Matlab code for a level set-based topology optimization method using a reaction diffusion equation

Abstract

This paper presents a simple Matlab implementation for a level set-based topology optimization method in which the level set function is updated using a reaction diffusion equation, which is different from conventional level set-based approaches (Allaire et al. 2002, 2004; Wang et al. 2003) that use the Hamilton-Jacobi equation to update the level set function. With this method, the geometrical complexity of optimized configurations can be easily controlled by appropriately setting a regularization parameter. We explain the code in detail, and also the derivation of the topological derivative that is used in the level set-based topology optimization. Numerical results for stiffness maximization problems are provided to facilitate the reader's understanding. The presented code is intended for educational purposes only. This paper was inspired by previously published papers presenting Matlab code for a SIMP method (Sigmund 2001; Andreassen et al. 2011), a level set-based method (Challis 2010), and FreeFem ++ code for a structural optimization method (Allaire and Pantz 2006). Readers can investigate results provided by these different methods and discover the prominent aspects of each particular method. The code presented here can be downloaded from http://www.osdel.me.kyoto-u.ac.jp/members/yamada/codes.html.