Simons Hour Talk

Overview of Shape Optimization with Finite Element Methods
Date
Mar 28, 2024, 10:00 am11:00 am
Location
Virtual

Details

Event Description

Abstract: I will start with an introduction to shape derivatives and shape optimization.  Next, I will give a general discussion on how shape optimization is done numerically and some of the issues that can arise (e.g. the classic debate between the optimize-then-discretize and discretize-then-optimize approaches).

Then, I will talk about an unfitted finite element method (FEM) for PDE-constrained shape optimization.  The geometry is represented (and optimized) using a level set approach and we consider objective functionals that are defined over bulk domains.  For a discrete objective functional (i.e. one defined in the unfitted FEM framework), we show that the *exact* shape derivative can be computed rather easily.  In other words, one gains the benefits of both the optimize-then-discretize and discretize-then-optimize approaches.

We illustrate the method on a simple model (geometric) problem with known exact solution, as well as shape optimization of structural designs (linear elasticity).

Talk time in other timezones:
AEDT  1:00 AM Fri 29 Mar,
JST  11:00 PM Thu 28 Mar,
CET   3:00 PM Thu 28 Mar,
GMT   2:00 PM Thu 28 Mar,
UTC  14:00    Thu 28 Mar,
EDT  10:00 AM Thu 28 Mar,
CDT   9:00 AM Thu 28 Mar,
MDT   8:00 AM Thu 28 Mar,
MST   7:00 AM Thu 28 Mar,
PDT   7:00 AM Thu 28 Mar
Sponsor
Simons Foundation