DBPapers
DOI: 10.5593/SGEM2014/B62/S26.019

EVOLUTIONARY METHOD FOR RE-TRIANGULATION

A.D. Danciu, D. I. Danciu, C. Moga, S. I Gutiu
Wednesday 1 October 2014 by Libadmin2014

References: 14th International Multidisciplinary Scientific GeoConference SGEM 2014, www.sgem.org, SGEM2014 Conference Proceedings, ISBN 978-619-7105-21-6 / ISSN 1314-2704, June 19-25, 2014, Book 6, Vol. 2, 145-152 pp

ABSTRACT
One of the most important aspects in the Finite Elements Method is the refinement of a coarse mesh that should take into account a number of parameters given by the necessities of the problem: singularities, error estimation, etc. Following this idea and taking into account that the best suited algorithms nowadays for optimization problems are the genetic and evolutionary algorithms, the authors pursued the idea of optimizing and refining a given triangular mesh using evolutionary procedures. The paper presents the proposed evolutionary procedure and it shows that, after just a few generations one can obtain acceptable triangular meshes that can be used in analysis after a minimum correction. The triangulations obtained are optimized after two parameters: the quality of the triangles obtained and the refinement of the mesh. Through the implemented operators we tried to keep the quality of the newly generated triangles and, where possible, to improve the quality of the initial triangles. All the steps of the procedure are presented in detail. The operators presented in the literature have been implemented and their performance evaluated for the new procedure proposed. Two new cross-over operators have been proposed and implemented, as well as a new mutation operator responsible for the mesh refinement. A situation appearing during mutation was named as fan mutation and ways to resolve it have been presented. The fitness of the individual is evaluated through a cumulative function that takes into account the quality of the individual though the deviation fitness and the refinement obtained through the refinement fitness. For a plane octagonal domain the influence of the number of generations, the division rate, the mutation rate, the cross-over rate and the initial triangulation are investigated. Next the issue of solving a domain with holes is addressed. The procedure starts with a set of initial triangles that take into account the geometry of the body to be meshed and the operators proposed are not modifying the geometry; therefore, any type of geometry can be meshed. The strong and the weak points of the procedure are investigated and ways of improving it are proposed.

Keywords: Evolutionary procedure, triangulation, meshing, mesh refinement, finite
element method.