This paper presents an adjoint method for the optimal control of unsteady flows. The goal is to develop the continuous and discrete unsteady adjoint equations and their corresponding boundary conditions for the timeaccuratemethod. First, this paper presents the complete formulation of the time-dependent optimal design problem. Second, we present the time-accurate unsteady continuous and discret...

We derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as “inadmissible”. For example, a cost functional which depends on the density, rather than on the pressure, is considered “inadmissible” for an optimization problem governed by the Euler equations. We show that for such problems additional terms should be included in the Lagrangian function...

This paper presents a systematic procedure based on the adjoint method for solving a class of inverse directional alloy solidification design problems in which a desired growth velocity v f is achieved under stable growth conditions. To the best of our knowledge, this is the first time that a continuum adjoint formulation is proposed for the solution of an inverse problem with simultaneous heat...

We present a generalization of the Pontryagin Maximum Principle, in which the usual adjoint equation, which contains derivatives of the system vector fields with respect to the state, is replaced by an integrated form, containing only differentials of the reference flow maps. In this form, the conditions of the maximum principle make sense for a number of control dynamical laws whose right-hand...

This paper introduces and analyzes a new parallel-in-time gradient type method for the solution of convex linear-quadratic discrete-time optimal control (DTOC) problems. Each iteration of the classical gradient method requires the solution of the forward-in-time state equation followed by the solution of the backward-in-time adjoint equation to compute the gradient. To introduce parallelism, th...

We consider the solution of a (generalized) eigenvalue problem arising in physical oceanography that involves the evaluation of both the tangent-linear and adjoint versions of the underlying numerical model. Two different approaches are discussed. First, tangent-linear and adjoint models are generated by the software tool TAF and used separately. Second, the two models are combined into a singl...