Renumbering effectiveness for finite element mesh applied to finite element method for solving three-dimensional problems of solid mechanics

Abstract

Renumbering effectiveness for finite element mesh applied to finite element method for solving three-dimensional problems of solid mechanics

A.R. Filatov

Incoming article date: 13.05.2013

This paper presents a comparative analysis of the effectiveness of the method Cuthill-McKee algorithm and fill-reducing ordering of a sparse matrix, based on multi-level nested dissection paradigm, developed at the Department of "Computer Science and Engineering," University of Minnesota. For short, we shall call the algorithm Cuthill-McKee CM, and the algorithm of the University of Minnesota — NodeND (Node nested dissection). This article uses a modification of the CM algorithm — RCM (reverse Cuthill-McKee), because in practice the reverse numbering index allows you to get a greater advantage than using a direct algorithm CM. The reason for using these algorithms are high speed computational algorithm, as it is necessary to solve the system proximal to the diagonal, the great acceleration of algorithms for solving FE problems using technology such as CUDA  

Keywords: finite element mesh renumbering methods, three-dimensional mathematical modeling, elasticity theory problems, finite element method, finite element meshes