Master Thesis Proposals Multiscale Techniques for the Optimal Control of PDEs with Application to the Design of Catalysts
Domenico J. P. Lahaye, Marc‐Olivier Coppens · 2008
Chemicalcatalystsareessentialforthefastandselectivetransformationofrawmaterialstoendproductssuchasintheproduction of gasoline, diesel and plastics from crude oil. Discovery of more efficient catalysts therefore has a largeeconomical impact. In this thesis we aim at contributing to this research by developing fast and robust mathematicaloptimization techniquesThe transport of chemical species through a catalyst is modeled by a system of coupled reaction-diffusion equa-tions [3]. Solving these systems via numerical techniques remains to date a computationally challenging task. Thestraightforward inclusion of these modeling tools in optimization procedures is therefore prohibitevily expensive.In this thesis we therefore aim at exploiting previously developed expertise in multiscale optimization techniquestothecatalystdesignproblemandtoapplyspace-mappingtechniques[2]. TheideahereistoconsiderthePDEsmodelas a accurate (fine) model and to complement this model with a computationally cheap (coarse) model. A mappingbetweenthemodelsallowstoshifttheoptimizationtothecoarsemodelandtocorrectthismodelwhenneededbyusingthe fine model. This approach is expected to result in a considerable speedup of the overall optimization procedure.Inparalleltotheapplicationofspace-mappingtechniques,wewillalsolookintotheapplicationofadjointequationmethods to compute the sensitivity of the cost function [1]. It is expected that information on the gradient of the costfunction will again allow to speed up the optimization procedure.