Colocación con funciones de base radial para la solución de modelos matemáticos en fenoménos de transporte
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Flórez-Escobar, W. F. . (2021). Colocación con funciones de base radial para la solución de modelos matemáticos en fenoménos de transporte. RACCEFYN, 45(176), 916–937. https://doi.org/10.18257/raccefyn.1370

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Resumen

En este trabajo se presentan los principales métodos con funciones de base radial, para la solución de modelos matemáticos en  fenómenos de transporte, basados en ecuaciones diferenciales parciales. Como casos de aplicación, se presentan algunos ejemplos de la solución de problemas acoplados de dinámica de fluidos, para ilustrar la potencia, generalidad y simplicidad de estas técnicas.

https://doi.org/10.18257/raccefyn.1370

Palabras clave

Colocación | Funciones radiales
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Referencias

Aftab, W., Moinuddin, M., y Shaikh, M. S. (2014). A Novel Kernel for RBF Based Neural Networks. Abstract and Applied Analysis, 2014(), 176253. doi: 10.1155/2014/176253

Berg, P., y Ladipo, K. (2009). Exact solution of an electro-osmotic flow problem in a cylindrical channel of polymer electrolyte membranes. Proceedings of the Royal Society of London Series A, 465(), 2663–2679.

Bird, R. B., Armstrong, R. C., y Hassager, O. (1987). Dynamics of polymeric liquids. vol. 1: Fluid mechanics. Wiley Interscience,(), .

Bochner, S. (1941, may). Hilbert Distances and Positive Definite Functions. Annals of Mathematics, 42(3), 647–656. Descargado de http://www.jstor.org/stable/1969252 doi: 10.2307/1969252

Boztosun, I., y Charafi, A. (2002). An analysis of the linear advection–diffusion equation using mesh-free and mesh-dependent methods. Engineering Analysis with Boundary Elements, 26(10), 889–895. doi: https://doi.org/10.1016/S0955-7997(02)00053-X

Buhmann, M. D. (2000). Radial basis functions. Acta Numerica, 9(), 1–38. doi: 10.1017/S0962492900000015

Carroll, C. P., y Joo, Y. L. (2006). Electrospinning of viscoelastic Boger fluids: Modeling and experiments. Physics of Fluids,(),. doi: 10.1063/1.2200152

Chantasiriwan, S. (2004). Cartesian grid methods using radial basis functions for solving Poisson, Helmholtz, and diffusion–convection equations. Engineering Analysis with Boundary Elements, 28(12), 1417–1425. doi: https://doi.org/10.1016/j.enganabound.2004.08.004

Chejne J, F. (2016, jul.). Una aproximación a la construcción de modelos matemáticos para la descripción de la naturaleza. Rev. Acad. Colomb. Cienc. Ex. Fis. Nat., 40(155),353-365. doi: 10.18257/raccefyn.339

Chen, C. S., Fan, C. M., y Wen, P. H. (2012). The method of approximate particular solutions for solving certain partial differential equations. Numerical Methods for Partial Differential Equations, 28(2), 506–522. doi: 10.1002/num.20631

Cheng, A.-D. (2000). Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions. Engineering Analysis with Boundary Elements, 24(7), 531–538. doi: https://doi.org/10.1016/S0955-7997(00)00033-3

Cheng, A. H. D., y Hong, Y. (2020). An overview of the method of fundamental solutions -Solvability, uniqueness, convergence, and stability. Engineering Analysis with Boundary Elements, 120(), 118–152. doi: https://doi.org/10.1016/j.enganabound.2020.08.013

Chinchapatnam, P. P., Djidjeli, K., y Nair, P. B. (2007). Radial basis function meshless method for the steady incompressible Navier–Stokes equations. International Journal of Computer Mathematics, 84(10), 1509–1521. doi: 10.1080/00207160701308309

Dehghan, M., Abbaszadeh, M., y Mohebbi, A. (2014). The numerical solution of nonlinear high dimensional generalized benjamin–bona–mahony–burgers equation via the meshless method of radial basis functions. Computers Mathematics with Applications, 68(3), 212 - 237.

Dehghan, M., y Nikpour, A. (2013). Numerical solution of the system of second-order boundary value problems using the local radial basis functions based differential quadrature collocation method. Applied Mathematical Modelling, 37(18), 8578–8599. doi: https://doi.org/10.1016/j.apm.2013.03.054

Fasshauer, G. E. (1997). Solving partial differential equations by collocation with radial basis functions. En In: Surface fitting and multiresolution methods a. le m’ehaut’e, c. rabut and l.l. schumaker (eds.), vanderbilt (pp. 131–138). University Press.

Fasshauer, G. E. (2007). Meshfree Approximation Methods with Matlab. WORLD SCIENTIFIC. Descargado de https://www.worldscientific.com/doi/abs/10.1142/6437 doi: 10.1142/6437

Feng, J. (2002). The stretching of an electrified non-newtonian jet: A model for electrospinning. Physics of fluids, 14(11), 3912–3926.

Feng, J. J. (2003). Stretching of a straight electrically charged viscoelastic jet. Journal of Non-Newtonian Fluid Mechanics,(),. doi: 10.1016/S0377-0257(03)00173-3

Florez, W., Bustamante, C., Giraldo, M., y Hill, A. (2012). Local mass conservative Hermite interpolation for the solution of flow problems by a multi-domain boundary element approach. Applied Mathematics and Computation, 218(11), . doi: 10.1016/j.amc.2011.12.015

Fornberg, B., y Lehto, E. (2011). Stabilization of RBF-generated finite difference methods for convective PDEs. Journal of Computational Physics, 230(6), 2270–2285. doi: https://doi.org/10.1016/j.jcp.2010.12.014

Franke, C., y Schaback, R. (1998, jul). Solving partial differential equations by collocation using radial basis functions. Applied Mathematics and Computation, 93(1), 73–82. doi: 10.1016/s0096-3003(97)10104-7

Granados, J., Power, H., y Bustamante, C. (2018). A global particular solution meshless approach for the four-sided lid-driven cavity flow problem in the presence of magnetic fields. Computers and Fluids, 160(), . doi: 10.1016/j.compfluid.2017.10.027

Haider, A., Haider, S., y Kang, I.-K. (2018). A comprehensive review summarizing the effect of electrospinning parameters and potential applications of nanofibers in biomedical and biotechnology. Arabian Journal of Chemistry, 11(8), 1165–1188.

Hohman, M. M., Shin, M., Rutledge, G., y Brenner, M. P. (2001). Electrospinning and electrically forced jets. I. Stability theory. Physics of Fluids,(), . doi: 10.1063/1.1383791

Hon, Y. C., y Schaback, R. (2001). On unsymmetric collocation by radial basis functions. Applied Mathematics and Computation, 119(2), 177–186. doi: https://doi.org/10.1016/S0096-3003(99)00255-6

Hubbert, S., L.Gia, Q. T., y Morton, T. M. (2015). Spherical Radial Basis Functions, Theory and Applications. Springer.

Jackson, S. J., Power, H., Giddings, D., y Stevens, D. (2017). The stability of immiscible viscous fingering in Hele-Shaw cells with spatially varying permea bility. Computer Methods in Applied Mechanics and Engineering, 320(), 606–632. Descargado de https://www.sciencedirect.com/science/article/pii/S0045782516312373 doi: https://doi.org/10.1016/j.cma.2017.03.030

Jumarhon, B., Amini, S., y Chen, K. (2000, sep). The Hermite collocation method using radial basis functions. Engineering Analysis with Boundary Elements, 24(7-8), 607–611. doi: 10.1016/s0955-7997(00)00041-2

Kamyabi, A., Kermani, V., y Kamyabi, M. (2019). Improvements to the meshless generalized finite difference method. Engineering Analysis with Boundary Elements, 99(), 233–243. doi: https://doi.org/10.1016/j.enganabound.2018.11.002

Kansa, E. J. (1990). Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—II solutions to parabolic, hyperbolic and elliptic partial differential equations. Computers & Mathematics with Applications, 19(8), 147–161. doi: https://doi.org/10.1016/0898-1221(90)90271-K

Levesley, J., y Ragozin, D. L. (2007). Radial basis interpolation on homogeneous manifolds: convergence rates. Advances in Computational Mathematics, 27(2), 237–246.doi: 10.1007/s10444-005-9000-1

Li, D. (2004). Electrokinetics in microfluidics (Vol. 2). Elsevier.

Madych, W., y Nelson, S. (1990, jan). Multivariate interpolation and conditionally positive definite functions. II. Mathematics f Computation, 54(189), 211–230. doi: 10.1090/S0025-5718-1990-0993931-7

Madych, W. R., y Nelson, S. A. (1990). Multivariate interpolation and conditionally positive definite functions. ii. Mathematics of Computation, 54(189), 211–230.

Mai-Duy, N., y Tran-Cong, T. (2002). Mesh-free radial basis function network methods with domain decomposition for approximation of functions and numerical solution of Poisson’s equations. Engineering Analysis with Boundary Elements, 26(2), 133–156. doi: https://doi.org/10.1016/S0955-7997(01)00092-3

Micchelli, C. A. (1986). Interpolation of scattered data: Distance matrices and conditionally positive definite functions. Constructive Approximation, 2(1), 11–22. doi: 10.1007/BF01893414

Orsini, P., Power, H., y Lees, M. (2011). The Hermite radial basis function control volume method for multi-zones problems; A non-overlapping domain decomposition algorithm. Computer Methods in Applied Mechanics and Engineering, 200(5), 477–493. doi: https://doi.org/10.1016/j.cma.2010.05.001

Orsini, P., Power, H., Morvan, H., y Lees, M. (2010). An implicit upwinding volume element method based on meshless radial basis function techniques for modelling transport phenomena. International Journal for Numerical Methods in Engineering, 81(1), 1–27. doi: 10.1002/nme.2682

Oruc¸,Ö. (2021). A radial basis function finite difference (RBF-FD) method for numerical simulation of interaction of high and low frequency waves: Zakharov–Rubenchik equations. Applied Mathematics and Computation, 394(), 125787. doi: https://doi.org/10.1016/j.amc.2020.125787

Popov, H., V. Power. (1996). A domain decomposition on the dual reciprocity approach. Boundary Elements Communications,(), .

Powell, M. J. D. (1994). The uniform convergence of thin plate splineinterpolation in two dimensions. Numerische Mathematik, 68(1), 107–128. doi: 10.1007/s002110050051

Russo, G., Capasso, V., Nicosia, G., y Romano, V. (2016). Progress in industrial mathematics at ecmi 2014. Springer.

Sadeghi, A., Azari, M., y Chakraborty, S. (2017, dec). H2 forced convection in rectangular microchannels under a mixed electroosmotic and pressure-driven flow. International Journal of Thermal Sciences, 122(), 162–171. doi: 10.1016/j.ijthermalsci.2017.08.019

Sadeghi, A., Kazemi, Y., y Saidi, M. H. (2013, aug). Joule heating effects in electrokinetically driven flow through rectangular microchannels: An analytical approach. Nanoscale and Microscale Thermophysical Engineering, 17(3), 173–193. doi: 10.1080/15567265.2013.776150

Sarra, S. A. (2006). Integrated multiquadric radial basis function approximation methods. Computers Mathematics with Applications, 51(8), 1283–1296. Descargado de https://www.sciencedirect.com/science/article/pii/S0898122106000848 doi: https://doi.org/10.1016/j.camwa.2006.04.014

Schaback, R. (1995). Multivariate interpolation and approximation by translates of a basis function the space of functions (1.1) often..

Schaback, R. (2007). A practical guide to radial basis functions..

Schoenberg, I. J. (1938, may). Metric Spaces and Completely Monotone Functions. Annals of Mathematics, 39(4), 811–841. Descargado de http://www.jstor.org/stable/1968466 doi: 10.2307/1968466

Shampine, L., Muir, P., y Xu, H. (2006). A user-friendly fortran bvp solver. J. Numer. Anal. Ind. Appl. Math, 1(2), 201–217.

Stevens, D., y Power, H. (2015). The radial basis function finite collocation approach for capturing sharp fronts in time dependent advection problems. Journal of Computational Physics, 298(), 423–445. Descargado de https://www.sciencedirect.com/science/article/pii/S0021999115003666 doi: https://doi.org/10.1016/j.jcp.2015.05.032

Stevens, D., Power, H., y Cliffe, K. A. (2013). A solution to linear elasticity using locally supported RBF collocation in a generalised finite-difference mode. Engineering Analysis with Boundary Elements, 37(1), 32–41. doi: https://doi.org/10.1016/j.enganabound.2012.08.005

Stevens, D., Power, H., Meng, C. Y., Howard, D., y Cliffe, K. A. (2013). An alternative local collocation strategy for high-convergence meshless PDE solutions, using radial basis functions. J. Comput. Phys., 254(1), 52–75.

Tiago, C. M., y Leitão, V. M. A. (2006). Application of radial basis functions to linear and nonlinear structural analysis problems. Computers Mathematics with Applications, 51(8), 1311–1334. doi: https://doi.org/10.1016/j.camwa.2006.04.008

Wendland, H. (1995). Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Advances in Computational Mathematics, 4(1), 389–396. Descargado de https://doi.org/10.1007/BF02123482 doi: 10.1007/BF02123482

Wertz, J., Kansa, E. J., y Ling, L. (2006). The role of the multiquadric shape parameters in solving elliptic partial differential equations. Computers Mathematics with Applications, 51(8), 1335–1348. doi: https://doi.org/10.1016/j.camwa.2006.04.009

Wu, Z. (1998). Solving pde with radial basis function and the error estimation, advances in computational mathematics, lecture notes on pure and applied mathematics. En In: Proceedings of the guangzhou international symposium,z. chen, y. li, c.a. micchelli,y. xu (eds.) (Vol. 202).

Wu, Z., y Zhang, S. (2013). Conservative multiquadric quasi-interpolation method for Hamiltonian wave equations. Engineering Analysis with Boundary Elements, 37(7), 1052–1058. doi: https://doi.org/10.1016/j.enganabound.2013.04.011

Zerroukat, M., Power, H., y Chen, C. S. (1998a). A numerical method for heat transfer problems using collocation and radial basis functions. International Journal for Numerical Methods in Engineering, 42(7), 1263-1278.

Zerroukat, M., Power, H., y Chen, C. S. (1998b). A numerical method for heat transfer problems using collocation and radial basis functions. International Journal for Numerical Methods in Engineering, 42(7), 1263-1278. doi: https://doi.org/10.1002/(SICI)1097-0207(19980815)42:7.1263::AID-NME431.3.0.CO;2-I

Zhang, X., Chen, C., Chen, M., y Li, Z. (2016). Localized method of approximate particular solutions for solving unsteady Navier-Stokes problem. j, 40(3), . doi: 10.1016/j.apm.2015.09.048

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