Applied Math Seminar: Topology Optimization: Challenges, Algorithms and Applications

Event Type: 
Eric Cyr
Event Date: 
Monday, March 20, 2017 - 3:30pm
SMLC 356

Event Description: 

Topology Optimization: Challenges, Algorithms and Applications

Topology optimization is a computational technique for designing an engineering system optimized for a quantity of interest (e.g energy) subject to a constraint (e.g. some prescribed mass). A popular approach it to use a field approximated by finite elements representing the distribution of material throughout the domain. The behavior of the material under some natural loading is represented by the solution of a PDE state constraint. This is used to realize the quantity of interest (objective) and satisfaction of physical constraints. Given a discretization of the PDE and the material field, a numerical optimizer can be employed to find a distribution of material that satisfies the PDE, the physical constraints, and optimizes the quantity of interest. 
This talk will explore three aspects of the topology optimization problem. First, using a simple analytic system representing topology optimization problems, we will explore the structure of the objective function. In particular, to elucidate the challenges associated with numerical optimization, several algorithms will be applied to this problem. The convergence properties to the known solution will be considered, as well as the path to the solution. This naturally leads into a discussion of numerical optimization algorithms that can be applied to these problems. Our focus will be on methods that have the potential to yield mesh independent convergence. Finally, progress towards a novel application of topology optimization to an electromagnetic problem will be presented. 
Eric has been a technical staff member at Sandia National Laboratories for 7 years. Prior to that he was a postdoctoral research at Sandia studying under the tutelage of John Shadid and Ray Tuminaro. He received his PhD in Computer Science from University of Illinois at Urbana-Champaign in 2008, and his BS in Computer Science from Clemson University in 2002. His interests include a range of topics relevant to scientific computing, including finite element methods, adjoint methods, block preconditioning, uncertainty quantification, PDE constrained optimization, and software design of high-performance PDE codes.
Coffee and tea will be served in the lounge at 15.00