A Reduced-Order Strategy for Solving Inverse Bayesian Shape Identification Problems in Physiological Flows

Andrea Manzoni (), Toni Lassila (), Alfio Quarteroni () and Gianluigi Rozza ()
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Andrea Manzoni: École Polytechnique Fédérale de Lausanne, MATHICSE-CMCS Modelling and Scientific Computing
Toni Lassila: École Polytechnique Fédérale de Lausanne, MATHICSE-CMCS Modelling and Scientific Computing
Alfio Quarteroni: École Polytechnique Fédérale de Lausanne, MATHICSE-CMCS Modelling and Scientific Computing
Gianluigi Rozza: École Polytechnique Fédérale de Lausanne, MATHICSE-CMCS Modelling and Scientific Computing

A chapter in Modeling, Simulation and Optimization of Complex Processes - HPSC 2012, 2014, pp 145-155 from Springer

Abstract: Abstract A reduced-order strategy based on the reduced basis (RB) method is developed for the efficient numerical solution of statistical inverse problems governed by PDEs in domains of varying shape. Usual discretization techniques are infeasible in this context, due to the prohibitive cost entailed by the repeated evaluation of PDEs and related output quantities of interest. A suitable reduced-order model is introduced to reduce computational costs and complexity. Furthermore, when dealing with inverse identification of shape features, a reduced shape representation allows to tackle the geometrical complexity. We address both challenges by considering a reduced framework built upon the RB method for parametrized PDEs and a parametric radial basis functions approach for shape representation. We present some results dealing with blood flows modelled by Navier-Stokes equations.

Keywords: Inverse Problem; Radial Basis Function; Reduce Order Model; Forward Problem; Reduce Basis (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-09063-4_12

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DOI: 10.1007/978-3-319-09063-4_12

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