Title
Adaptive simulation, the adjoint state method, and optimization
Document Type
Book Chapter
Publication Date
2003
Abstract
Adaptive grids in inverse and control problems can lead to computed objective functions that are nonsmooth, even though the underlying problem is well-behaved. This leads to the question of how to compute the linearization of the scheme—how should a nonsmooth function be differentiated? The C++ class afdtd uses automatic differentiation techniques to implement an abstract marching scheme in an object-oriented fashion, making it possible to use the resulting simulator to solve inverse or control problems. The class takes a complete specification of a single step of the scheme, and assembles from it a complete simulator, along with the linearized and adjoint simulations. The result is a (nonlinear) operator in the sense of the Hilbert Class Library, a C++ package for optimization. Moreover, afdtd supports locally “frozen” grids, allowing the implementation of an operator that is piecewise smooth in spite of the use of adaptivity.
Publication Title
Large-Scale PDE-Constrained Optimization
ISBN
978-3-540-05045-2
Recommended Citation
Gockenbach, M.,
&
Symes, W. W.
(2003).
Adaptive simulation, the adjoint state method, and optimization.
Large-Scale PDE-Constrained Optimization, 281-297.
http://doi.org/10.1007/978-3-642-55508-4_17
Retrieved from: https://digitalcommons.mtu.edu/math-fp/31
Publisher's Statement
© Springer-Verlag Berlin Heidelberg 2003. Publisher's version of record: https://doi.org/10.1007/978-3-642-55508-4_17