×

zbMATH — the first resource for mathematics

Steady-state nonlinear heat conduction in composite materials using the method of fundamental solutions. (English) Zbl 1194.74054
Summary: The steady-state heat conduction in composite (layered) heat conductors with temperature dependent thermal conductivity and mixed boundary conditions involving convection and radiation is investigated using the method of fundamental solutions with domain decomposition. The locations of the singularities outside the solution domain are optimally determined using a non-linear least-squares procedure. Numerical results for non-linear bimaterials are presented and discussed.

MSC:
74F05 Thermal effects in solid mechanics
74E30 Composite and mixture properties
80A20 Heat and mass transfer, heat flow (MSC2010)
65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N38 Boundary element methods for boundary value problems involving PDEs
65H10 Numerical computation of solutions to systems of equations
Software:
HYBRJ; minpack
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alves, C.J.S.; Chen, C.S., A new method of fundamental solutions applied to nonhomogeneous elliptic problems, Adv. comput. math., 23, 125-142, (2005) · Zbl 1070.65119
[2] Azevedo, J.P.S.; Wrobel, L.C., Non-linear heat conduction in composite bodies: a boundary element formulation, Int. J. numer. meth. engrg., 26, 19-38, (1988) · Zbl 0633.65117
[3] Berger, J.R.; Karageorghis, A., The method of fundamental solutions for heat conduction in layered materials, Int. J. numer. meth. engrg., 45, 1681-1694, (1999) · Zbl 0972.80014
[4] Berger, J.R.; Karageorghis, A., The method of fundamental solutions for layered elastic materials, Engrg. anal. boundary elements, 25, 877-886, (2001) · Zbl 1008.74081
[5] Berger, J.R.; Karageorghis, A.; Martin, P.A., Stress intensity factor computation using the method of fundamental solutions: mixed mode problems, Int. J. numer. meth. engrg., 69, 469-483, (2007) · Zbl 1194.74086
[6] Bialecki, R.; Nahlik, R., Solving nonlinear steady-state potential problems in inhomogeneous bodies using the boundary-element method, Numer. heat transfer, part B, 16, 79-96, (1989) · Zbl 0693.76036
[7] Bialecki, R.; Nowak, A.J., Boundary value problems in heat conduction with nonlinear material and nonlinear boundary conditions, Appl. math. modell., 5, 417-421, (1981) · Zbl 0475.65078
[8] Bialecki, R.; Kuhn, G., Boundary element solution of heat conduction problems in multizone bodies of non-linear material, Int. J. numer. meth. engrg., 36, 799-809, (1993) · Zbl 0825.73910
[9] Bogomolny, A., Fundamental solutions method for elliptic boundary value problems, SIAM J. numer. anal., 22, 644-669, (1985) · Zbl 0579.65121
[10] Burgess, G.; Mahajerin, E., A comparison of the boundary element method and superposition methods, Comput. struct., 19, 697-705, (1984) · Zbl 0552.73075
[11] Carslaw, H.S.; Jaeger, J.C., Conduction of heat in solids, (1959), Clarendon Press Oxford · Zbl 0972.80500
[12] Donea, J.; Giuliani, S., Finite element analysis of steady-state nonlinear heat transfer problems, Nucl. engrg. des., 30, 205-213, (1974)
[13] G. Fairweather, The method of fundamental solutions – a personal perspective, in: Plenary Talk at the First International Workshop on the Method of Fundamental Solutions (MFS 2007), Ayia Napa, Cyprus, June 11-13, 2007.
[14] Fairweather, G.; Karageorghis, A., The method of fundamental solutions for elliptic boundary value problems, Adv. comput. math., 9, 69-95, (1998) · Zbl 0922.65074
[15] Fenner, R.T., A force superposition approach to plane elastic stress and strain analysis, J. strain anal., 36, 517-529, (2001)
[16] Garbow, B.S.; Hillstrom, K.E.; Moré, J.J., MINPACK project, (1980), Argonne National Laboratory
[17] Gatica, G.N.; Hsiao, G.C., Boundary-field equation methods for a class of nonlinear problems, (1995), Pitman Publishing London · Zbl 0698.65070
[18] Golberg, M.A., The method of fundamental solutions for poisson’s equation, Engrg. anal. boundary elements, 16, 205-213, (1995)
[19] Golberg, M.A.; Chen, C.S., The method of fundamental solutions for potential, Helmholtz and diffusion problems, (), 103-176 · Zbl 0945.65130
[20] Ingham, D.B.; Heggs, P.J.; Manzoor, M., Boundary integral equation solution of non-linear plane potential problems, IMA J. numer. anal., 1, 415-426, (1981) · Zbl 0485.65076
[21] Karageorghis, A.; Fairweather, G., The method of fundamental solutions for the solution of the biharmonic equation, J. comput. phys., 69, 434-459, (1987) · Zbl 0618.65108
[22] Karageorghis, A.; Fairweather, G., The method of fundamental solutions for the solution of nonlinear plane potential problems, IMA J. numer. anal., 9, 231-242, (1989) · Zbl 0676.65110
[23] A. Karageorghis, D. Lesnic, The method of fundamental solutions for steady-state heat conduction in nonlinear materials, Commun. Comput. Phys., accepted for publication. · Zbl 1364.80007
[24] Katsurada, M., Asymptotic error analysis of the charge simulation method in a Jordan region with an analytic boundary, J. fac. sci. univ. Tokyo sect. 1A math., 37, 635-657, (1990) · Zbl 0723.65093
[25] Leitão, V.M.A.; Alves, C.J.S.; Duarte, C.A., Advances in meshfree techniques, Comput. meth. appl. sci., vol. 5, (2007), Springer Berlin
[26] Mathon, R.; Johnston, R.L., The approximate solution of elliptic boundary-value problems by fundamental solutions, SIAM J. numer. anal., 14, 638-650, (1977) · Zbl 0368.65058
[27] Ozisik, M.N., Boundary value problems of heat conduction, (1968), International Textbook Scranton
[28] Sawaf, B.; Ozisik, M.N.; Jarny, Y., An inverse analysis to estimate linearly dependent thermal conductivity components and heat capacity of an orthotropic medium, Int. J. heat mass transfer, 38, 3005-3010, (1995) · Zbl 0925.73072
[29] Smyrlis, Y-S.; Karageorghis, A., Numerical analysis of the MFS for certain harmonic problems, M2AN math. model. numer. anal., 38, 495-517, (2004) · Zbl 1079.65108
[30] Tankelevich, R.; Fairweather, G.; Karageorghis, A.; Smyrlis, Y.-S., Potential field based geometric modelling using the method of fundamental solutions, Int. J. numer. meth. engrg., 68, 1257-1280, (2006) · Zbl 1130.65035
[31] Touloukian, Y.S., Thermophysical properties of high temperature solid materials, (1967), MacMillan New York
[32] Tsai, C.C.; Young, D.L.; Lo, D.C.; Wong, T.K., Method of fundamental solutions for three-dimensional Stokes flow in exterior field, J. engrg. mech., 132, 317-326, (2006)
[33] Wei, T.; Hon, Y.C.; Ling, L., Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators, Engrg. anal. boundary elements, 31, 373-385, (2007) · Zbl 1195.65206
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.