Aerodynamic design via control theory
Journal of Scientific Computing
The adjoint method for an inverse design problem in the directional solidification of binary alloys
Journal of Computational Physics
Recipes for adjoint code construction
ACM Transactions on Mathematical Software (TOMS)
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Spectral methods in MatLab
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
Perspectives in Flow Control and Optimization
Perspectives in Flow Control and Optimization
A computational framework for the regularization of adjoint analysis in multiscale PDE systems
Journal of Computational Physics
Algorithm 851: CG_DESCENT, a conjugate gradient method with guaranteed descent
ACM Transactions on Mathematical Software (TOMS)
An extended level set method for shape and topology optimization
Journal of Computational Physics
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Optimal control of the free boundary in a two-phase Stefan problem
Journal of Computational Physics
Optimal Control of the Classical Two-Phase Stefan Problem in Level Set Formulation
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Hi-index | 31.45 |
In this investigation we address the problem of adjoint-based optimization of PDE systems in moving domains. As an example we consider the one-dimensional heat equation with prescribed boundary temperatures and heat fluxes. We discuss two methods of deriving an adjoint system necessary to obtain a gradient of a cost functional. In the first approach we derive the adjoint system after mapping the problem to a fixed domain, whereas in the second approach we derive the adjoint directly in the moving domain by employing methods of the noncylindrical calculus. We show that the operations of transforming the system from a variable to a fixed domain and deriving the adjoint do not commute and that, while the gradient information contained in both systems is the same, the second approach results in an adjoint problem with a simpler structure which is therefore easier to implement numerically. This approach is then used to solve a moving boundary optimization problem for our model system.