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Transient heat conduction in anisotropic and functionally graded media by local integral equations. (English) Zbl 1182.80016
Summary: Reliable computational techniques are developed for the solution of two-dimensional (2-d) transient heat conduction problems in anisotropic media with continuously variable material coefficients. Two kinds of the domain-type interpolation, namely the standard domain elements and the meshless point interpolation, are adopted for the approximation of the spatial variation of the temperature field or its Laplace-transform. The coupling among the nodal values of the approximated field is given by integral equations considered on local sub-domains. Three kinds of local integral equations are derived from physical principles instead of using a weak-form formulation. The accuracy and the convergence of the proposed techniques are tested by several examples and compared with exact benchmark solutions, which are derived too.

80M25 Other numerical methods (thermodynamics) (MSC2010)
80A20 Heat and mass transfer, heat flow (MSC2010)
65M80 Fundamental solutions, Green’s function methods, etc. for initial value and initial-boundary value problems involving PDEs
Full Text: DOI
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