Interpolating meshless local Petrov-Galerkin method for steady state heat conduction problem

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.