×
Wang, Chao; Gu, Yan; Qiu, Lin; Wang, Fajie

Analysis of 3D transient heat conduction in functionally graded materials using a local semi-analytical space-time collocation scheme. (English) Zbl 1521.80038

Eng. Anal. Bound. Elem. 149, 203-212 (2023).

Cited in 1 Document

MSC:

80M99 Basic methods in thermodynamics and heat transfer
65M80 Fundamental solutions, Green’s function methods, etc. for initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
80A19 Diffusive and convective heat and mass transfer, heat flow

Keywords:

localized space-time method of fundamental solutions; functionally graded materials; meshless method; Green’s function; transient heat conduction
Cite Review PDF
Full Text: DOI

References:

[1] Wang, C.; Qiu, Z.-. P., Fuzzy finite difference method for heat conduction analysis with uncertain parameters, Acta Mech Sin, 30, 3, 383-390 (2014) · Zbl 1346.80007
[2] Li, X.; Zhao, Q.; Long, K.; Zhang, H., Multi-material topology optimization of transient heat conduction structure with functional gradient constraint, Int Commun Heat Mass Transfer, 131, Article 105845 pp. (2022)
[3] Azis, M. I.; Clements, D. L., Nonlinear transient heat conduction problems for a class of inhomogeneous anisotropic materials by BEM, Eng Anal Bound Elem, 32, 12, 1054-1060 (2008) · Zbl 1244.80008
[4] Wang, H.; Qin, Q. H.; Kang, Y. L., A meshless model for transient heat conduction in functionally graded materials, Comput Mech, 38, 1, 51-60 (2006) · Zbl 1097.80001
[5] Marin, L.; Lesnic, D., The method of fundamental solutions for nonlinear functionally graded materials, Int J Solids Struct, 44, 21, 6878-6890 (2007) · Zbl 1166.80300
[6] Fairweather, G.; Karageorghis, A., The method of fundamental solutions for elliptic boundary value problems, Adv Comput Math, 9, 1, 69 (1998) · Zbl 0922.65074
[7] Chen, Z.; Sun, L., A boundary meshless method for dynamic coupled thermoelasticity problems, Appl Math Lett, 134, Article 108305 pp. (2022) · Zbl 1502.65159
[8] Cheng, S.; Wang, F.; Wu, G., A semi-analytical and boundary-type meshless method with adjoint variable formulation for acoustic design sensitivity analysis, Appl Math Lett, 131, Article 108068 pp. (2022) · Zbl 1494.76064
[9] Fu, Z.; Chen, W.; Wen, P.; Zhang, C., Singular boundary method for wave propagation analysis in periodic structures, J Sound Vib, 425, 170-188 (2018)
[10] Wei, X.; Luo, W., 2.5D singular boundary method for acoustic wave propagation, Appl Math Lett, 112, Article 106760 pp. (2021) · Zbl 1462.76149
[11] Qiu, L.; Wang, F.; Lin, J., A meshless singular boundary method for transient heat conduction problems in layered materials, Comput Math Appl, 78, 11, 3544-3562 (2019) · Zbl 1443.65251
[12] Fu, Z.; Xi, Q.; Gu, Y., Singular boundary method: a review and computer implementation aspects, Eng Anal Bound Elem, 147, 231-266 (2023) · Zbl 1521.74318
[13] Wang, F.; Wang, C.; Chen, Z., Local knot method for 2D and 3D convection-diffusion-reaction equations in arbitrary domains, Appl Math Lett, 105, Article 106308 pp. (2020) · Zbl 1524.65915
[14] Yue, X.; Wang, F.; Li, P.-. W.; Fan, C.-. M., Local non-singular knot method for large-scale computation of acoustic problems in complicated geometries, Comput Math Appl, 84, 128-143 (2021) · Zbl 1524.35174
[15] Wang, C.; Wang, F.; Gong, Y., Analysis of 2D heat conduction in nonlinear functionally graded materials using a local semi-analytical meshless method, AIMS Mathematics, 6, 11, 12599-12618 (2021) · Zbl 1515.65266
[16] Fan, C.-. M.; Huang, Y. K.; Chen, C. S.; Kuo, S. R., Localized method of fundamental solutions for solving two-dimensional Laplace and biharmonic equations, Eng Anal Bound Elem, 101, 188-197 (2019) · Zbl 1464.65267
[17] Sun, L.; Fu, Z.; Chen, Z., A localized collocation solver based on fundamental solutions for 3D time harmonic elastic wave propagation analysis, Appl Math Comput, 439, Article 127600 pp. (2023) · Zbl 07689961
[18] Wang, F.; Fan, C.-. M.; Hua, Q.; Gu, Y., Localized MFS for the inverse Cauchy problems of two-dimensional Laplace and biharmonic equations, Appl Math Comput, 364, Article 124658 pp. (2020) · Zbl 1433.65338
[19] Li, X.; Li, S., On the augmented moving least squares approximation and the localized method of fundamental solutions for anisotropic heat conduction problems, Eng Anal Bound Elem, 119, 74-82 (2020) · Zbl 1464.65274
[20] Chen, Z.; Wang, F., Localized method of fundamental solutions for acoustic analysis inside a car cavity with sound-absorbing material, Adv Appl Math Mech, 15, 182-201 (2022) · Zbl 1513.65494
[21] Yue, X.; Wang, F.; Hua, Q.; Qiu, X.-. Y., A novel space-time meshless method for nonhomogeneous convection-diffusion equations with variable coefficients, Appl Math Lett, 92, 144-150 (2019) · Zbl 1414.65025
[22] Hamaidi, M.; Naji, A.; Charafi, A., Space-time localized radial basis function collocation method for solving parabolic and hyperbolic equations, Eng Anal Bound Elem, 67, 152-163 (2016) · Zbl 1403.65091
[23] Bank, R. E.; Vassilevski, P. S.; Zikatanov, L. T., Arbitrary dimension convection-diffusion schemes for space-time discretizations, J Comput Appl Math, 310, 19-31 (2017) · Zbl 1348.65139
[24] Young, D.; Tsai, C.; Murugesan, K.; Fan, C.-. M.; Chen, C., Time-dependent fundamental solutions for homogeneous diffusion problems, Eng Anal Bound Elem, 28, 12, 1463-1473 (2004) · Zbl 1098.76622
[25] Li, M.; Chen, C.; Chu, C.; Young, D., Transient 3D heat conduction in functionally graded materials by the method of fundamental solutions, Eng Anal Bound Elem, 45, 62-67 (2014) · Zbl 1297.80011
[26] Tsai, C.; Young, D.; Fan, C.-. M.; Chen, C., MFS with time-dependent fundamental solutions for unsteady Stokes equations, Eng Anal Bound Elem, 30, 10, 897-908 (2006) · Zbl 1195.76324
[27] Dou, F.; Hon, Y., Kernel-based approximation for Cauchy problem of the time-fractional diffusion equation, Eng Anal Bound Elem, 36, 9, 1344-1352 (2012) · Zbl 1352.65309
[28] Dizaji, A. F.; Jafari, A., Three-dimensional fundamental solution of wave propagation and transient heat transfer in non-homogenous media, Eng Anal Bound Elem, 33, 10, 1193-1200 (2009) · Zbl 1200.74085
[29] Wang, F.; Fan, C.-. M.; Zhang, C.; Lin, J., A localized space-time method of fundamental solutions for diffusion and convection-diffusion problems, Adv Appl Math Mech, 12, 4, 940-958 (2020) · Zbl 1488.65542
[30] Qiu, L.; Lin, J.; Qin, Q.-. H.; Chen, W., Localized space-time method of fundamental solutions for three-dimensional transient diffusion problem, Acta Mech Sin, 36, 5, 1051-1057 (2020)
[31] Qiu, L.; Wang, F.; Lin, J.; Qin, Q.-. H.; Zhao, Q., A novel combined space-time algorithm for transient heat conduction problems with heat sources in complex geometry, Comput Struct, 247, Article 106495 pp. (2021)
[32] Sutradhar, A.; Paulino, G. H.; Gray, L., Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method, Eng Anal Bound Elem, 26, 2, 119-132 (2002) · Zbl 0995.80010
[33] Kupradze, V. D.; Aleksidze, M. A., The method of functional equations for the approximate solution of certain boundary value problems, USSR Comput Math Math Phys, 4, 4, 82-126 (1964) · Zbl 0154.17604
[34] Cui, X. Y.; Li, Z. C.; Feng, H.; Feng, S. Z., Steady and transient heat transfer analysis using a stable node-based smoothed finite element method, Int J Therm Sci, 110, 12-25 (2016)
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.