Browsing by Author "Kokkolaras, Michael"

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    Mixed Variable Optimization of the Number and Composition of Heat Intercepts in a Thermal Insulation System
    (2000-06) Kokkolaras, Michael; Audet, Charles; Dennis, J.E. Jr.
    In the literature, thermal insulation systems with a fixed number of heat intercepts have been optimized with respect to intercept locations and temperatures. The number of intercepts and the types of insulators that surround them were chosen by parametric studies. This was because the optimization methods used could not treat such categorical variables. Discrete optimization variables are categorical if the objective function or the constraints can not be evaluated unless the variables take one of a prescribed enumerable set of values. The key issue is that categorical variables can not be treated as ordinary discrete variables are treated by relaxing them to continuous variables with a side constraint that they be discrete at the solution. A new mixed variable programming (MVP) algorithm makes it possible to optimize directly with respect to mixtures of discrete, continuous, and categorical decision variables. The result of applying MVP is shown here to give a 65% reduction in the objective function over the previously published result for a thermal insulation model from the engineering literature. This reduction is largely because MVP optimizes simultaneously with respect to the number of heat intercepts and the choices from a list of insulator types as well as intercept locations and temperatures. The main purpose of this paper is to show that the mixed variable optimization algorithm can be applied effectively to a broad class of optimization problems in engineering that could not be easily solved with earlier methods.
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    Utilizing parallel optimization in computational fluid dynamics
    (1998) Kokkolaras, Michael; Meade, Andrew J., Jr.
    General problems of interest in computational fluid dynamics are investigated by means of optimization. Specifically, in the first part of the dissertation, a method of optimal incremental function approximation is developed for the adaptive solution of differential equations. Various concepts and ideas utilized by numerical techniques employed in computational mechanics and artificial neural networks (e.g. function approximation and error minimization, variational principles and weighted residuals, and adaptive grid optimization) are combined to formulate the proposed method. The basis functions and associated coefficients of a series expansion, representing the solution, are optimally selected by a parallel direct search technique at each step of the algorithm according to appropriate criteria; the solution is built sequentially. In this manner, the proposed method is adaptive in nature, although a grid is neither built nor adapted in the traditional sense using a-posteriori error estimates. Variational principles are utilized for the definition of the objective function to be extremized in the associated optimization problems, ensuring that the problem is well-posed. Complicated data structures and expensive remeshing algorithms and systems solvers are avoided. Computational efficiency is increased by using low-order basis functions and concurrent computing. Numerical results and convergence rates are reported for a range of steady-state problems, including linear and nonlinear differential equations associated with general boundary conditions, and illustrate the potential of the proposed method. Fluid dynamics applications are emphasized. Conclusions are drawn by discussing the method's limitations, advantages, and possible extensions. The second part of the dissertation is concerned with the optimization of the viscous-inviscid-interaction (VII) mechanism in an airfoil flow analysis code. The VII mechanism is based on the concept of a transpiration velocity boundary condition, whose convergence to steady state is accelerated. The number of variables in the associated optimization problem is reduced by means of function approximation concepts to ensure high number of parallel processors to number of necessary function evaluations ratio. Numerical results are presented for the NACA-0012 and the supercritical RAE-2822 airfoils subject to transonic flow conditions using a parallel direct search technique. They exhibit a satisfactory level of accuracy. Speed-up depends on the number of available computational units and increases for more challenging flow conditions and airfoil geometries. The enhanced code constitutes a useful tool for airfoil flow analysis and design and an acceptable alternative to computationally expensive high fidelity codes.