adjoints – Optimization Online

On Theoretical and Numerical Aspects of the Shape Sensitivity Analysis for the 3D Time-dependent Maxwell’s Equations

Published: 2015/08/26

Optimization of Systems modeled by PDEs adjoints, inverse problems, maxwell's equations, parameter identification, pde constrained optimization problem, shape optimization

We propose a novel approach using shape derivatives to solve inverse optimization problems governed by Maxwell’s equations, focusing on identifying hidden geometric objects in a predefined domain. The target functional is of tracking type and determines the distance between the solution of a 3D time-dependent Maxwell problem and given measured data in an $L_2$-norm. Minimization … Read more

A framework for automated PDE-constrained optimisation

Published: 2013/03/01

P. E. Farrell

S. W. Funke

Problem Solving Environments adjoints, automatic differentiation, data assimilation, inverse problems, optimisation, pde constraints

A generic framework for the solution of PDE-constrained optimisation problems based on the FEniCS system is presented. Its main features are an intuitive mathematical interface, a high degree of automation, and an efficient implementation of the generated adjoint model. The framework is based upon the extension of a domain-specific language for variational problems to cleanly … Read more