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Analysis of transient heat conduction in 3D anisotropic functionally graded solids, by the MLPG method. (English) Zbl 1232.80006
Summary: A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously non-homogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for the set of governing equations is transformed into local integral equations on local subdomains by using a unit test function. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by a spherical subdomain to which a local integral equation is applied. The meshless approximation based on the Moving Least-Squares (MLS) method is employed for the implementation. Several example problems with Dirichlet, mixed, and/or convection boundary conditions, are presented to demonstrate the veracity and effectiveness of the numerical approach.

80M25 Other numerical methods (thermodynamics) (MSC2010)
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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