ABSTRACT: About a decade ago, my group starting looking at eigendecompositions to try to understand error in unstructured mesh finite volume solutions. After success there, we moved on to using eigenanalysis to study stability, and in particular to improve stability by making changes to the mesh and/or discretization scheme. More recently, we tried to apply eigenanalysis to the problem of identifying flow solutions with missing features (in particular, separation). That work has led us to principal component analysis, which is more successful in guiding those predictions. This talk will explore all of these topics, with more emphasis on the outcomes than on algorithmic details in performing the decompositions.
BIO: Carl Ollivier-Gooch has bachelor's degrees in Russian and in Mechanical Engineering from Rice University and master's and PhD degrees in Aeronautics and Astronautics from Stanford University. After post-doc stints at NASA and the US Department of Energy, he joined the University of British Columbia in 1997. His research interests are in high-order finite-volume methods for unstructured meshes, mesh generation, and error and stability analysis, with applications primarily in aerodynamics. Like everyone else with any interest in applied math these days, he is also machine learning-curious