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# ACMD Seminar: Two Applications of PDE Constrained Optimization

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Thomas Brown*Department of Mathematical Sciences, George Mason University*

Tuesday, Nov 12, 2019, 3:00–4:00 PM	Building 227, Room A202	Gaithersburg

Tuesday, Nov 12, 2019, 1:00–2:00 PM	Building 1, Room 4072	Boulder

This talk will be broadcast on-line using BlueJeans.  Contact acmdseminar [at] nist.gov (acmdseminar[at]nist[dot]gov) for details.

**Host:** Ryan Evans

**Abstract:**Optimization problems with partial differential equations (PDEs) as constraints are known as PDE constrained optimization. In this talk, we will discuss an abstract formulation of the problem as well as methods for solving such problems.  We then present two specific problems.  One application involves elastic waves propagating through a piezoelectric solid where the PDE constraints take the form of a coupled PDE system.  The other application involves fractional (nonlocal) PDE constraints, which have various applications including image denoising. 

**Bio:**Thomas S. Brown grew up in central Virginia.  He received a BA in Music Performance/Mathematics and later an MEd in Science Education from Lynchburg College.  After teaching high school mathematics for five years for Pittsylvania County Schools, he resumed his studies and earned an MS and a PhD in mathematics from the University of Delaware.  His graduate research, conducted under the advisement and supervision of Francisco-Javier Sayas, involved the analysis and implementation of numerical methods for elastic waves propagating through solids, in particular piezoelectric solids.  Since obtaining his PhD, Thomas has worked as a lecturer in the Computational and Applied Mathematics department at Rice University, and is currently a Postdoctoral Researcher in the department of mathematical sciences at George Mason University.  His continuing research focuses on PDE constrained optimization, or so-called optimal control problems.

**Note:** Visitors from outside NIST must contact Cathy Graham; (301) 975-3800; at least 24 hours in advance.

Mathematics and statistics

## Contacts

                -  Ryan Evans  ryan.evans@nist.gov      (301) 975-5456   
                -  Stephen Langer  stephen.langer@nist.gov      (301) 975-5423   

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