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GRASP Lab Seminar 2003-2004
September 19, 11:00 AM, Levine Hall 307, hosted by Vijay Kumar.
George
Biros
University of Pennsylvania
Towards efficient computational methods for simulation, and optimization of systems governed by partial differential equations
Abstract: Large scale optimization of systems governed by partial differential equations (PDEs) is a frontier problem in scientific computation. In practice, one is rarely content with performing a simulation of a physical or engineered system; sensitivity analysis, parameter estimation, and optimization are required for a complete analysis and to reflect design goals. Instead of traditional trial-and-error approaches, optimization techniques that are efficient for large-scale systems have been devised, and their use results in orders-of-magnitude savings over traditional methods.
In the first part of my talk I will describe the Lagrange-Newton-Krylov-Schur (LNKS) method. LNKS enables efficient and scalable solution of PDE-constrained optimization problems. I will present an anthology of examples in which LNKS (and its variants) have been successfully applied: control of viscous incompressible flows, shape optimization of bodies immersed in Stokesian flows, source inversion in convective-diffusive systems, and parameter estimation in acoustic wave propagation. Efficient optimization methods strongly depend on the availability of scalable and high accuracy solvers for the underlying physical systems. In the second part of my talk I will describe the Embedded Boundary Integral method (EBI), a new numerical method for viscous flows with dynamic boundaries. Applications of the new technique include physically-based animation, haemodynamics, and shape optimization.Biography: George Biros holds a BS in Mechanical Engineering from Aristotle University, an MS in Biomedical Engineering from Carnegie Mellon University, and a PhD in Computational Science and Engineering also from CMU. In 2000 he joined the Courant Institute of Mathematical Sciences at New York University as a postdoctoral researcher, and in 2003 he joined the Department of Mechanical Engineering and Applied Mechanics at the University of Pennsylvania as an assistant professor. His research includes work in medical robotics and computer assisted surgery, optimization algorithms, scientific computing, computational physics, parallel algorithms and fast multipole methods.
