Mathematics: The Enabling Science For Ultra Large Space Structures, Ultra Small Nano-Devices and Net Zero Energy Buildings

UAH Distinguished Lecture in Applied Mathematics

Prof. John Burns, Hatcher Professor of Mathematics

Interdisciplinary Center for Applied Mathematics
Virginia Tech, Blacksburg, VA 24061-0531, USA

November 14, 2008
219 Shelby Center
3:00 (Refreshements at 2:30)

Abstract

Computational science has already become one of the key tools in modern engineering. However, engineering design in the 21st century will require new and advanced computational tools for simulation, optimization, design and control of complex systems of partial differential equations (PDEs). The construction of practical approximation schemes for optimal design is much more complex than one might first imagine. The issue of approximation is of paramount importance in the practical design, optimization and implementation of control laws for PDE systems. A key question is: when should this approximation take place? The construction of a reduced order or lumped model is one form of approximation. Approximating a PDE system by a numerical scheme developed primarily for simulation and using the corresponding lumped model for optimization based design and control of the PDE system leads to technical and practical issues that are not present if one is interested only in simulation. This observation is often stated in the form: An approximation scheme good for simulation may not be suitable for design, control or optimization. In this presentation we discuss several theoretical and computational issues that arise in the development and analysis computational algorithms for optimal design and control of complex infinite dimensional systems . We motivate the talk by discussing examples from nano-technology, inflatable space structures, aerodynamic design and high performance buildings. Several of these problems involve shape as one of the design variables and fall into a class of design problems known as shape optimization. We provide a general methodology based on infinite dimensional optimization theory and close with numerical examples to illustrate the ideas. The examples also demonstrate the efficiencies that can be obtained with algorithms based on the delaying the introduction of approximations.

Biographical Sketch

Professor Burns is the distinguished Hatcher Professor of Mathematics at Virginia Tech and the Director of the Center for Optimal Design and Control. He is a world class interdisciplinary applied mathematician and an international figure in his research. He has published over 150 research papers in distinguished journals on applied mathematics and computational methods for identification, optimization and control of systems governed by partial differential equations. He has given more than 100 invited lectures and serves on 5 editorial boards of distinguished journals. He has served on numerous national committees and boards. He is a Fellow of the IEEE. He is the Founding Editor of the SIAM book series on Advances in Design and Control. His research has been funded by NSF, NASA, AFOSR, ONR and DARPA. Dr. Burns has been a consultant and advisor to Booz Allen and Hamilton, NASA Langley Research Center, The Air Force Research Labs, DARPA, The Babcock and Wilcox Company, Solers Inc. and United Technologies. He has held several academic visiting positions in the U.S. and Europe.