The discipline of shape and topology optimization has aroused a growing enthusiasm among mathematicians, physicists and engineers since the seventies, fostered by its impressive technological and industrial achievements. Nowadays, problems pertaining to fields so diverse as mechanical engineering, fluid mechanics or quantum chemistry are currently tackled with such techniques, and raise new, challenging issues.

This webpage gather useful resources of various nature, with the aim to popularize this subject and disseminate possible numerical implementations. In particular, you will find:

• Lecture notes and review articles.
• Slides and records of graduate courses.
• Open source implementations, ranging from simple, educational toy codes, to more involved frameworks allowing to deal with challenging personal test cases.
• Useful links to similar resources, emanating from other researchers.

Pedagogical articles and presentations

Article in the "Gazette des mathématiciens"	Large-audience presentation in prep. school	Review chapter about level set based shape optimization
A popularization article aimed at mathematicians about shape and topology optimization (in French).	The slides (in French) of a large-audience presentation, given in the French prep school of Saint-Brieuc.	This chapter in Vol. 22 of the Handbook of Numerical Analysis, written with G. Allaire and F. Jouve contains: A comprehensive overview of a few general concepts about shape optimization, A description of the practical aspects of the level set implementation.

Educational article about geometric shape optimization for fluids	Educational article about level set -- mesh evolution shape optimization
This educational article in the journal Structural and Multidisplinary Optimization, written with P. Frey, F. Omnes and Y. Privat, contains: A presentation of the basic stakes of geometric optimization in the context of fluid mechanics. Educational, open-source codes in FreeFem, explained by a thorough a tutorial.	This article, written with F. Feppon contains: An in-depth presentation of the level set based mesh evolution method for shape optimization. A tutorial for an open-source implementation.

Teaching material

An introduction to the level set method and its applications	An introduction to shape and topology optimization
The material for this graduate course about the level set method is available: A set of slides. A set of lecture notes.	The webpage of this graduate course, prepared with E. Bonnetier contains: A complete set of slides. The video records (in French) of an online version taught at the University of Tripoli. Open-source codes (in FreeFem) illustrating the various aspects of the course.

Open-source implementations

Disclaimer: However much attention has been devoted to these implementations, they only reflect the (limited) practice and knowledge of the author(s).

Demonstration examples in FreeFem	Material for practical sessions in FreeFem	Open-source FreeFem implementation: geometric optimization for fluids
Visit the webpage of the course An introduction to shape and topology optimization for FreeFem codes illustrating the various aspects of the graduate course An introduction to shape and topology optimization.	This repository contains the material (including a primer and corrections in FreeFem) of the practical sessions of a course about shape and topology optimization taught at the occasion of the GDR MOA days.	This Github repository contains the open-source FreeFem implementation associated to the journal article Geometrical shape optimization in Fluid Mechanics using FreeFem++.

SoTuto	Totuto
This open-source implementation of the level set based mesh evolution method for shape optimization is a Python framework calling external libraries in a black-box fashion: The finite element environment FreeFem, The remeshing library mmg, The libraries mshdist and advect. It is intended as a pedagogical implementation which is simple to modify, and is thoroughly described in the companion article Shape optimization using a level set based mesh evolution method: an overview and tutorial .	This code is an open-source implementation of the density-based topology optimization method.

Resources from other authors

The list below is by no means exhaustive of the material available on the web.

• The webpage of the course Optimal design of structures, taught by G. Allaire at Ecole Polytechnique contains much useful material.
• The educational article Structural Optimization with FreeFem, written by G. Allaire and O. Pantz, describes a user-friendly implementation of geometric shape optimization.
• The educational article Efficient topology optimization in MATLAB using 88 lines of code written by E. Andreassen, A. Clausen, M. Schevenels, B.S. Lazarov and O. Sigmund is devoted to an open-source Matlab implementation of the famous SIMP method.
• The webpage of the graduate course "Aspects théoriques et numériques pour les fluides incompressibles", taught by P. Frey and Y. Privat in Paris Sorbonne Universités.
• An article written by F. Feppon devoted to, and accompanied with an open-source implementation of density-based topology optimization.
• The lecture notes of a graduate course devoted to shape optimization, taught by S. Amstutz in the Master of Paris Sorbonne Universités.