This article presents a new approach for the efficient calculation of sensitivities in radiation dose estimates, subject to imprecisely known nuclear material cross-section data. The method is combined application adjoint-based models perform, simultaneously, both sensitivity together with optimal adaptive mesh refinement. Adjoint-based methods are their efficiency since they enable all paramet...

In simple electrical flow problems the Dirichlet integral of the potential function gives the electrical conductance. Moreover the Dirichlet integral of an arbitrary function satisfying the boundary condition gives an upper bound for the conductance. This last property (Dirichlet's principle) does not hold if the boundary value problem is not self-adjoint. This paper develops new algorithms for...

In this work, we present a new constructive technique which is based on Green’s functional concept. According to this technique, a linear completely nonhomogeneous nonlocal problem for a second-order ordinary differential equation is reduced to one and only one integral equation in order to identify the Green’s solution. The coefficients of the equation are assumed to be generally variable nons...

In general, chaotic dynamical systems produce ill-conditioned direct and adjoint sensitivity equations, so these conventional sensitivity analysis methods do not provide useful derivatives for design optimization of chaotic systems. The least-squares shadowing (LSS) method is a recently proposed regularization of the sensitivity equations that leads to useful derivative information; however, th...

The purpose of this paper is an optimal control problem of temperature using the Newton based method and the finite element method. This method is based on the first and second order adjoint technique allowing to obtained a better approximation to the Newton line search direction. The formulation is based on the optimal control theory in which the performance function is expressed by the comput...

Adjoint methods have become fundamental ingredients of the scientific computing toolbox over the past decades. Large-scale parameter sensitivity analysis, uncertainty quantification and nonlinear optimization as well as modern approaches to deep learning would otherwise turn out computationally infeasible. For nontrivial real-world problems the algorithmic derivation of adjoint numerical simula...