A Simple Introduction to the SiMPL Method for Density-Based Topology Optimization
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915169075986432 |
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| author | Kim, Dohyun Lazarov, Boyan Stefanov Surowiec, Thomas M. Keith, Brendan |
| author_facet | Kim, Dohyun Lazarov, Boyan Stefanov Surowiec, Thomas M. Keith, Brendan |
| contents | We introduce a novel method for solving density-based topology optimization problems: Sigmoidal Mirror descent with a Projected Latent 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. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_19421 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Simple Introduction to the SiMPL Method for Density-Based Topology Optimization Kim, Dohyun Lazarov, Boyan Stefanov Surowiec, Thomas M. Keith, Brendan Optimization and Control Numerical Analysis We introduce a novel method for solving density-based topology optimization problems: Sigmoidal Mirror descent with a Projected Latent 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. 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. |
| title | A Simple Introduction to the SiMPL Method for Density-Based Topology Optimization |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/2411.19421 |