Adjoint state method is a well-known method to efficiently compute the gradient of a cost or objective function for a simulation-driven optimization problem. Essentially, it computes the adjoint action of Born operator (the linearized forward map) on any given vector. This report presents a derivation of adjoint state algorithm for an acoustic system discretized by staggered grid finite differe...

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...

An adjoint sensitivity method is presented for parameter-dependent differentialalgebraic equation systems (DAEs). The adjoint system is derived, along with conditions for its consistent initialization, for DAEs of index up to two (Hessenberg). For stable linear DAEs, stability of the adjoint system (for semi-explicit DAEs) or of an augmented adjoint system (for fully implicit DAEs) is shown. In...

A new scheme for differentiating complex mesh-based numerical models (e.g. finite element models), the Independent Set Perturbation Adjoint method (ISP-Adjoint), is presented. Differentiation of the matrices and source terms making up the discrete forward model is realized by a graph colouring approach (forming independent sets of variables) combined with a perturbation method to obtain gradien...

We present an adjoint-based optimization for electromagnetic design. It embeds commercial Maxwell solvers within a steepest-descent inverse-design optimization algorithm. The adjoint approach calculates shape derivatives at all points in space, but requires only two "forward" simulations. Geometrical shape parameterization is by the level set method. Our adjoint design optimization is applied t...

2 Discretization 9 2.1 The Discontinuous Galerkin Method . . . . . . . . . . . . . . . . . . . . . 9 2.1.1 Conservation Equations . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.2 Solution Approximation . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 Weak Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.4 Discrete System . . . . . . . . . . . . . . . . . ....

Hybrid methods represent a classic discretization paradigm for elliptic equations. More recently, hybrid methods have been formulated for convection-diffusion problems, in particular compressible fluid flow. In [25], we have introduced a hybrid mixed method for the compressible Navier-Stokes equations as a combination of a hybridized DG scheme for the convective terms, and an H(div,Ω)-method fo...

Optimization using finite element analysis and the adjoint variable method to solve engineering problems appears in various application areas. However, best of authors’ knowledge, there is a lack detailed explanation on implementation context electromagnetic modeling. This paper aimed provide simplest possible general framework. Then, an extended offered electromagnetism. A discrete design meth...

Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. The following paper presents a new method for sensitivity ana...