Session Chair: Dr. Margaret Francel, The Citadel
2:15-2:30 David Szurley, Clemson University
Optimal Control Of Non-Isothermal Viscous Fluid Flow
The fibers and films industry provides a wealth of mathematical modeling opportunities. For example, the processes by which the polymeric fibers and films are manufactured can be formulated as a system of nonlinear partial differential equations. Accurate simulation can significantly reduce trial-and-error experiments needed to determine optimal operating conditions for the process lines. The introduction of optimization techniques moves the simulation effort from prediction to design, automating the search for optimal process conditions.
In this talk, we will examine an adjoint-based optimization algorithm applied to modified non-isothermal Stokes-Oldroyd equations. These equations are a simplified form of the equations used to model the flow of a molten polymer. The domain for this model is a four-to-one contraction. In the corner close to the contraction, the fluid will recirculate, creating a vortex. If the fluid stays in the vortex, it will degrade and could become detrimental to the final product. We will derive an adjoint system of equations to solve, and present an algorithm that will minimize this vortex, along with considering the problem of matching a prescribed temperature along the outflow boundary.
2:35-2:50 Allison Carter, University of Tennessee- Knoxville
Optimal Control of Discrete Time Models
We present a solution method for Optimal Control problems in discrete time. Derivation of the necessary conditions will be described. An illustrative example with numerical solution will be given.
2:55-3:10 Nicholas Luke, North Carolina State University
Noise Reduction in a Cylindrical Duct
In this talk, we propose a method of noise reduction in a cylindrical geometry (such as a duct) which uses waveguides to cause destructive interference, resulting in the desired noise reduction. We present an outline of the proposed method, along with experimental data pertaining to the fundamental frequencies of different waveguides, representing a variety of geometries. Using the commercially available finite element software, ANSYS, we attempt to create a computational model that reproduces the experimental data and may be used to predict more complicated geometries.
3:15-3:30 Adnan Sabuwala, University of Florida
Gaussian Spectral Rules for Three-Point Finite Differences
In this talk, we present an introduction to optimal grids and their application to solving end-point approximation problems. This method of grid optimization was first suggested by Druskin and Knizhnerman (SIAM J. Numer. Anal, Vol.37, No.2, pp.403-422). We will outline the steps involved in calculating the grid steps based on the Pade-Chebyshev rational approximation of our impedance function. A great advantage of using these optimal grids is an increase in the order of convergence at the endpoint(s) from second to exponential order without increasing the stencil size or compromising on stability. Inverse problems which require receiver-end data are an immediate application of these optimal grids.
3:35-3:50 John David, North Carolina State University
Optimal Design of Traveling Wave Tubes
The traveling wave tube amplifier (TWT) is a vacuum device invented in the early 1940Ős for amplification of radio frequency (RF) power. This device is critical for communications and electronic warfare missions in the military, as well as in commercial applications. In this talk, we will discuss the optimal design of these devices to improve essential performance criteria including efficiency, linear power range and phase distortion. The simulation code, CHRISTINE, was used to evaluate the performance of TWTs given a set of design parameters. Current capability of CHRISTINE allows only for a limited number of basic TWT designs including a limited number of design goal functions, and employs a modified steepest descent method to carry out the optimization process. However, in this type of application the landscapes of the goal functions are, in general, very noisy which can defeat most gradient based methods. The objectives of our work are two-fold: (i) to improve the design capabilities for TWT (including basic geometry and new goal functions) and (ii) to investigate optimization techniques that are better suited for problems with complex and noisy landscapes (for example, simplex type methods such as Nelder-Mead and DIRECT).