Browsing by Author "Quarteroni, Alfio"
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Item Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization(2015-09) Ballarin, Francesco; Faggiano, Elena; Ippolito, Sonia; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi; Scrofani, Roberto; MathematicsIn this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD–Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach.Item Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries(2015) Iapichino, Laura; Quarteroni, Alfio; Rozza, Gianluigi; ; MathematicsThe aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for. The continuity of the latter is assured by a classical domain decomposition approach. Test results on Poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed, or the set of boundary conditions used for defining locally the basis functions. The proposed approach simplifies the pre-computation of the reduced basis space by splitting the global problem into smaller local subproblems. Thanks to this feature, it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed.Item A Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics(2013) Lassila, Toni; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi; MathematicsItem A reduced-order strategy for solving inverse Bayesian identification problems in physiological flows(SISSA, 2013) Lassila, Toni; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi; Mathematics