IACM Colloquium
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: