Relaxed error control in shape optimization that utilizes remeshing
Article first published online: 1 FEB 2013
Copyright © 2013 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering
Volume 94, Issue 3, pages 273–289, 20 April 2013
How to Cite
Wilke, D. N., Kok, S. and Groenwold, A. A. (2013), Relaxed error control in shape optimization that utilizes remeshing. Int. J. Numer. Meth. Engng., 94: 273–289. doi: 10.1002/nme.4445
- Issue published online: 25 MAR 2013
- Article first published online: 1 FEB 2013
- Manuscript Accepted: 14 OCT 2012
- Manuscript Revised: 9 MAY 2012
- Manuscript Received: 17 JAN 2010
- South African National Research Foundation (NRF). Grant Number: 2769
- error indicator;
- shape optimization;
- radial basis function;
- analytical sensitivities;
- gradient-only optimization;
Shape optimization strategies based on error indicators usually require strict error control for every computed design during the optimization run. The strict error control serves two purposes. Firstly, it allows for the accurate computation of the structural response used to define the shape optimization problem itself. Secondly, it reduces the discretization error, which in turn reduces the size of the step discontinuities in the objective function that result from remeshing in the first place. These discontinuities may trap conventional optimization algorithms, which rely on both function and gradient evaluations, in local minima. This has the drawback that multiple analyses and error computations are often required per design to control the error.
In this study we propose a methodology that relaxes the requirements for strict error control for each design. Instead, we rather control the error as the iterations progress. Our approach only requires a single analysis and error computation per design. Consequently, large discontinuities may initially be accommodated; their intensities reduce as the iterations progress. To circumvent the difficulties associated with local minima due to remeshing, we rely on gradient-only optimization algorithms, which have previously been shown to be able to robustly overcome these discontinuities. Copyright © 2013 John Wiley & Sons, Ltd.