Node-by-node parallel finite elements: a virtually meshless method

A FEM-based meshfree method named the free mesh method (FMM) or the node-by-node finite element method (NBN-FEM), and a short review of recent meshless and meshfree methods are presented. Attempts to apply particle-like finite element analysis to problems that are difficult to handle using global mesh generation, especially on massively parallel processors, are presented. Local finite elements are generated around each node, with local mesh data structures and a system of equations based on these nodes. Accordingly, the FMM or NBN-FEM can overcome difficulties arising from the distortion of elements by simply adding or deleting nodes, similar to particle methods. This property is particularly advantageous for use in parallel computing environments. While parallelization of mesh generation is generally difficult, only the distribution of nodes needs to be considered to perform parallel remeshing computing. This node-based finite element computation is realized by a robust local mesh generation technique based on the gift-wrapping method. The method is implemented on parallel computers, including a PC cluster and a Hitachi SR8000 supercomputer. Numerical examples show that the method achieves high parallel performance, both in pre-processing and main-processing