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A local Petrov-Galerkin approach with moving Kriging interpolation for solving transient heat conduction problems. (English) Zbl 1241.80005
This paper presents and develops a local Kriging method using the Heaviside step function as the test function to solve transient heat conduction problems in 2D and 3D spaces. This local Kriging (LoKriging) method employs the moving Kriging interpolation to construct shape functions at scattered points that possess the delta function property. This property of the shape functions facilitates direct treatment of boundary conditions. The traditional two-point difference method is selected for the time discretization scheme. A novel definition of the local 3D subdomain is used, which enables numerical integrations to be performed in an accurate and efficient way. Several numerical examples are presented to show the applicability and the performance of the LoKriging method.

80A20 Heat and mass transfer, heat flow (MSC2010)
80M25 Other numerical methods (thermodynamics) (MSC2010)
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
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