×

Application of compact local integrated RBF (CLI-RBF) for solving transient forward and backward heat conduction problems with continuous and discontinuous sources. (English) Zbl 1521.65068


MSC:

65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65D12 Numerical radial basis function approximation
34B15 Nonlinear boundary value problems for ordinary differential equations
80A19 Diffusive and convective heat and mass transfer, heat flow
Full Text: DOI

References:

[1] Gu, Y.; Wang, L.; Chen, W.; Zhang, C.; He, X., Application of the meshless generalized finite difference method to inverse heat source problems, Int J Heat Mass Transfer, 108, 721-729 (2017)
[2] Lee, S. Y.; Yan, Q. Z., Inverse analysis of heat conduction problems with relatively long heat treatment, Int J Heat Mass Transfer, 105, 401-410 (2017)
[3] Jhao, W. S.; Liu, C. S.; Kuo, C. L., The multiple-scale polynomial trefftz method for solving inverse heat conduction problems, Int J Heat Mass Transfer, 95, 936-943 (2016)
[4] Maciejewska, B.; Piasecka, M., Trefftz function-based thermal solution of inverse problem in unsteady-state flow boiling heat transfer in a minichannel, Int J Heat Mass Transfer, 107, 925-933 (2017)
[5] Kansa, E. J.; Amirfakhrian, M.; Arghand, M., A new approximate method for an inverse time-dependent heat source problem using fundamental solutions and RBFs, Eng Anal Bound Elem, 64, 278-289 (2016) · Zbl 1403.65051
[6] Yang, L.; Deng, Z. C.; Hon, Y. C., Simultaneous identification of unknown initial temperature and heat source, Dynam Systems Appl, 25, 4, 583-602 (2016) · Zbl 1362.35337
[7] Chen, Y. W., High order implicit and explicit Lie-group schemes for solving backward heat conduction problems, Int J Heat Mass Transfer, 101, 1016-1029 (2016)
[8] Frackowiak, A.; Wolfersdorf, J.v.; Cialkowski, M., An iterative algorithm for the stable solution of inverse heat conduction problems in multiply-connected domains, Int J Therm Sci, 96, 268-276 (2015)
[9] Yu, Y.; Xu, D., On the inverse problem of thermal conductivity determination in nonlinear heat and moisture transfer model within textiles, Appl Math Comput, 264, 284-299 (2015) · Zbl 1410.80010
[10] Liu, C. S., Lie-group differential algebraic equations method to recover heat source in a Cauchy problem with analytic continuation data, Int J Heat Mass Transfer, 78, 538-547 (2014)
[11] Chang, J. R.; Kuo, C. L.; Liu, C. S., The modified polynomial expansion method for identifying the time dependent heat source in two-dimensional heat conduction problems, Int J Heat Mass Transfer, 92, 658-664 (2016)
[12] Wang, B.; Liao, A., A meshless method to determine a source term in heat equation with radial basis functions, Chinese J Math, 2013, Article 761272 pp. (2013) · Zbl 1301.35217
[13] Han, H.; Yin, D., A non-overlap domain decomposition method for the forward-backward heat equation, J Comput Appl Math, 159, 35-44 (2003) · Zbl 1032.65107
[14] Hon, Y. C.; Takeuchi, T., Discretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem, Adv Comput Math, 34, 167-183 (2011) · Zbl 1208.65141
[15] Li, M.; Jiang, T.; Hon, Y. C., A meshless method based on RBFs method for nonhomogeneous backward heat conduction problem, Eng Anal Bound Elem, 34, 785-792 (2010) · Zbl 1244.80023
[16] Ostrowski, Z.; Białecki, R. A.; Kassab, A. J., Solving inverse heat conduction problems using trained POD-RBF network inverse method, Inverse Probl Sci Eng, 16, 39-54 (2008) · Zbl 1158.35433
[17] Xia, H.; Gu, Y., Generalized finite difference method for electroelastic analysis of three-dimensional piezoelectric structures, Appl Math Lett, 117, Article 107084 pp. (2021) · Zbl 1462.74165
[18] Gu, Y.; Fan, C. M.; Fu, Z., Localized method of fundamental solutions for three-dimensional elasticity problems: Theory, Adv Appl Math Mech, 13, 6, 1520-1534 (2021) · Zbl 1488.74026
[19] Abbaszadeh, M.; Dehghan, M., Numerical and analytical investigations for solving the inverse tempered fractional diffusion equation via interpolating element-free galerkin (iefg) method, J Therm Anal Calorim, 143, 3, 1917-1933 (2021)
[20] Dehghan, M.; Shafieeabyaneh, N.; Abbaszadeh, M., A local meshless procedure to determine the unknown control parameter in the multi-dimensional inverse problems, Inverse Probl Sci Eng, 29, 10, 1369-1400 (2021) · Zbl 07479288
[21] Baby, R.; Balaji, C., Experimental investigations on phase change material based finned heat sinks for electronic equipment cooling, Int J Heat Mass Transfer, 55, 1642-1649 (2012)
[22] Jakkareddy, P. S.; Balaji, C., A non-intrusive technique to determine the spatially varying heat transfer coefficients in a flat plate with flush mounted heat sources, Int J Therm Sci, 131, 144-159 (2018)
[23] Kumar, S.; Jakkareddy, P. S.; Balaji, C., A novel method to detect hot spots and estimate strengths of discrete heat sources using liquid crystal thermography, Int J Therm Sci, 154, Article 106377 pp. (2020)
[24] Godi, S. C.; Pattamatta, A.; Balaji, C., Heat transfer from a single and row of three dimensional wall jets - A combined experimental and numerical study, Int J Heat Mass Transfer, 159, Article 119801 pp. (2020)
[25] Balaji, C.; Hölling, M.; Herwig, H., A temperature wall function for turbulent mixed convection from vertical, parallel plate channels, Int J Therm Sci, 47, 6, 723-729 (2008)
[26] Banei, S.; Shanazari, K., On the convergence analysis and stability of the RBF-adaptive method for the forward-backward heat problem in 2D, Appl Numer Math (2020), in press · Zbl 1491.65087
[27] Shanazari, K.; Banei, S., A meshfree method with a non-overlapping domain decomposition method based on TPS for solving the forward-backward heat equation in two-dimension, Numer Algorithms (2020) · Zbl 1491.65087
[28] Mai-Duy, N.; Tran-Cong, T., An efficient indirect RBFN-based method for numerical solution of PDEs, Numer Meth PDE, 21, 4, 770-790 (2005) · Zbl 1077.65125
[29] Sarra, S., Integrated multiquadric radial basis function approximation methods, Comput Math Appl, 51, 8, 1283-1296 (2006) · Zbl 1146.65327
[30] Mohebbi, A.; Abbaszadeh, M.; Dehghan, M., The use of a meshless technique based on collocation and radial basis functions for solving the time fractional nonlinear schrödinger equation arising in quantum mechanics, Eng Anal Bound Elem, 37, 2, 475-485 (2013) · Zbl 1352.65397
[31] Yoon, J., Spectral approximation orders of radial basis function interpolation on the sobolov space, SIAM J Math Anal, 33, 946-958 (1999) · Zbl 0996.41002
[32] Tien, C. M.T.; Thai-Quang, N.; Mai-Duy, N.; Tran, C.-D.; Tran-Cong, T., A three-point coupled compact integrated RBF scheme for second-order differential problems, Comput Model Eng Sci, 104, 6, 425-469 (2015)
[33] Thai-Quang, N.; Mai-Duy, N.; Tran, C.-D.; Tran-Cong, T., High-order alternating direction implicit method based on compact integrated-RBF approximations for unsteady/steady convection-diffusion equations, Comput Model Eng Sci, 89, 3, 189-220 (2012) · Zbl 1357.65138
[34] Mai-Duy, N.; Tran-Cong, T., A compact five-point stencil based on integrated RBFs for 2D second-order differential problems, J Comput Phys, 235, 302-321 (2013)
[35] Tien, C. M.T.; Mai-Duy, N.; Tran, C. D.; Tran-Cong, T., A numerical study of compact approximations based on flat integrated radial basis functions for second-order differential equations, Comput Math Appl, 72, 9, 2364-2387 (2016) · Zbl 1368.65126
[36] ul Islam, S.; Ismail, S., Meshless collocation procedures for time-dependent inverse heat problems, Int J Heat Mass Transfer, 113, 1152-1167 (2017)
[37] Yeih, W.; Liu, C. S., A three-point bvp of time dependent inverse heat source problems and solving by a TSLGSM, Comput Model Eng Sci CMES, 46, 2 (2009) · Zbl 1231.65164
[38] Lima, F. R.; Machado, A. R.; Guimaraes, G.; Guths, S., Numerical and experimental simulation for heat flux and cutting temperature estimation using three-dimensional inverse heat conduction technique, Inverse Probl Eng, 8, 6, 553-577 (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.