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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.

MSC:
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
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