A Simple Introduction to the SiMPL Method for Density-Based Topology Optimization
Abstract
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.
Cite
@article{arxiv.2411.19421,
title = {A Simple Introduction to the SiMPL Method for Density-Based Topology Optimization},
author = {Dohyun Kim and Boyan Stefanov Lazarov and Thomas M. Surowiec and Brendan Keith},
journal= {arXiv preprint arXiv:2411.19421},
year = {2025}
}