Type of Document Dissertation Author Shenoy, Ajit R. URN etd-402101939761081 Title Optimization Techniques Exploiting Problem Structure: Applications to Aerodynamic Design Degree PhD Department Aerospace and Ocean Engineering Advisory Committee
Advisor Name Title Grossman, Bernard M. Herdman, Terry L. Kapania, Rakesh K. Lutze, Frederick H. Jr. Cliff, Eugene M. Committee Chair Keywords
- Sequential Quadratic Programming
- Reduced Hessian
- Trust Region
- Sparse Optimization
- Airfoil Design
Date of Defense 1997-04-11 Availability unrestricted AbstractThe research presented in this dissertation investigates the use of all-at-once
methods applied to aerodynamic design. All-at-once schemes are usually based on
the assumption of sufficient continuity in the constraints and objectives, and
this assumption can be troublesome in the presence of shock discontinuities.
Special treatment has to be considered for such problems and we study several
Our all-at-once methods are based on the Sequential Quadratic Programming
method, and are designed to exploit the structure inherent in a given problem.
The first method is a Reduced Hessian formulation which projects the
optimization problem to a lower dimension design space. The second method
exploits the sparse structure in a given problem which can yield significant
savings in terms of computational effort as well as storage requirements. An
underlying theme in all our applications is that careful analysis of the given
problem can often lead to an efficient implementation of these all-at-once
Chapter 2 describes a nozzle design problem involving one-dimensional transonic
flow. An initial formulation as an optimal control problem allows us to solve
the problem as as two-point boundary problem which provides useful insight into
the nature of the problem. Using the Reduced Hessian formulation for this
problem, we find that a conventional CFD method based on shock capturing
produces poor performance. The numerical difficulties caused by the presence of
the shock can be alleviated by reformulating the constraints so that the shock
can be treated explicitly. This amounts to using a shock fitting technique.
In Chapter 3, we study variants of a simplified temperature control problem.
The control problem is solved using a sparse SQP scheme. We show that for
problems where the underlying infinite-dimensional problem is well-posed, the
optimizer performs well, whereas it fails to produce good results for problems
where the underlying infinite-dimensional problem is ill-posed. A transonic
airfoil design problem is studied in Chapter 4, using the Reduced SQP
formulation. We propose a scheme for performing the optimization subtasks that
is based on an Euler Implicit time integration scheme. The motivation is to
preserve the solution-finding structure used in the analysis algorithm.
Preliminary results obtained using this method are promising. Numerical results
have been presented for all the problems described.
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