Speakers: Efthymios Karatzas, Aristotle University of Thessaloniki

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy, room 134.

Abstract:

We investigate and control PDE systems defined on random domains and discretized by an unfitted domain finite element method. Key ingredients of the study are to manage cases considering the usually computationally forbidden combination of poorly conditioned equation system matrices due to challenging geometries, possible optimal control searches with iterative methods, slow convergence to system solutions on deterministic and non-deterministic levels, and expensive remeshing due to geometrical changes. We overcome all these difficulties, utilising the advantages of proper preconditioners adapted to unfitted mesh methods, improved types of Monte Carlo methods, and mainly employing the embedded FEMs advantages combined with new efficient model order reduction techniques, based on a fixed background mesh computed once even if geometrical changes are taking place.