| Autor: |
Kim, Dohyun, Lazarov, Boyan Stefanov, Surowiec, Thomas M., Keith, Brendan |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We introduce a novel method for solving density-based topology optimization problems: \underline{Si}gmoidal \underline{M}irror descent with a \underline{P}rojected \underline{L}atent variable (SiMPL). The SiMPL method (pronounced as "the simple method") optimizes a design using only first-order derivative information of the objective function. The bound constraints on the density field are enforced with the help of the (negative) Fermi--Dirac entropy, which is also used to define a non-symmetric distance function called a Bregman divergence on the set of admissible designs. This Bregman divergence leads to a simple update rule that is further simplified with the help of a so-called latent variable. %Introducing a generalized Barzilai-Borwein step size rule accelerates the convergence of SiMPL. Because the SiMPL method involves discretizing the latent variable, it produces a sequence of pointwise-feasible iterates, even when high-order finite elements are used in the discretization. Numerical experiments demonstrate that the method outperforms other popular first-order optimization algorithms. To outline the general applicability of the technique, we include examples with (self-load) compliance minimization and compliant mechanism optimization problems. |
| Databáze: |
arXiv |
| Externí odkaz: |
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