Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1249 prodotti
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11/2019 - 26/03/2019
Benacchio, T.; Klein, R.
A semi-implicit compressible model for atmospheric flows with seamless access to soundproof and hydrostatic dynamics | Abstract | | We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in conservation form while relying on Exner pressure for the pressure gradient term. It discretises the rotating compressible equations by evolving full variables rather than perturbations around a background state, and operates with time steps constrained by the advection speed only. Perturbation variables are only used as auxiliary quantities in the formulation of the elliptic problem. Borrowing ideas on forward-in-time differencing, the algorithm reframes the authors' previously proposed schemes into a sequence of implicit midpoint, advection, and implicit trapezoidal steps that allows for a time integration unconstrained by the internal gravity wave speed. Compared with existing approaches, results on a range of benchmarks of nonhydrostatic- and hydrostatic-scale dynamics are competitive. The test suite includes a new planetary-scale inertia-gravity wave test highlighting the properties of the scheme and its large time step capabilities. In the hydrostatic-scale cases the model is run in pseudo-incompressible and hydrostatic mode with simple switching within a uniform discretization framework. The differences with the compressible runs return expected relative magnitudes. By providing seamless access to soundproof and hydrostatic dynamics, the developments represent a necessary step towards an all-scale blended multimodel solver. |
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10/2019 - 26/03/2019
Abramowicz, K.; Pini, A.; Schelin, L.; Sjostedt de Luna, S.; Stamm, A.; Vantini, S.
Domain selection and family-wise error rate for functional data: a unified framework | Abstract | | Functional data are smooth, often continuous, random curves, which can be seen as an extreme case of multivariate data with infinite dimensionality. Just as component-wise inference for multivariate data naturally performs feature selection, subset-wise inference for functional data performs domain selection. In this paper, we present a unified null-hypothesis testing framework for domain selection on populations of functional data. In detail, $p$-values of hypothesis tests performed on point-wise evaluations of functional data are suitably adjusted for providing a control of the family-wise error rate (FWER) over a family of subsets of the domain. We show that several state-of-the-art domain selection methods fit within this framework and differ from each other by the choice of the family over which the control of the FWER is provided. In the existing literature, these families are always defined a priori. In this work, we also propose a novel approach, coined threshold-wise testing, in which the family of subsets is instead built in a data-driven fashion. The method seamlessly generalizes to multidimensional domains in contrast to methods based on a-priori defined families. We provide theoretical results with respect to exactness, consistency, and strong and weak control of FWER for the methods within the unified framework. |
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09/2019 - 26/03/2019
Antonietti, P.F.; Facciola', C.; Verani, M.
Unified analysis of Discontinuous Galerkin approximations of flows in fractured porous media on polygonal and polyhedral grids | Abstract | | We propose a unified formulation based on discontinuous Galerkin methods on polygonal/polyhedral grids for the simulation of flows in fractured porous media. We adopt a model for single-phase flows where the fracture is modeled as a (d-1)-dimensional interface in a d-dimensional bulk domain, and model the flow in the porous medium and in the fracture by means of the Darcy’s law. The two problems are then coupled through physically consistent conditions. We focus on the numerical approximation of the coupled bulk-fracture problem and present and analyze, in the unified setting of [Arnold, Brezzi, Cockburn, Marini. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal., 39(5):1749-1779, 2001/02], all the possible combinations of primal-primal, mixed-primal, primal-mixed and mixed-mixed formulations for the bulk and fracture problems, respectively. For all the possible combinations, we prove their well-posedness and derive a priori hp-version error estimates in a suitable (mesh-dependent) energy norm. Finally, several numerical experiments assess the theoretical error estimates and verify the practical performance of the proposed schemes. |
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08/2019 - 09/02/2019
Prouse, G.; Stella, S.; Vergara, C.; Engelberger, S.; Trunfio, R.; Canevascini, R.; Quarteroni, A.; Giovannacci, L.
Computational analysis of turbulent haemodynamics in radiocephalic arteriovenous fistulas with different anastomotic angles | Abstract | | ABSTRACT
Objective: Hemodynamics has been known to play a major role in the development of intimal hyperplasia (IH) leading to arteriovenous fistula failure. The goal of our study is to investigate the influence of different angles of side-to-end radiocephalic anastomosis upon the hemodynamic parameters that promote intimal dysfunction and therefore IH.
Methods: Realistic 3D meshes were reconstructed using ultrasound measurements from distal side-to-end radiocephalic fistulas. The velocity at the proximal and distal radial inflows and at specific locations along the anastomosis and cephalic vein was measured through single examiner duplex ultrasound. A computational parametric study, virtually changing the inner angle of anastomosis, was performed. For this purpose we used advanced computational models that include suitable tools to capture the pulsatile and turbulent nature of the blood flow found in arteriovenous fistulas. The results were analysed in terms of velocity fields, wall shear stress distribution and oscillatory shear index (OSI).
Results: Results show that the regions with high OSI, that are more prone to the development of hyperplasia, are greater and progressively shift toward the anastomosis area and the proximal vein segment with the decrease of the inner angle of anastomosis.
Conclusions: The results of this study show that inner anastomosis angles approaching 60°-70° seem to yield the best hemodynamic conditions for maturation and long term patency of distal radiocephalic fistulas. Inner angles greater than 90°, representing the smooth loop technique, did not show a clear hemodynamic advantage.
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07/2019 - 04/02/2019
Dal Santo, N.; Manzoni, A.
Hyper-reduced order models for parametrized unsteady Navier-Stokes equations on domains with variable shape | Abstract | | In this work we set up a new, general and computationally efficient way to tackle parametrized fluid flows modeled through unsteady Navier-Stokes equations defined on domains with variable shape, when relying on the reduced basis method. We easily describe a domain by flexible boundary parametrizations, and generate domain (and mesh) deformations by means of a solid extension, obtained by solving an harmonic extension or a linear elasticity problem. The proposed procedure is built over a two-stages reduction: (i) first, we construct a reduced basis approximation for the mesh motion problem, irrespectively of the fluid flow problem we focus on; (ii) then, we generate a reduced basis approximation of the unsteady Navier-Stokes problem, relying on finite element snapshots evaluated over a set of reduced deformed configuration, and approximating both velocity and pressure fields simultaneously. To deal with unavoidable nonaffine parametric dependencies arising in both the mesh motion and the state problem, we apply a matrix version of the discrete empirical interpolation method, allowing to treat geometrical deformations in a non-intrusive, efficient and purely algebraic way. The same strategy is used to per- form hyper-reduction of nonlinear terms. To assess the numerical performances of the proposed technique, we address the solution of parametrized fluid flows where the parameters describe both the shape of the domain, and relevant physical features. Complex flow patterns such as the ones appearing in a patient specific carotid bifurcation are accurately approximated, as well as derived quantities of potential clinical interest. |
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06/2019 - 04/02/2019
Pagani, S.; Manzoni, A.; Carlberg, K.
Statistical closure modeling for reduced-order models of stationary systems by the ROMES method | Abstract | | This work proposes a technique for constructing a statistical closure model for reduced-order models (ROMs) applied to stationary systems modeled as parameterized systems of algebraic equations. The proposed technique extends the reduced-order-model error surrogates (ROMES) method to closure modeling. The original ROMES method applied Gaussian-process regression to construct a statistical model that maps cheaply computable error indicators (e.g., residual norm, dual-weighted residuals) to a random variable for either (1) the norm of the state error or (2) the error in a scalar-valued quantity of interest. Rather than target these two types of errors, this work proposes to construct a statistical model for the state error itself; it achieves this by constructing statistical models for the generalized coordinates characterizing both the in-plane error (i.e., the error in the trial subspace) and a low-dimensional approximation of the out-of-plane error. The former can be considered a statistical closure model, as it quantifies the error in the ROM generalized coordinates. Because any quantity of interest can be computed as a functional of the state, the proposed approach enables any quantity-of-interest error to be statistically quantified a posteriori, as the state-error model can be propagated through the associated quantity-of-interest functional. Numerical experiments performed on both linear and nonlinear stationary systems illustrate the ability of the technique (1) to improve (expected) ROM prediction accuracy by an order of magnitude, (2) to statistically quantify the error in arbitrary quantities of interest, and (3) to realize a more cost-effective methodology for reducing the error than a ROM-only approach in the case of nonlinear systems. |
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05/2019 - 04/02/2019
Gasperoni, F.; Ieva, F.; Paganoni, A.M.; Jackson, C.; Sharples, L.
Evaluating the effect of healthcare providers on the clinical path of Heart Failure patients through a novel semi-Markov multi-state model | Abstract | | This paper introduces a novel exploratory statistical tool for investigating healthcare performance through clinical administrative databases. In particular, we propose a Semi-Markov multi state model in which the transition-specific hazards are estimated through a Cox model with a nonparametric discrete frailty term. The proposed model can be interpreted as probabilistic clustering technique. The main goal of this work is to investigate clusters (latent populations) of providers in each specific transition and then to investigate which are the most frequent and most extreme latent populations across all transitions.
Transitions are defined by rates of readmission to, discharge from providers and death in or outside a provider. Rates of transitions are adjusted for patients' characteristics. It is important to notice that this model does not require the selection of providers characteristics to perform the clustering. Finally, we show the impact of the proposed model through a real application on the administrative database related to Heart Failure patients hospitalised in Lombardia, a northern region in Italy. |
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04/2019 - 04/02/2019
Delpopolo Carciopolo, L.; Formaggia, L.; Scotti, A.; Hajibeygi, H.
Conservative multirate multiscale simulation of multiphase flow in heterogeneous porous media | Abstract | | Accurate and efficient simulation of multiphase flow in heterogeneous porous media motivates the development of space-time multiscale strategies for the coupled nonlinear flow (pressure) and saturation transport equations. The flow equation entails heterogeneous high-resolution (fine-scale) coefficients
and is global (elliptic or parabolic). The time-dependent saturation profile, on the other hand, has local sharp gradients (fronts) where the accuracy of the solution demands for tight time-step sizes. Therefore, accurate flow solvers need to resolve the spatial multiscale challenge, while advanced transport solvers need to also resolve the challenge related to time-step size. In this work, we develop the first integrated multirate multiscale method which implements a space-time conservative multiscale framework for sequentially coupled flow and transport equations. The method solves the pressure equation with a multiscale finite volume method at the spatial coarse scale, the
transport equation is solved by taking different time-step sizes at different locations of the domain. At each time step, a coarse time step is taken, and then based on an adaptive recursive strategy, the front region is sharpened through a local-fine-scale time stepping strategy. The accuracy and efficiency of the method is investigated for a wide range of heterogeneous test cases. The results demonstrate that the proposed method provides a promising strategy to minimise the accuracy-efficiency tradeoff by developing an integrated space-time multiscale simulation strategy. |
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