Given a causal analytic nonlinear input-output system represented as a Chen-Fliess functional series, this paper investigates how to apply an existing notion of a nonlinear Hilbert adjoint operator to explicitly compute a corresponding adjoint operator. The method is demonstrated for the bilinear case.

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...

Abstract The paper suggests a new technique for solution of the inverse problem for Maxwell’s equations in a dissipating medium. Being non-self-adjoint, the problem generally requires computing an adjoint operator on each step of gradient descent minimization procedure. The suggested approach introduces a conjugation operator and develops a representation of the system of Maxwell’s equations ba...

Abstract: A conservation law theorem stated by N. Ibragimov along with its subsequent extensions are shown to be a special case of a standard formula that uses a pair consisting of a symmetry and an adjoint-symmetry to produce a conservation law through a well-known Fréchet derivative identity. Furthermore, the connection of this formula (and of Ibragimov’s theorem) to the standard action of sy...

The aim of this work is to solve an identification problem in plug-flow chemical reactors. This leads to an optimization problem involving parameters and for which the adjoint method is introduced for calculating the gradient of the objective function. An adjoint-based algorithm for parameter identification problems in systems of partial differential equations is presented. The algorithm calcul...

The adjoint variable method is applied for the first time to perform sensitivity analysis with transmission line modeling exploiting rubber cells. Rubber cells allow for the conformal modeling of off-grid boundaries in the transmission line modeling computational domain using modified tensor properties. The scattering matrix of the rubber cell is analytically dependent on the dimensions of the ...

Many applications of various self-adjoint differential equations, whose solutions are complex, are produced Arfken, 1985; Gandarias, 2011; and Delkhosh, 2011 . In this work we propose a method for the solving some self-adjoint equations with variable change in problem, and then we obtain a analytical solutions. Because this solution, an exact analytical solution can be provided to us, we benefi...

This paper presents an adjoint method for the optimum shape design of unsteady flows. The goal is to develop a set of discrete unsteady adjoint equations and their corresponding boundary conditions for both the time accurate and non-linear frequency domain methods. First, this paper presents the complete formulation of the time dependent optimal design problem. Second, we present the time accur...

One major challenge in applying the adjoint method to large industrial cases is the lack of robustness of the flow and adjoint solvers. Discrete adjoints transpose the Jacobian of the system of discretised equations exactly, and hence inherit the linear stability from the primal flow solver. Typically the linear stability properties of the iterative scheme of the flow solver is very well unders...

Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer & Hermand, J. Acoust. Soc. Am. 117, 2937–2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a...