Many optimization problems in electrical engineering consider a large number of design parameters. A sensitivity analysis identifies the parameters with strongest influence on problem interest. This paper introduces adjoint variable method as an efficient approach to study sensitivities nonlinear electroquasistatic time domain. In contrast more common direct method, has computational cost nearl...

Abstract The primal-dual method of Chambolle and Pock is a widely used algorithm to solve various optimization problems written as convex-concave saddle point problems. Each update step involves the application both forward linear operator its adjoint. However, in practical applications like computerized tomography, it often computationally favourable replace adjoint by more efficient approxima...

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...

We use C∗-algebra theory to provide a new method of decomposing the essential spectra of self-adjoint and non-self-adjoint Schrödinger operators in one or more space dimensions.