sample of publications

• articles 

  • RBF based quadrature on the sphere.  International Journal of Applied Mathematics and Computer Science.  32:467-478. 2022
  • Micro-combustion modelling with RBF-FD: A high-order meshfree method for reactive flows in complex geometries.  APPLIED MATHEMATICAL MODELLING.  94:635-655. 2021
  • A local radial basis function method for the Laplace-Beltrami operator.  JOURNAL OF SCIENTIFIC COMPUTING.  86. 2021
  • Frequency optimized RBF-FD for wave equations.  JOURNAL OF COMPUTATIONAL PHYSICS.  371:564-580. 2018
  • Optimized Finite Difference Formulas for Accurate High Frequency Components.  Mathematical Problems in Engineering.  2016. 2016
  • Radial basis function interpolation in the limit of increasingly flat basis functions.  JOURNAL OF COMPUTATIONAL PHYSICS.  307:225-242. 2016
  • Laurent series based RBF-FD method to avoid ill-conditioning.  ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS.  52:24-31. 2015
  • Laurent expansion of the inverse of perturbed, singular matrices.  JOURNAL OF COMPUTATIONAL PHYSICS.  299:307-319. 2015
  • Optimal shape parameter for the solution of elastostatic problems with the RBF method.  JOURNAL OF ENGINEERING MATHEMATICS.  85:115-129. 2014
  • Application of the RBF meshless method to laminar flame propagation.  ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS.  37:1617-1624. 2013
  • Propagation of premixed laminar flames in 3D narrow open ducts using RBF-generated finite differences.  COMBUSTION THEORY AND MODELLING.  17:789-803. 2013
  • Gaussian RBF-FD weights and its corresponding local truncation errors.  ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS.  36:1361-1369. 2012
  • Optimal variable shape parameter for multiquadric based RBF-FD method.  JOURNAL OF COMPUTATIONAL PHYSICS.  231:2466-2481. 2012
  • Optimal constant shape parameter for multiquadric based RBF-FD method.  JOURNAL OF COMPUTATIONAL PHYSICS.  230:7384-7399. 2011
  • RBF-FD Formulas and Convergence Properties.  JOURNAL OF COMPUTATIONAL PHYSICS.  229:8281-8295. 2010
  • Application of the RBF Meshless Method to the Solution of the Radiative Transport Equation.  JOURNAL OF COMPUTATIONAL PHYSICS.  229:1897-1908. 2010
  • Radial Basis Function Solution of the Motz Problem.  ENGINEERING COMPUTATIONS.  27:606-620. 2010
  • Método de colocación simétrico RBF para la solución numérica de la ecuación de difusión en estado transiente = Colocation Simetric Method RBF for Numeric Solution of the Difusion Equation Transient State.  Revista colombiana de fisica.  41:652-655. 2009
  • On the Enriched RBF Method for Singular Potential Problems.  ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS.  33:1062-1073. 2009
  • Use of Singularity Capturing Functions in the Solution of Problems with Discontinuous Boundary Conditions.  ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS.  33:200-208. 2009
  • Reservoir Characterization Using Stochastic Initializations and the Level Set Method.  COMPUTERS & MATHEMATICS WITH APPLICATIONS.  56:697-708. 2008

• book chapters 

  • Radial Basis Function (RBF) Solution of the Motz Problem. In: Progress in Industrial Mathematics at ECMI 2008.  Springer Berlin / Heidelberg. 907-912. 2010
  • Meshless Solution of Singular Potential Flows in Strong Formulation. In: Progress in Industrial Mathematics at ECMI 2008.  Springer Berlin / Heidelberg. 727-732. 2010
  • A Meshless Solution to the p-Laplace Equation. In: Progress on Meshless Methods: (Computational Methods in Apllied Science).  SPRINGER. 17-35. 2008
  • Meshless Simulation of Hele-Shaw Flow. In: Progress in Industrial Mathematics at ECMI 2006.  Springer Berlin / Heidelberg. 677-682. 2008

• conference contributions 

  • Frequency optimized RBF-FD for wave equations.  279-279. 2019
  • Computation and use of the Laurent series of the inverse in RBF-FD problems 2016
  • Gaussian RBF-FD Weigths and Its Corresponding Local Truncation Errors.  97-108. 2012
  • Spectral Modeling of The Dynamics of Optically Injected One-Dimensional Currents 2012
  • Meshless Solution of Singular Potential Flows in Strong Formulation 2008
  • Meshless simulation of Hele-Shaw flow 2008
  • Radial Basis Function (RBF) Solution of the Motz Problem 2008