Linear boundary value problems in heat conduction have been investigated extensively for a diverse variety of boundary conditions, but almost invariably these have been of the type that produce self-adjoint problems. The property of selfadjointness makes it possible to obtain readily the solution of steady and unsteady-state heat conduction problems in the form of a series expansion of orthogon...

An adjoint model for a 2D finite element Galerkin shallow water model is developed using the Independent Set Perturbation Adjoint method (ISP-Adjoint, [33]). Its performance in a full 4-D VAR setup with a limited area is assessed by comparing with the adjoint model derived by the automatic differentiation approach, where it is used for optimising the initial conditions. It is shown that ISP-Adj...

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 the corresponding boundary condition for the non-linear frequency domain method. First, this paper presents the complete formulation of the time dependent optimal design problem. Second, we present the non-linear frequency domain adjoint e...

For models described by ordinary differential equation boundary value problems (ODE BVPs), we derive adjoint equations for sensitivity analysis, giving explicit forms for the boundary conditions of the adjoint boundary value problem. The solutions of the adjoint equations are used to efficiently compute gradients of both integral-form and pointwise constraints. Existence and stability results a...

We present a version of the Pontryagin Maximum Principle for control dynamics with a possibly non smooth, nonlipschitz and even discontinuous righthand side. The usual adjoint equation, where state derivatives occur, is replaced by an integrated form, containing only differentials of the reference flow maps. The resulting “integrated adjoint equation” leads to “adjoint vectors” that need not be...

A Bargmann symmetry constraint is proposed for the Lax pairs and the adjoint Lax pairs of the Dirac systems. It is shown that the spatial part of the nonlinearized Lax pairs and adjoint Lax pairs is a finite dimensional Liouville integrable Hamiltonian system and that under the control of the spatial part, the time parts of the nonlinearized Lax pairs and adjoint Lax pairs are interpreted as a ...

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential αx−2 . Although the problem is quite old and well-studied, we believe that our consideration, based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in o...

This paper presents an adjoint method for the calculation of non-collocated sensitivities in supersonic flow. The goal is to develop a set of discrete adjoint equations and their corresponding boundary conditions in order to quantify the influence of geometry modifications on the pressure distribution at an arbitrary location within the domain of interest. First, this paper presents the complet...

This paper presents an adjoint method for the calculation of remote sensitivities in supersonic flow. The goal is to develop a set of adjoint equations and their corresponding boundary conditions in order to quantify the influence of geometry modifications on the pressure distribution at an arbitrary location within the domain of interest. First, this paper presents the formulation and discreti...

An adjoint preprocess for an adjoint-based turbomachinery design process is described. The resulting process is compared to a previously established adjoint process based on three-dimensional adjoint solutions and deformed meshes. Within the new process, the calculation of sensitivities is performed using shape sensitivities and surface displacements, where the design parameters are computer-ai...