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The problems of exact state reconstruction and approximate state estimation based on wall information in a wall-bounded incompressible unsteady flow are addressed. It is shown that, if in an arbitrarily small neighborhood of time t precise measurements are made of the two components of wall skin friction and the wall pressure, all terms in the Taylor-series… (More)

This paper examines the regularization opportunities available in the adjoint analysis and optimization of multiscale PDE systems. Regularization may be introduced into such optimization problems by modifying the form of the evolution equation and the forms of the norms and inner products used to frame the adjoint analysis. Typically, L2 brackets are used… (More)

- Bartosz Protas
- J. Comput. Physics
- 2008

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… (More)

- Oleg Volkov, Bartosz Protas
- J. Comput. Physics
- 2009

This paper reformulates the two–phase solidification problem (i.e., the Stefan problem) as an inverse problem in which a cost functional is minimized with respect to the position of the interface and subject to PDE constraints. An advantage of this formulation is that it allows for a thermodynamically consistent treatment of the interface conditions in the… (More)

- Bartosz Protas, Wenyuan Liao
- J. Comput. Physics
- 2008

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… (More)

- Vladislav Bukshtynov, Bartosz Protas
- J. Comput. Physics
- 2013

- Jeff C.-F. Wong, Bartosz Protas
- Optimization Methods and Software
- 2013

The inverse natural convection problem (INCP) in a porous medium is a highly non-linear problem because of the nonlinear convection and Forchheimer terms. The INCP can be converted into the minimization of a least-squares discrepancy between the observed and the modelled data. It has been solved using different classical optimization strategies that require… (More)

- Bartosz Protas, Bernd R. Noack, Marek Morzynski
- J. Nonlinear Science
- 2014

- Jonathan Gustafsson, Bartosz Protas
- J. Computational Applied Mathematics
- 2010

We address the question of constructing simple inviscid vortex models that optimally approximate realistic flows as solutions of an inverse problem. Assuming the model to be incompressible, inviscid and stationary in the frame of reference moving with the vortex, the ‘structure’ of the vortex is uniquely characterized by the functional relation between the… (More)