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PDE-constrained optimization with error estimation and control
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DOI：10.1016/j.jcp.2013.12.050.png)
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Abstract
En 中文
The paper describes an algorithm for PDE-constrained optimization that controls numerical errors using error estimates and grid adaptation during the optimization process. A key aspect of the algorithm is the use of adjoint variables to estimate errors in the first-order optimality conditions. Multilevel optimization is used to drive the optimality conditions and their estimated errors below a specified tolerance. The error estimate requires two additional adjoint solutions, but only at the beginning and end of each optimization cycle. Moreover, the adjoint systems can be formed and solved with limited additional infrastructure beyond that found in typical PDE-constrained optimization algorithms. The approach is general and can accommodate both reduced-space and full-space formulations of the optimization problem. The algorithm is illustrated using the inverse design of a nozzle constrained by the quasi-one-dimensional Euler equations. (C) 2014 Elsevier Inc. All rights reserved.
Keywords:
PDE-constrained optimization
Adjoint-weighted residual method
Output error estimation
A posteriori error estimation
Journal
IF:
3.8
Papers:
1.5W
Citations:
7.4W