Browsing by Author "Rozza, Gianluigi"
Now showing 1 - 8 of 8
Results Per Page
Sort Options
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 Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes(Springer, AMOS Advanced Modelling and Simulation in Engineering Sciences, 2016) Salmoiraghi, Filippo; Ballarin, Francesco; Heltai, Luca; Rozza, Gianluigi; MathematicsIn this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model.Item Reduced basis approaches in time-dependent noncoercive settings for modelling the movement of nuclear reactor control rods(SISSA, 2015) Sartori, Alberto; Cammi, Antonio; Luzzi, Lelio; Rozza, Gianluigi; MathematicsIn this work, two approaches, based on the certified Reduced Basis method, have been developed for simulating the movement of nuclear reactor control rods, in time-dependent non-coercive settings featuring a 3D geometrical framework. In particular, in a first approach, a piece-wise affine transformation based on subdomains division has been implemented for modelling the movement of one control rod. In the second approach, a “staircase” strategy has been adopted for simulating the movement of all the three rods featured by the nuclear reactor chosen as case study. The neutron kinetics has been modelled according to the so-called multi-group neutron diffusion, which, in the present case, is a set of ten coupled parametrized parabolic equations (two energy groups for the neutron flux, and eight for the precursors). Both the reduced order models, developed according to the two approaches, provided a very good accuracy compared with high-fidelity results, assumed as “truth” solutions. At the same time, the computational speed-up in the Online phase, with respect to the fine “truth” finite element discretization, achievable by both the proposed approaches is at least of three orders of magnitude, allowing a real-time simulation of the rod movement and control.Item Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system(2015) Martini, Immanuel; Rozza, Gianluigi; Haasdonk, Bernard; mathematicsThe coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technolo gies. We present a reduced basis method for such coupled problems. The re duced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decompo sition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accu racy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimationItem 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; MathematicsItem Reduction Strategies for Shape Dependent Inverse Problems in Haemodynamics(SISSA, 2013) Lassila, Toni; Manzoni, Andrea; Rozza, Gianluigi; Mathematics