On reducing computational effort in topology optimization: We can go at least this far!

Asger Limkilde*, Anton Evgrafov, Jens Gravesen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

In this work we attempt to answer the question posed in Amir O., Sigmund O.: On reducing computational effort in topology optimization: how far can we go? Struct. Multidiscip. Optim. 44(1), 25–29 (2011). Namely, we are interested in assessing how inaccurately we can solve the governing equations during the course of a topology optimization process while still obtaining accurate results. We consider this question from a “PDE-based” angle, using a posteriori residual estimates to gain insight into the behaviour of the residuals over the course of Krylov solver iterations. Our main observation is that the residual estimates are dominated by discretization error after only a few iterations of an iterative solver. This provides us with a quantitative measure for early termination of iterative solvers. We illustrate this approach using benchmark examples from linear elasticity, and demonstrate that the number of Krylov solver iterations can be significantly reduced, even when compared to previous heuristic recommendations, although each Krylov iteration becomes considerably more expensive.
Original languageEnglish
JournalStructural and Multidisciplinary Optimization
Volume58
Issue number6
Pages (from-to)2481-2492
ISSN1615-147X
DOIs
Publication statusPublished - 2018

Keywords

  • Topology optimization
  • Approximation
  • Iterative solvers
  • A posteriori estimates

Cite this

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title = "On reducing computational effort in topology optimization: We can go at least this far!",
abstract = "In this work we attempt to answer the question posed in Amir O., Sigmund O.: On reducing computational effort in topology optimization: how far can we go? Struct. Multidiscip. Optim. 44(1), 25–29 (2011). Namely, we are interested in assessing how inaccurately we can solve the governing equations during the course of a topology optimization process while still obtaining accurate results. We consider this question from a “PDE-based” angle, using a posteriori residual estimates to gain insight into the behaviour of the residuals over the course of Krylov solver iterations. Our main observation is that the residual estimates are dominated by discretization error after only a few iterations of an iterative solver. This provides us with a quantitative measure for early termination of iterative solvers. We illustrate this approach using benchmark examples from linear elasticity, and demonstrate that the number of Krylov solver iterations can be significantly reduced, even when compared to previous heuristic recommendations, although each Krylov iteration becomes considerably more expensive.",
keywords = "Topology optimization, Approximation, Iterative solvers, A posteriori estimates",
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On reducing computational effort in topology optimization: We can go at least this far! / Limkilde, Asger; Evgrafov, Anton ; Gravesen, Jens.

In: Structural and Multidisciplinary Optimization, Vol. 58, No. 6, 2018, p. 2481-2492.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - On reducing computational effort in topology optimization: We can go at least this far!

AU - Limkilde, Asger

AU - Evgrafov, Anton

AU - Gravesen, Jens

PY - 2018

Y1 - 2018

N2 - In this work we attempt to answer the question posed in Amir O., Sigmund O.: On reducing computational effort in topology optimization: how far can we go? Struct. Multidiscip. Optim. 44(1), 25–29 (2011). Namely, we are interested in assessing how inaccurately we can solve the governing equations during the course of a topology optimization process while still obtaining accurate results. We consider this question from a “PDE-based” angle, using a posteriori residual estimates to gain insight into the behaviour of the residuals over the course of Krylov solver iterations. Our main observation is that the residual estimates are dominated by discretization error after only a few iterations of an iterative solver. This provides us with a quantitative measure for early termination of iterative solvers. We illustrate this approach using benchmark examples from linear elasticity, and demonstrate that the number of Krylov solver iterations can be significantly reduced, even when compared to previous heuristic recommendations, although each Krylov iteration becomes considerably more expensive.

AB - In this work we attempt to answer the question posed in Amir O., Sigmund O.: On reducing computational effort in topology optimization: how far can we go? Struct. Multidiscip. Optim. 44(1), 25–29 (2011). Namely, we are interested in assessing how inaccurately we can solve the governing equations during the course of a topology optimization process while still obtaining accurate results. We consider this question from a “PDE-based” angle, using a posteriori residual estimates to gain insight into the behaviour of the residuals over the course of Krylov solver iterations. Our main observation is that the residual estimates are dominated by discretization error after only a few iterations of an iterative solver. This provides us with a quantitative measure for early termination of iterative solvers. We illustrate this approach using benchmark examples from linear elasticity, and demonstrate that the number of Krylov solver iterations can be significantly reduced, even when compared to previous heuristic recommendations, although each Krylov iteration becomes considerably more expensive.

KW - Topology optimization

KW - Approximation

KW - Iterative solvers

KW - A posteriori estimates

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DO - 10.1007/s00158-018-2121-1

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ER -