Infeasible path methods for an aerodynamic shape optimization problem

Abstract: "We consider optimal design problems of systems governed by suitable discretizations of nonlinear partial differential equations. We present and examine a coordinate basis infeasible path method tailored to such design problems. We employ a particular null space representation which exploits the structure of the constraint Jacobian. The resulting method avoids resolution of the nonlinear behavior for each design iterate. Three variants of the method are developed which require the solution of either two or three linear systems involving the stiffness matrix of the discrete boundary value problem. The method is used to solve an aerodynamic design problem governed by nonlinear potential flow. Numerical results demonstrate a substantial performance improvement."