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

Abstract

SUMMARYA 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.

Micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity

“…Although the meshfree methods perform satisfactorily in these specific fields, they have not succeeded in replacing the finite element method (FEM). The primary reasons for the lack of wide adoption of the meshfree are (1) they are weak at representing the threedimensional complex shapes required in practical engineering, (2) they are less reliable in terms of analysis accuracy than the FEM (Yagawa, 2004), and (3) are computationally more costly than the conventional FEM (Rajesh and Rao, 2010). In addition, the application of MLS interpolation schemes in meshfree methods complicates the imposition of essential boundary conditions as the MLS interpolants lack the delta function property of the usual FEM shape functions (Mukherjee and Mukherjee, 1997).…”

A Virtual Crack Closure-Integral Method for Generalized Finite Element with Drilling and Strain Degrees of Freedoms

“…Proposed VCCM was found to give very accurate solutions, as presented in their articles (6) (7) . The outcomes of this research opened a possibility for FMM to adopt the VCCM, since FMM is based on tetrahedral finite element (4) .…”

“…In order to obviate such time consuming processes, methodologies that can simplify/eliminate the mesh generation have been proposed. They are eXtended finite element method (X-FEM) (2) , S-version finite element method (SFEM) (3) and free mesh method (FMM) (4) , etc.…”

A stable meshfree method for fully coupled flow-deformation analysis of saturated porous media

“…To date, MMs have been applied to a range of engineering problems, including solid mechanics [1,19], heat conduction [20][21][22][23][24], fluid flow [25][26][27], consolidation [28][29][30] and wave propagation [31,32] among others. Lucy [2] and Gingold and Monaghan [3] used MMs in astrophysics and fluid dynamics.…”