*Article* **A Simple Matlab Code for Material Design Optimization Using Reduced Order Models**

**George Kazakis † and Nikos D. Lagaros \*,†**

Institute of Structural Analysis and Antiseismic Research, School of Civil Engineering, National Technical University of Athens, 9, Heroon Polytechniou Str., Zografou Campus, GR-15780 Athens, Greece; kzkgeorge@gmail.com

**\*** Correspondence: nlagaros@central.ntua.gr; Tel.: +30-210-772-2625

† These authors contributed equally to this work.

**Abstract:** The main part of the computational cost required for solving the problem of optimal material design with extreme properties using a topology optimization formulation is devoted to solving the equilibrium system of equations derived through the implementation of the finite element method (FEM). To reduce this computational cost, among other methodologies, various model order reduction (MOR) approaches can be utilized. In this work, a simple Matlab code for solving the topology optimization for the design of materials combined with three different model order reduction approaches is presented. The three MOR approaches presented in the code implementation are the proper orthogonal decomposition (POD), the on-the-fly reduced order model construction and the approximate reanalysis (AR) following the combined approximations approach. The complete code, containing all participating functions (including the changes made to the original ones), is provided.

**Keywords:** topology optimization; microstructure; homogenization; Matlab; reduced order models; reduced basis; on-the-fly construction; POD; approximate reanalysis
