A FEM-BASED MESHFREE METHOD WITH A PROBABILISTIC NODE GENERATION TECHNIQUE

Abstract

In this paper, a FEM-based meshfree method with a probabilistic node generation technique is presented. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed seamlessly in parallel in terms of nodes. Local finite element mesh is generated robustly around each node, even for acute boundary shapes such as cracks. The algorithm and the data structure of finite element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. In addition, the node-based finite element method is accompanied by a probabilistic node generation technique, which generates good-natured points for nodes of finite element mesh. Furthermore, the probabilistic node generation technique can be performed in parallel environments. As a numerical example of the proposed method, we perform a compressible flow simulation containing strong shocks. Numerical simulations with frequent mesh refinement, which are required for such kind of analysis, can be effectively performed on parallel processors by using the proposed method.