This paper presents a formulation for the obtainment of the sensitivity analysis of a point wise error estimator with respect to the nodal coordinates using the adjoint state method. The proposed point wise error estimator is based on the SPR method. The numerical accuracy of the presented sensitivity analysis has been tested by perturbing a mesh. The capability of the presented sensitivity ana...

This paper presents a new computationally efficient unified approach to the numerical simulation of sensitivity and noise in majority-carrier semiconductor devices, based on the extension to device simulation of the adjoint method, well known in the sensitivity and noise analysis of electrical networks. Sensitivity and device noise analysis based on physical models are shown to have a common ba...

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...

‎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.

Implicit–explicit multistep methods for nonlinear parabolic equations were recently analyzed in [2, 3, 1]. In these papers the linear operator of the equation is assumed time-independent, self-adjoint and positive definite; then, the linear part is discretized implicitly and the remaining part explicitly. Here we slightly relax the hypotheses on the linear operator by allowing part of it to be ...

We consider SU(N) gauge theory in 1+1 dimensions coupled to chiral fermions in the adjoint representation of the gauge group. With all fields in the adjoint representation the gauge group is actually SU(N)/ZN , which possesses nontrivial topology. In particular, there are N distinct topological sectors and the physical vacuum state has a structure analogous to a θ vacuum. We show how this featu...

In order to decrease the fluid drag on an underwater robot manipulator, an optimal trajectory method based on the variational method is presented. By introducing the adjoint variables, which are Lagrange multipliers, we formulate a Lagrange function under certain constraints related to the target angle, target angular velocity, and dynamic equation of the robot manipulator. The state equation (...

Adaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes uniformly refined grids computationally prohibitive. Adaptive refinement of meshes and time steps allows to capture the phenomena of interest while keeping the cost of a simulation tractable on the current hardware. Many fields in scienc...

We demonstrate the power of adaptive mesh refinement with adjointbased error estimates in verification of simulations governed by the steady Euler equations. The flow equations are discretized using a finite volume scheme on a Cartesian mesh with cut cells at the wall boundaries. The discretization error in selected simulation outputs is estimated using the method of adjoint-weighted residuals....