Optimization under adaptive error control for finite element based simulations |
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Authors: | Bart G van Bloemen Waanders Brian R Carnes |
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Affiliation: | 1.Sandia National Laboratories,Albuquerque,USA |
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Abstract: | Optimization problems constrained by complex dynamics can lead to computationally challenging problems especially when high
accuracy and efficiency are required. We present an approach to adaptively control numerical errors in optimization problems
approximated using the finite element method. The discrete adjoint equation serves as a key tool to efficiently compute both
parameter sensitivities and goal-oriented error estimates at the same discretized levels. By using a recovery method for the
error estimators, we avoid expensive higher order adjoint calculations. We nest the adaptivity of the mesh within the optimization
algorithm, which is responsible for converging both the state and optimization algorithms and thereby allowing the reuse of
state, parameters, and reduced Hessian in subsequent optimization iterations. Our approach is demonstrated on a parameter
estimation problem for contamination transport in a contact tank reactor. Significant efficiency and accuracy improvements
are realized in comparison to uniform grid refinement strategies and black-box optimization methods. A flexible and maintainable
software interface was developed to provide access between the underlying linear algebra of a production simulator and advanced
numerical algorithms such as optimization and error estimation. |
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Keywords: | |
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