Considering different implication operators, such as Lukasiewicz, Gödel or product implication in the same logic program, naturally leads to the allowance of several adjoint pairs in the lattice of truthvalues. In this paper we apply this idea to introduce multi-adjoint logic programs as an extension of monotonic logic programs. The continuity of the immediate consequences operators is proved a...

‎in this paper‎, ‎we study spectral element approximation for a constrained‎ ‎optimal control problem in one dimension‎. ‎the equivalent a posteriori error estimators are derived for‎ ‎the control‎, ‎the state and the adjoint state approximation‎. ‎such estimators can be used to‎ ‎construct adaptive spectral elements for the control problems.

Multi-adjoint logic programming represents a very recent, extremely exible attempt for introducing fuzzy logic into logic programming. Inspired by previous approaches largely used in other (crisp) declarative paradigms, in this paper we propose the development of a fold/unfold based transformation system for optimizing such kind of fuzzy logic programs. We prove that our set of transformation r...

Reductants are a special kind of fuzzy rules which constitute an essential theoretical tool for proving correctness properties. A multi-adjoint logic program, when interpreted on an arbitrary lattice, has to include all its reductants in order to preserve the approximate completeness property. In this work, after revisiting the different notions of reductant arisen in the framework of multi-adj...

The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient...

In this investigation we address the problem of adjoint–based optimization of PDE systems in moving domains. As an example we consider the one–dimensional heat equation with prescribed boundary temperatures and heat fluxes. We discuss two methods of deriving an adjoint system necessary to obtain a gradient of a cost functional. In the first approach we derive the adjoint system after mapping th...

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...

This paper compares the continuous and discrete viscous adjoint-based automatic aerodynamic optimization. The objective is to study the complexity of the discretization of the adjoint equation for both the continuous and discrete approach, the accuracy of the resulting estimate of the gradient, and its impact on the computational cost to approach an optimum solution. First, this paper presents ...

Optimal control of fractional linear systems on a finite horizon can be classically formulated using the adjoint system. But the adjoint of a causal fractional integral or derivative operator happens to be an anti-causal operator: hence, the adjoint equations are not easy to solve in the first place. Using an equivalent diffusive realization helps transform the original problem into a coupled s...

We present a discrete adjoint version of OpenFOAM obtained by operator overloading which yields, in comparison to continuous adjoint versions, a greater flexibility and robustness. We discuss our implementation and how the discrete adjoint version of OpenFOAM differs from existing continuous implementations. To reduce the inherent memory requirement of discrete adjoint code we introduce a check...