Abstract
Many optimal design problems can be described as seeking the maximum/minimum of a design objective function that depends on design parameters through the solution of a partial differential equation. We demonstrate several advantages in using adaptive refinement strategies to approximate this PDE. For example, error estimates which are used to perform the mesh refinement can be used to get estimates on how well the objective function and its gradient are being approximated. These estimates can be used in selecting appropriate stopping criteria in the algorithm.
This work supported in part by the Air Force Office of Scientific Research under Grant F49620–96–1–0329.
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Borggaard, J., Pelletier, D. (1998). Observations in Adaptive Refinement Strategies for Optimal Design. In: Borggaard, J., Burns, J., Cliff, E., Schreck, S. (eds) Computational Methods for Optimal Design and Control. Progress in Systems and Control Theory, vol 24. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1780-0_4
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DOI: https://doi.org/10.1007/978-1-4612-1780-0_4
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