DEVELOPMENT OF A PARALLEL MLPG SOLVER FOR HEAT CONDUCTION PROBLEM

Abstract

Over the decades, the finite element method (FEM) has been the most commonly used tool for solving partial differential equations (PDEs). Although it is powerful, well-established, and accessible, it has some drawbacks. It needs an intensive process of construction of mesh for complex geometry problems. Generating the initial mesh is quite challenging for a complex geometrical domain, and re-meshing makes the case even more difficult. Various discretization techniques have been developed to overcome the requirement of mesh generation. Meshless methods are an example of such methods. They only require scattered nodes to get the approximate solution.

The journey of meshfree methods originates from the development of the smooth particle hydrodynamics (SPH) method. After that, several meshfree methods such as diffuse el-ement method (DEM), element-free Galerkin (EFG), reproducing kernel particle method (RKPM), partition of unity method (PUM), natural element method (NEM), and meshless local Petrov-Galerkin (MLPG) were developed. The MLPG method proposed by Atluri and Zhu is claimed to be a truly meshless method, as there is no need for background mesh.