The structure of the paper is as follows. In Section 2, we introduce the preliminary concepts necessary for the definition of the syntax and semantics of sorted multi-adjoint logic programs, presented in Section 3. In Section 4, we state the basic results regarding the termination properties of our semantics, which are extended later in Section 5. The paper finishes with some conclusions and po...

Common velocity analysis is based on the invariance of migrated images with respect to the experiment index (shot number, plane-wave take-off angle, etc.) or extension parameters (reflection angle, correlation lags in extended images, etc.). All the information available, i.e. the entire survey, is used for assessing the quality of the model used for imaging. This approach is effective but forc...

This paper deals with the application of the adjoint transport theory in order to optimize Monte Carlo based radiotherapy treatment planning. The technique is applied to Boron Neutron Capture Therapy where most often mixed beams of neutrons and gammas are involved. In normal forward Monte Carlo simulations the particles start at a source and lose energy as they travel towards the region of inte...

We consider one-dimensional steady-state conservation laws with discontinuous solutions. Giles and Pierce [7] realized that a shock leads to a new term in the adjoint error representation for target functionals. This term disappears if and only if the adjoint solution satisfies an internal boundary condition. Curiously, most computer codes implementing adjoint error estimation ignore the new te...

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...