Bartosz Protas

Learn 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)
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)
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)
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)