Nodally Integrated Local Maximum-Entropy Approximation-Based Element-Free Galerkin Method for the Analysis of Steady Heat Conduction

This research aims to study the performance of local maximum-entropy approximation (LME)-based element-free Galerkin meshfree (EFG) method and its integration in the heat conduction application. EFG methods have undergone significant development over the past two decades and have come to the forefront to solve partial differential equations. Being non-polynomial functions, LME is smooth and appears to be a viable substitute for the approximation in EFG methods. It possesses weak Kronecker delta property that allows the implementation of essential boundary conditions like FEM. In the present work, stabilized conforming nodal integration (SCNI) and its modified version with additional stability called modified SCNI (MSCNI) is used to perform the integration of LME-based EFG and tested against different discretization node sets. Poisson heat conduction equation with a different set of boundary conditions is chosen to study these integration schemes and compared with several Gaussian integration point schemes. It is found that the 3 or 4 point Gauss integration scheme is optimal for unstructured discretization and MSCNI is optimal for distorted discretization. SCNI and MSCNI are observed to be converging faster than the other methods, irrespective of the grid type.