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USACM Large-Scale TTA Early-Career Colloquium (virtual)
Wednesday, November 03, 2021, 1:00 PM - 2:00 PM CDT
Category: Events

USACM Large-Scale TTA Early-Career Colloquium (virtual)

High-order and reduced-order methods for improved engineering analysis and design

Matthew J. Zahr
University of Notre Dame



Optimization problems governed by partial differential equations are ubiquitous in modern science, engineering, and mathematics. They play a central role in optimal design and control of engineering systems, data assimilation, and inverse problems. However, as the complexity of the underlying PDE increases, efficient and robust methods to compute the objective function and its gradient become paramount. To this end, I will present a model reduction framework to reduce the time and resources required to solve optimization problems governed by PDEs. The framework is demonstrated in the context of aerodynamic shape optimization and structural topology optimization. In addition, I will demonstrate the role of optimization in computational physics extends beyond traditional design and control problems. I will introduce a novel optimization-based numerical method for high-order accurate approximation of PDE solutions with non-smooth features, e.g., flows with shock waves and fracture of solid media. I will demonstrate the method with a suite of two- and three-dimensional compressible flow problems and discuss the extension to fracture. In all cases, discontinuities in the flow are fit to high-order accuracy with curved mesh elements, which leads to accurate solutions on extremely coarse meshes.


Matthew is an assistant professor in the Department of Aerospace and Mechanical Engineering at the University of Notre Dame. He received his PhD in Computational and Mathematical Engineering from Stanford University in 2016 and from 2016-2018 was the Luis W. Alvarez Postdoctoral Fellow in the Department of Mathematics at Lawrence Berkeley National Laboratory. His research interests include high-order methods for computational physics, PDE-constrained optimization, model reduction, and numerical methods for resolving shocks and discontinuities. In 2020, he received the AFOSR Young Investigator Award. 

Sponsored by USACM Technical Thrust Area on Large Scale Structural Systems and Optimal Design.
Contact for information about the seminar: [email protected]