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Abstract
In airfoil design, one problem of great
interest is to find the target airfoil profile to achieve a given
target velocity distribution. It can be formulated as an optimal
control problem, with the control being the airfoil profile and
the governing equation being the full potential equation in the
transonic regime. To discretize the problem, one approach is to
employ the finite element method. In the discretized space, a
direct relationship between the objective function and the unknown
profile co-ordinates can be defined via the finite element basis
functions. Moreover, it is advantageous to derive the gradient in
the discretized space rather than the continuous space to avoid
contamination by discretization errors. In this paper, this
approach is studied. In particular, a new formulation is proposed.
A novel decomposition of the discrete space for the potential
function, the gradient is derived and an efficient algorithm using
the quasi-Newton method is described. In generating and adjusting
the mesh during iterations, the elliptic mesh generation technique
is used.
Mathematics Subject Classification: 93C20, 76H05, 49Q10.
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