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Hierarchical Model Reduction Methods for Incompressible Fluids: Basics, Direct & Inverse Problems, Applications.
Prof. Alessandro Veneziani, Emory University, Atlanta and School of Advanced Studies IUSS Pavia
Sala conferenze IMATI, Pavia - Martedì 7 Marzo 2017 h.15:00
Abstract. Reduction of computational costs is becoming mandatory as scienti c computing progressively becomes an important decision-making tool in engineering and practical daily activities. We mention in particular computational hemodynamics that has been incorporated in medical research and clinical practice and it is becoming an important part of Clinical Trials (CACT- Computer Aided Clinical Trials) and Surgical Planning (SP). In this respect, a possible way for reducing computational costs is to take advantage of the speci c features of the problem at hand - as opposed to general purpose strategies. Speci cally, we can devise methods for incompressible fluids in pipe-like domains. Hierarchical Model-Reduction (HiMod) is an approach where the solution is properly split into mainstream and transverse components. The former is solved with nite elements] or isogeometric analysis, to be versatile in following the centerline of the pipe; the latter is solved with spectral methods, to be able of capturing the signi cant features of the dynamics with relatively few (and adaptively) degrees of freedom. We will present the basic features of this method at both the theoretical and practical level (selection of spectral basis, interplay with IGA, accuracy, etc.) and some preliminary results from cardiovascular applications that point out the excellent e ectiveness of the approach. Both the solution of direct and inverse problems (data assimilation) possibly coupled with Proper Orthogonal Decomposition techniques, will be illustrated.
This work is supported by the US National Science Foundation, DMS 1419060 in collaboration with M. Aletti, L.A. Mansilla Alvarez, P.J. Blanco, S. Guzzetti, S. Perotto, A.Reali, P. Rusconi, M. Lupo Pasini.
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