Jeff Borggaard

Title: POD-Based Model Reduction for Parametric Problems

Abstract:  Proper orthogonal decomposition (POD) is the basis for
virtually all model reduction of nonlinear problems.  In this talk, we
discuss two extensions of POD suitable for constructing models that
are valid over parameter ranges.  The first is an extension of the
principal interval decomposition (PID) to parameter space.  However it
requires a large number of simulations and is not feasible in many
applications.  The second extension is more practical. Using a small
number of simulations but including auxiliary "inexpensive"
sensitivity calculations, this approach "corrects" the POD basis as
parameters change.  Numerical results for a flow past a square
cylinder show that this second extension produces a much more accurate
basis as the Reynolds number is varied as well as improved
reduced-order models.