Massively parallel aerodynamic shape optimization

Abstract: "We consider the problem of finding the shape of an airfoil which produces a pressure distribution closest to a desired one. The flow is modeled by the nonlinear potential equations of compressible flow. The problem is formulated as an optimization problem constrained by a discrete approximation to a nonlinear boundary value problem. We present a new parallel infeasible path method for this class of optimization problem. The method is based on a null space representation tailored to the structure of the constraint Jacobian matrix. The resulting null space projections formally involve inverses of the stiffness matrix. The algorithm requires only two stiffness matrix solves per optimization iteration, in contrast to a conventional path-following method, which resolves the full physics at each iteration. The algorithm has been implemented on a CM-2, and requires no new data structures or communication patterns beyond those needed for numerical solution of the boundary value problem. We discuss numerical evidence for the superiority of the new method relative to a conventional path-following approach."