The UTC Graduate School is pleased to announce that Tanner Smith will present Doctoral research titled, Optimization for a Sturm-Liouville Problem with the Spectral Parameter in the Boundary Condition on 10/06/2022 at 1:00-3:00pm in Grote 317. Everyone is invited to attend.
Computational Science
Chair: Boris Belinskiy
Co-Chair:
Abstract:
We find an optimal mass of a structure described by a Sturm-Liouville (S-L) problem with a spectral parameter in the boundary conditions. While previous work on the subject focused on a somewhat simplified model, we consider a more general S-L problem. We use the calculus of variations approach to determine a set of critical points of a corresponding mass functional, yet these critical points – which we call \textit{predesigns} – do not themselves represent meaningful solutions. It is natural to expect a mass to be real and positive. To this end, we additionally introduce a set of solvability conditions on the S-L problem data, confirming that these critical points represent meaningful solutions we refer to as \textit{designs}. We further present the analytic continuation of these predesigns in regards to the spectral parameter as well as a discussion of the stability of these (pre)designs. We present a code that allows us to for the given data of the S-L problem to check conditions of solvability, plot the design, and calculate the value of the functional that represents the optimal mass.