The goal of this paper is to briefly recall the importance of the adjoint method in many problems of sensitivity analysis, uncertainty quantification and optimization when the model is a differential equation. We illustrate this notion with some recent examples. As is well known, from a computational point of view the adjoint method is intrusive, meaning that it requires some changes in the num...

The present paper shows the embedding of the adjoint method in multibody dynamics and its broad applicability for examples for both, parameter identification and optimal control. Especially, in case of parameter identifications in engineering multibody applications, a theoretical enhancement of the proposed adjoint method by an error control of accelerations is inevitable in order to meet the c...

We consider the numerical solution of an inverse problem of finding the shape and location of holes in an elastic body. The problem is solved by minimizing a functional depending on the eigenvalues and traces of corresponding eigenmodes. We use the adjoint method to calculate the shape derivative of this functional. The optimization is performed by BFGS, using a genetic algorithm as a preproces...

A method for generating inflow conditions for direct numerical simulations (DNS) of spatially-developing flows is presented. The proposed method is based on variational data assimilation and adjoint-based optimization. The estimation is conducted through an iterative process involving a forward integration of a given dynamical model followed by a backward integration of an adjoint system define...

In this paper we derive a posteriori error estimates for linear functionals of the solution to an elliptic problem discretized using a multiscale nonoverlapping domain decomposition method. The error estimates are based on the solution of an appropriately defined adjoint problem. We present a general framework that allows us to consider both primal and mixed formulations of the forward and adjo...

An optimal estimation method for state and distributed parameters in 1-D hyperbolic system based on adjoint method is proposed in this paper. A general form of the partial differential equations governing the dynamics of system is first introduced. In this equation, the initial condition or state variable as well as some empirical parameters are supposed to be unknown and need to be estimated. ...

Gradient-based optimisation relies on the response Jacobian whose evaluation constitutes a major computational overhead in full-wave numerical analysis. Adjoint-based techniques may offer numerically efficient solutions, but their implementation is too involved in the case of fullwave computations. A simple approach that uses the self-adjoint sensitivity analysis and Broyden’s update is propose...

Let H be a symmetric operator in a separable Hilbert space H. Suppose that H has some gap J . We shall investigate the question about what spectral properties the self{adjoint extensions of H can have inside the gap J and provide methods how to construct self{adjoint extensions of H with prescribed spectral properties inside J . Under some weak assumptions about the operator H which are satised...

An efficient model-order reduction technique for general RLC networks is proposed. The method is extended from the previous projection-base moment matching method with considering both the circuit network and its corresponding adjoint network. By exploring symmetric properties of the MNA formulation, the proposed method needs only one half of the system moment information compared with the prev...