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Meshless local Petrov-Galerkin method for heat conduction problem in an anisotropic medium. (English) Zbl 1084.80002
It is developed a local boundary integral equation formulation in a Laplace transform-domain with meshless approximation in order to solve a 2-d initial boundary value problem in anisotropic continuous non-homogeneous solids. The Heaviside step function and parametrix are used, alternatively as test functions in the local symmetric form. The method with the Heaviside step function as the test function is leading to a simpler integral formulation than in the case with the parametrix. The moving least square method is used for the approximation of physical quantities in local boundary integral equations.

MSC:
80A20 Heat and mass transfer, heat flow (MSC2010)
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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