Full Article - Open Access.

Idioma principal


Braga, L. M.; Anflor, C. T. M; Albuquerque, E. L.;

Full Article:

The objective of this work is to compare topologies resulting from direct BEM (Boundary Element Method) with a BEM accelerated by Fast Multipole Method (FMM). A formulation of fast multipole boundary element (FMBEM) is introduced in order to turn the optimization process more attractive in the point of view of the computational cost. The formulation of the fast multipole is briefly summarized. A topological-shape sensitivity approach is used to select the points showing the lowest sensitivities, where material is removed by opening a cavity. As the iterative process evolves, the original domain has holes progressively removed, until a given stop criteria is achieved. A benchmark is investigated by imposing different FMBEM parameters. For effect of comparison the topology resulting from an analytical BEM optimization process is used. The topologies resulting due to this set of parameters imposed are presented. The CPU time x DOF’s are also investigated. The accelerated BEM demonstrated good feasibility in an optimization routine.

Full Article:

Palavras-chave: Topology optimization, topological derivative, fast multipole method, boundary element methods.,


DOI: 10.5151/meceng-wccm2012-16782

Referências bibliográficas
  • [1] Roklin V., “Rapid Solution of integral equations of classical potential theory”. J. Comput Phys, 60, 187-207, 1985.
  • [2] Greengard L.F., “The rapid evaluation of potentials fields in particle systems”, Cambridge: The MIT Press, 1988.
  • [3] Peirce A.P., Napier J.A.L. A spectral multipole method for efficient solutions of large scale boundary element models in elastostatics. Int J Numer Meth Eng. 38, 4009-4034, 1995.
  • [4] Mammoli A. and Ingber M., “Stokes flow around cylinders in a bounded two-dimensional domain using multipole accelerated boundary element methods”, International Journal for Numerical Methods in Engineering, 44, 897-917 (1999).
  • [5] Liu Y.J., Nishimura N., “The fast multipole boundary element method for potential problems: A tutorial”. Engineering Analysis with Boundary Elements, 30, 371-381, 2006.
  • [6] Liu Y.J., “A new fast multipole boundary element method for solving 2-D Stokes flow problems based on a dual BIE formulation”. Engineering Analysis with Boundary Elements, 32, 139-151, 2008.
  • [7] Liu Y.J., “Fast Multipole Boundary Element Method: Theory and applications in Engineering”, Cambridge 2009.
  • [8] Dondero M., Cisilino A.P., Carella J.M., Tomba J. P., “Effective thermal conductivity of functionally graded random micro-heteregeneous materials using representative volume element and BEM”. International Journal of Heat and Mass transfer, 54, 3874-3881 2011.
  • [9] Feijóo R., Novotny A., Taroco E., Padra C., “The topological derivative for the Poisson’s problem”. Mathematical Model and Methods in Applied Sciences, 13, 1825-1844, 2003.
  • [10] Wrobel L.C. and Aliabadi M.H, “The Boundary Element Method, Vol2: Applications in Solids and Structures”, Wiley 2002.
  • [11] Anflor C.T.M., Marczak R.J., “Topological optimization of anisotropic heat conducting devices using Bézier-smoothed Boundary Representation”. Computer Modeling in Engineering Andamp; Sciences (Print), 1970, 151-168, 20
Como citar:

Braga, L. M.; Anflor, C. T. M; Albuquerque, E. L.; "OPTIMIZATION USING TOPOLOGICAL DERIVATIVE AND BOUNDARY ELEMENT METHOD WITH FAST MULTIPOLE", p. 397-408 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-16782

últimos 30 dias | último ano | desde a publicação