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Interpolating meshless local Petrov-Galerkin method for steady state heat conduction problem. (English) Zbl 1464.80031
Summary: In many meshfree methods, moving least squares scheme (MLS) has been used to generate meshfree shape functions. Imposition of Dirichlet boundary conditions is difficult task in these methods as the MLS approximation is devoid of Kronecker delta property. A new variant of the MLS approximation scheme, namely interpolating moving least squares scheme, possesses Kronecker delta property. In the current work, a novel interpolating meshless local Petrov-Galerkin (IMLPG) method has been developed based on the interpolating MLS approximation for two and three dimensional steady state heat conduction in regular and complex domain. The interpolating MLPG method shows two advantages over standard meshless local Petrov-Galerkin (MLPG) method i.e. higher computational efficiency and ease to impose EBCs at similar accuracy level. Performance of three different test functions in-conjunction with interpolating MLPG method has been shown.

##### MSC:
 80M15 Boundary element methods applied to problems in thermodynamics and heat transfer 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 80A19 Diffusive and convective heat and mass transfer, heat flow 80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
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