had been investigated. As it is noted here, these equations are not adjoint equations and are referred to as quasi-adjoint equations. Equation (E) is a special case of linear nth-order difference equations with quasi-differences. Such equations have been widely studied in the literature, see, for example, [6, 11] and the references therein. The natural question which arises is to find the adjoi...

Adjoint consistency – in addition to consistency – is the key requirement for discontinuous Galerkin discretisations to be of optimal order in L as well as measured in terms of target functionals. We provide a general framework for analysing adjoint consistency and introduce consistent modifications of target functionals. This framework is then used to derive an adjoint consistent discontinuous...

A new scheme for differentiating complex mesh-based numerical models (e.g. finite element models), the Independent Set Perturbation Adjoint method (ISP-Adjoint), is presented. Differentiation of the matrices and source terms making up the discrete forward model is realized by a graph colouring approach (forming independent sets of variables) combined with a perturbation method to obtain gradien...

In this paper we investigate the efficient realization of sampling methods, based on solutions of certain adjoint problems. This adjoint approach does not require the explicit knowledge of a Green’s function for the background medium, and allows to sample for all points and all dipole directions simultaneously; thus several limitations of standard sampling methods are relieved. A detailed deriv...

The analytic properties of adjoint solutions are examined for the quasi-onedimensional Euler equations. For shocked flow, the derivation of the adjoint problem reveals that the adjoint variables are continuous with zero gradient at the shock, and that an internal adjoint boundary condition is required at the shock. A Green’s function approach is used to derive the analytic adjoint solutions cor...

The formulation and solution of the adjoint problem for unsteady flow simulations using the Reynolds-averaged Navier-Stokes equations in the presence of dynamically deforming unstructured meshes is demonstrated. A discrete adjoint approach is used, and the full linearization is built up in a systematic and modular fashion. Discrete conservation in the analysis problem is ensured through the geo...

The refined Gribov-Zwanziger (RGZ) action in the Landau gauge accounts for existence of infinitesimal Gribov copies as well dynamical formation condensates infrared Euclidean Yang-Mills theories. We couple scalar fields to RGZ and compute one-loop propagator adjoint representation group. compare our findings with existing lattice data. fate Becchi-Rouet-Stora-Tyutin symmetry this model is discu...

This paper explores the use of nonparallel adjoint methods to predict the receptivity of two and three-dimensional boundary layers. Solutions obtained from both adjoint Navier–Stokes (ANS) and adjoint parabolized stability equations (APSE) have been validated against linearized Navier–Stokes (LNS) solutions that provide a full description of the linear receptivity process. The adjoint methods a...

A neural approach to propositional multi-adjoint logic programming was recently introduced. In this paper we extend the neural approach to multi-adjoint deduction and, furthermore, modify it to cope with abductive multi-adjoint reasoning, where adaptations of the uncertainty factor in a knowledge base are carried out automatically so that a number of given observations can be adequately explained.