Application of the Free Mesh Method with Delaunay Tesselation in a 3-Dimensional Problem.

Numerical Meth Engineering

2004

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.

Section: Outline Of the Algorithmmentioning

confidence: 99%

Section: Algorithm Ii: Local Delaunay Triangulation Algorithm Employimentioning

confidence: 99%

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

Numerical Meth Engineering

2004

“…However, we can also select other rules. Selecting a rule based on the Delaunay method, we can easily expand FMM to a three-dimensional analysis (Yagawa and Hosokawa 1997). In the next step, local triangular elements around the current central node P i are constructed temporarily by connecting the satellites with P i (Fig.…”

Section: Basic Conceptmentioning

confidence: 99%

Parallel computing for incompressible flow using a Nodal-Based method

Computational Mechanics

Shirazaki

1999

In this paper, the development of a seamless system for parallel¯ow analysis using the``free-mesh method'', which is a kind of meshless method, is described. The system consists of two main parts: the computation of the global mass, advection, diffusion, gradient, and divergence matrices, and the time integration by the decoupled method with respect to velocity and pressure. This system is quite compatible with the parallel environment because the matrices are independently computed node-by-node without any node-element connectivity information, and furthermore because the fractional step method, with the interpolation functions for velocity and pressure being of equal order, is used with the conjugate gradient solver for the time integration. A parallel ef®ciency of approximately 83% was achieved for a large-scale problem with 480,000 degrees of freedom using 16 processors. IntroductionIn recent years, large-scale computer simulations for incompressible¯ow have become more important for¯ows in nuclear reactors, around automobiles and buildings, air ow in rooms, and so on. Numerical methods such as the ®nite difference method (FDM), the ®nite element method (FEM), and the ®nite volume method (FVM) have been used to analyze such¯ows. In these methods, FEM has been successful for simulation due to its ability to analyze domains of arbitrary shape.Nowadays, the degrees of freedom in analysis models tend to be extremely large and the geometries of the method have become extremely complex. To deal with such models with limited computer memory size and in a reasonable computation time, two main problems must be solved. First, the computational time must be reduced, and second, the dif®culties of global mesh generation over the whole domain of analysis must be avoided. For the ®rst problem, ef®cient parallel methods, such as parallelization of the processing loops (Kennedy et al. 1994, Nakabayashi et al. 1996 and the domain decomposition method (DDM) (Glowinski et al. 1983, Yagawa andShioya 1993), are currently being studied for this purpose. The former method has essentially the same algorithm as the usual FEM. After the whole domain of analysis is decomposed to processors as subdomains, the all-element matrices in each subdomain and the values on the nodes and/or elements (e.g. the velocity and pressure) are computed by each processor with interprocessor communication. In the latter method, the ®nite-element analysis in each subdomain is performed separately by giving the tentative shared boundary conditions. After the analysis, the values on the adjacent shared boundaries are exchanged, and the boundary conditions are updated so as to correlate the values on the shared boundaries. And again, the analysis in each subdomain is carried out with the updated shared boundary conditions. This process continues until the values on the shared boundaries converge. Because the tentative boundary conditions are given, the ®nite-element analysis in each subdomain can be done separately. These approaches provide parallelization wi...

“… 8 ) Following this, we review, here, some unique numerical examples of FMM and the Enriched Free Mesh Method (EFMM), which is a new version of FMM, selected from among fluid and solid mechanics. 9 – 27 )…”

Section: Introductionmentioning

confidence: 99%

Computational performance of Free Mesh Method applied to continuum mechanics problems

Proceedings of the Japan Academy. Ser. B: Physical and Biologic

2011

Self Cite

The free mesh method (FMM) is a kind of the meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, or a node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm. The aim of the present paper is to review some unique numerical solutions of fluid and solid mechanics by employing FMM as well as the Enriched Free Mesh Method (EFMM), which is a new version of FMM, including compressible flow and sounding mechanism in air-reed instruments as applications to fluid mechanics, and automatic remeshing for slow crack growth, dynamic behavior of solid as well as large-scale Eigen-frequency of engine block as applications to solid mechanics.