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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.03421 |
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Table of Contents:
- First order shape optimization methods, in general, require a large number of iterations until they reach a locally optimal design. While higher order methods can significantly reduce the number of iterations, they exhibit only local convergence properties, necessitating a sufficiently close initial guess. In this work, we present an unregularized shape-Newton method and combine shape optimization with homotopy (or continuation) methods in order to allow for the use of higher order methods even if the initial design is far from a solution. The idea of homotopy methods is to continuously connect the problem of interest with a simpler problem and to follow the corresponding solution path by a predictor-corrector scheme. We use a shape-Newton method as a corrector and arbitrary order shape derivatives for the predictor. Moreover, we apply homotopy methods also to the case of multi-objective shape optimization to efficiently obtain well-distributed points on a Pareto front. Finally, our results are substantiated with a set of numerical experiments.