2013•arXiv (Cornell University)Open access

Solving Heat Conduction Problems by the Direct Meshless Local\n Petrov-Galerkin (DMLPG) method

Davoud Mirzaei, Robert Schaback

Abstract

As an improvement of the Meshless Local Petrov-Galerkin (MLPG), the Direct\nMeshless Local Petrov-Galerkin (DMLPG) method is applied here to the numerical\nsolution of transient heat conduction problem. The new technique is based on\ndirect recoveries of test functionals (local weak forms) from values at nodes\nwithout any detour via classical moving least squares (MLS) shape functions.\nThis leads to an absolutely cheaper scheme where the numerical integrations\nwill be done over low-degree polynomials rather than complicated MLS shape\nfunctions. This eliminates the main disadvantage of MLS based methods in\ncomparison with finite element methods (FEM), namely the costs of numerical\nintegration.\n

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Key concepts: Petrov–Galerkin method, Moving least squares, Regularized meshless method, Finite element method, Mathematics, Thermal conduction, Galerkin method, Meshfree methods