Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
Iterative solution methods
Perspectives in Flow Control and Optimization
Perspectives in Flow Control and Optimization
A nonlinear programming perspective on sensitivity calculations for systems governed by state equations
Energy minimization using Sobolev gradients: application to phase separation and ordering
Journal of Computational Physics
A computational framework for the regularization of adjoint analysis in multiscale PDE systems
Journal of Computational Physics
Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations
SIAM Journal on Scientific Computing
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
SIAM Review
Journal of Computational Physics
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In this work we investigate a technique for accelerating convergence of adjoint-based optimization of PDE systems based on a nonlinear change of variables in the control space. This change of variables is accomplished in the ''differentiate - then - discretize'' approach by constructing the descent directions in a control space not equipped with the Hilbert structure. We show how such descent directions can be computed in general Lebesgue and Besov spaces, and argue that in the Besov space case determination of descent directions can be interpreted as nonlinear wavelet filtering of the adjoint field. The freedom involved in choosing parameters characterizing the spaces in which the steepest descent directions are constructed can be leveraged to accelerate convergence of iterations. Our computational examples involving state estimation problems for the 1D Kuramoto-Sivashinsky and 3D Navier-Stokes equations indeed show significantly improved performance of the proposed method as compared to the standard approaches.