In this paper we consider the problem of the existence of higher derivatives of the function t → ϕ(A + tK), where ϕ is a function on the real line, A is a self-adjoint operator, and K is a bounded self-adjoint operator. We improve earlier results by Sten'kin. In order to do this, we give a new approach to multiple operator integrals. This approach improves the earlier approach given by Sten'kin...

An adjoint based functional optimization technique in conjunction with the spectral stochastic finite element method is proposed for the solution of an inverse heat conduction problem in the presence of uncertainties in material data, process conditions and measurement noise. The ill-posed stochastic inverse problem is restated as a conditionally well-posed L2 optimization problem. The gradient...

The aim of this work is to solve an identification problem in plug-flow chemical reactors. This leads to an optimization problem involving parameters and for which the adjoint method is introduced for calculating the gradient of the objective function. An adjoint-based algorithm for parameter identification problems in systems of partial differential equations is presented. The algorithm calcul...

An adjoint model for a 2D finite element Galerkin shallow water model is developed using the Independent Set Perturbation (ISP, [46]) sensitivity analysis. 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 the ISP s...

The purpose of this study is to show some mathematical aspects of the adjoint method that is a numerical method for the Cauchy problem, an inverse boundary value problem. The adjoint method is an iterative method based on the variational formulation, and the steepest descent method minimizes an objective functional derived from our original problem. The conventional adjoint method is time-consu...

1. Introduction While aerodynamic prediction methods based CFD are now well established , and quite accurate and robust, the ultimate need in the design process is to find the optimum shape which maximizes the aerodynamic performance. One way to approach this objective is to view it as a control problem, in which the wing is treated as a device which controls the flow to produce lift with minim...

Including tracer data into geostatistically based methods of inverse modeling is computationally very costly when all concentration measurements are used and the sensitivities of many observations are calculated by the direct di€erentiation approach. Harvey and Gorelick (Water Resour Res 1995;31(7):1615±26) have suggested the use of the ®rst temporal moment instead of the complete concentration...

SUMMARY The objective of the paper is to construct adjoint consistent formulations of the Helmholtz 'slip' model for the simulation of electroosmotic flows. The motivation is to apply adjoint-based methods for the development of adaptive finite element tools and parameter sensitivity analyses to microfluidic problems. Issues in the current formulation of the 'slip' model lie in the fact that it...

In this study, we investigate the method for adjoint-based optimal control of linear and non-linear equations. In particular, we are interested in the formulation of the unsteady adjoint method based on the high-order spectral difference method. For the linear equation, we consider the simple 1D advection equation. For the non-linear equation, we consider the 1D viscous Burger’s equation. In bo...