As noted in my Research Page, one of my main areas of interest is sensitivity analysis. This includes computational techniques as well as exploring the applicability of this information. Some areas where sensitivity analysis may make a contribution are discussed below.
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This work began while working with John Burns, Gene Cliff and Max Gunzburger at ICAM along with Karl Kneile and Don Todd at Arnold Engineering Development Center. This included computation of sensitivities of 2D Euler equations, optimal design problems and studies such as the influence of shocks and sliding boundary conditions.
My later collaborations are with Dominique Pelletier at Ecole Polytechnique de Montreal. We implemented sensitivity analysis in an adaptive finite element method for steady Navier-Stokes equations and looked at computational issues associated with sensitivity analysis for these problems. We also studied a number of problems with heat transfer and phase change.
I am also working with Traian Iliescu and Alexey Miroshnikov as well as Paul Hovland at Argonne National Laboratory to compute sensitivities with our ViTLES flow solver. Along with Bill Layton at the University of Pittsburgh, we are exploring the use of this sensitivity information in developing new closure models for LES.