Large scale topology optimization using preconditioned krylov subspace recycling and continuous approximation of material distribution

Eric De Sturler, Chau Le, Shun Wang, Glaucio Paulino

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Large-scale topology optimization problems demand the solution of a large number of linear systems arising in the finite element analysis. These systems can be solved efficiently by special iterative solvers. Because the linear systems in the sequence of optimization steps change slowly from one step to the next, we can significantly reduce the number of iterations and the runtime of the linear solver by recycling selected search spaces from previous linear systems, and by using preconditioning and scaling techniques. We also provide a new implementation of the 8-node brick (B8) element for the continuous approximation of material distribution (CAMD) approach to improve designs of functionally graded materials. Specifically, we develop a B8/B8 implementation in which the element shape functions are used for the approximation of both displacements and material density at nodal locations. Finally, we evaluate the effectiveness of several solver and preconditioning strategies, and we investigate large-scale examples, including functionally graded materials, which are solved with a special version of the SIMP (solid isotropic material with penalization) model. The effectiveness of the solver is demonstrated by means of a topology optimization problem in a functionally graded material with 1.6 million unknowns on a fast PC.

Original languageEnglish (US)
Title of host publicationMultiscale and Functionally Graded Materials - Proceedings of the International Conference, FGM IX
Pages279-284
Number of pages6
DOIs
StatePublished - 2008
Event9th International Conference on Multiscale and Functionally Graded Materials, FGM IX - Oahu Island, HI, United States
Duration: Oct 15 2006Oct 18 2006

Publication series

NameAIP Conference Proceedings
Volume973
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

Other9th International Conference on Multiscale and Functionally Graded Materials, FGM IX
CountryUnited States
CityOahu Island, HI
Period10/15/0610/18/06

Keywords

  • Fast solution schemes
  • Finite elements
  • Functionally graded materials
  • Material distribution
  • Topology optimization

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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