009

• Adaptive discrete harmonic grid generation

  P Barrera-Sánchez, LC Noda, FJ Domínguez-Mota, GFG Flores, ...

  Mathematics and Computers in Simulation 79 (6), 1792-1809, 2009

• Numerical Modeling of Coupled Phenomena in Science and Engineering: Practical Use and Examples

  MCS Arriaga, J Bundschuh, FJ Dominguez-Mota

  CRC Press, 2008

• Mathematical and computational modeling in Mexico

  J Bundschuh, MCS Arriaga, FJ Dominguez-Mota

  Numerical Modeling of Coupled Phenomena in Science and Engineering, 35-42, 2008

• Area functionals for high quality grid generation

  P Barrera-Sánchez, GG Flores, F Domínguez-Mota, JLC Noda, ...

  Numerical Modeling of Coupled Phenomena in Science and Engineering, 63-76, 2008

• Geothermal water in oil reservoir: a new 2D model solved with Comsol

  MC Suárez-Arriaga, FJ Dominguez-Mota, J Bundschuh

  Proceedings of the COMSOL conference. Boston, MA, 203-9, 2007

• Robust discrete grid generation on plane irregular regions

  P Barrera Sánchez, GF González Flores, FJ Domínguez-Mota

  Журнал вычислительной математики и математической физики 43 (6), 884-892, 2003

• Some experiences on orthogonal grid generation

  P Barrera-Sánchez, GFG Flores, FJ Domı́nguez-Mota

  Applied Numerical Mathematics 40 (1-2), 179-190, 2002