Speaker:
Mats G Larson
Department of Mathematics and Mathematical Statistics, Umeå Universitet, Sweden
Title:
Finite Element Approximation of Constrained and Inverse Problems
Abstract:
We review recent advances in applying the augmented Lagrangian method as a general approach for generating stabilized methods without explicit multipliers. The augmented Lagrangian method consists of a standard Lagrange multiplier method augmented by a penalty term that penalizes the constraint equations. It is well known as the basis for iterative algorithms for constrained optimization problems. However, its use as a stabilization method in computational mechanics has only recently been recognized. We consider equality and inequality constraints and apply the framework to several examples in computational mechanics, including inverse problems. Finally, we present machine learning tools to speed up solving inverse problems and assimilate statistical observations into the solutions.
Short Bio:
Dr. Larson received his Ph.D. in 1997 with a thesis on Adaptive Finite Element Methods under the supervision of Prof. Claes Johnson. Then, he was a postdoc fellow at Stanford University, working with Prof. Tom Hughes. After a position as Assistant and Associate Professor at Chalmers University of Technology, he was appointed Professor of Applied Mathematics at Umea University in 2004. His research focuses on finite element methods, including works on adaptivity, discontinuous Galerkin, and immersed methods. He is the Chairman of the Nordic Association of Computational Mechanics and the ECCOMAS Technical Committee for Computational and Applied Mechanics. In 2024, he was elected fellow of the International Association for Computational Mechanics (IACM).
Time, Date & Location:
15:00, Tuesday, October 1st, 2024, Orphanoudakis Room
Host:
Charalampos Makridakis
Seminal Calendar:
https://www.iacm.forth.gr/news/seminars-colloquium