The Extend Adjoint Method
نویسندگان
چکیده
One method to solve topology optimization problems is the topological derivative. This approach has some drawbacks: it is limited to simple problems, we do not know how to fill holes, ... To overcome these limitations, an extension of the adjoint method is presented. Named the numerical vault, it allows us to consider new fields of applications and to explore new theoretical investigations in the area of topological derivative.
منابع مشابه
Optimal Control of Light Propagation Governed by Eikonal Equation within Inhomogeneous Media Using Computational Adjoint Approach
A mathematical model is presented in the present study to control the light propagation in an inhomogeneous media. The method is based on the identification of the optimal materials distribution in the media such that the trajectories of light rays follow the desired path. The problem is formulated as a distributed parameter identification problem and it is solved by a numerical met...
متن کاملOperator-valued tensors on manifolds
In this paper we try to extend geometric concepts in the context of operator valued tensors. To this end, we aim to replace the field of scalars $ mathbb{R} $ by self-adjoint elements of a commutative $ C^star $-algebra, and reach an appropriate generalization of geometrical concepts on manifolds. First, we put forward the concept of operator-valued tensors and extend semi-Riemannian...
متن کاملDiscretized Adjoint State Time and Frequency Domain Full Waveform Inversion: A Comparative Study
This study derives the discretized adjoint states full waveform inversion (FWI) in both time and frequency domains based on the Lagrange multiplier method. To achieve this, we applied adjoint state inversion on the discretized wave equation in both time domain and frequency domain. Besides, in this article, we introduce reliability tests to show that the inversion is performing as it should be ...
متن کاملAdjoint-based Mesh Adaptation for the 3D Navier-Stokes Equations with the High-order CPR Method
The objective of the present work is to extend the adjoint-based error estimate and the adaptive mesh refinement algorithm of the high-order CPR method to the 3D NavierStokes equations. A dual-consistent high-order correction procedure via reconstruction method is utilized to obtain the adjoint solution and derive the output-based local error indicator. Several inviscid and viscous flow cases a...
متن کاملAn Adjoint Consistency Analysis for a Class of Hybrid Mixed Methods
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...
متن کامل