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

In: Modeling, Simulation and Optimization of Complex Processes - HPSC 2012

Author

Listed:
  • Andrea Manzoni

    (École Polytechnique Fédérale de Lausanne, MATHICSE-CMCS Modelling and Scientific Computing
    Now at SISSA, MathLab, International school for Advanced Studies)

  • 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
    Politecnico di Milano, Dipartimento di Matematica, MOX Modeling and Scientific Computing)

  • Gianluigi Rozza

    (École Polytechnique Fédérale de Lausanne, MATHICSE-CMCS Modelling and Scientific Computing
    Now at SISSA, MathLab, International school for Advanced Studies)

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.

Suggested Citation

  • Andrea Manzoni & Toni Lassila & Alfio Quarteroni & Gianluigi Rozza, 2014. "A Reduced-Order Strategy for Solving Inverse Bayesian Shape Identification Problems in Physiological Flows," Springer Books, in: Hans Georg Bock & Xuan Phu Hoang & Rolf Rannacher & Johannes P. Schlöder (ed.), Modeling, Simulation and Optimization of Complex Processes - HPSC 2012, edition 127, pages 145-155, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-09063-4_12
    DOI: 10.1007/978-3-319-09063-4_12
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