MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1239 products
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09/2018 - 02/02/2018
Menafoglio, A.; Grasso, M.; Secchi, P.; Colosimo, B.M.
Profile Monitoring of Probability Density Functions via Simplicial Functional PCA with application to Image Data | Abstract | | The advance of sensor and information technologies is leading to data-rich industrial environments, where big amounts of data are potentially available. In this scenario, image data play a relevant role, as they can easily describe many phenomena of interest. This study focuses on images where several and similar features of interest are randomly distributed and characterized by no spatially correlated structure. Examples are pores in parts obtained via casting or additive manufacturing, voids in metal foams and light-weight components, grains in metallographic analysis, etc. The proposed approach consists of summarizing the random occurrences of the observed features via its (empirical) probability density function (PDF). In particular, a novel approach for PDF monitoring is proposed. It is based on simplicial functional principal component analysis (SFPCA), which is performed by applying an isometric isomorphism between the space of density functions, i.e., the Bayes space B^2, and the space of square integrable functions L^2. A simulation study shows the enhanced monitoring performances provided by the SFPCA-based profile monitoring against other competitors proposed in the literature. Eventually, a real case study dealing with the quality control of foamed materials production is discussed, to highlight a practical use of the proposed methodology.
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08/2018 - 01/28/2018
Bonaventura, L.; Casella, F.; Delpopolo, L.; Ranade, A.;
A self adjusting multirate algorithm based on the TR-BDF2 method | Abstract | | We propose a self adjusting multirate method based on the TR-BDF2 solver. The potential advantages of using TR-BDF2 as the key component of a
multirate framework are highlighted. A linear stability analysis of the resulting approach is presented and the stability features of the resulting algorithm are analysed. The analysis framework is completely general and allows to study along the same lines the stability of self adjusting multirate methods based on a generic one step solver. A number of numerical experiments demonstrate the efficiency and accuracy of the resulting approach also the time discretization of hyperbolic partial differential equations. |
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07/2018 - 01/23/2018
Ieva, F.; Bitonti, D.
Network Analysis of Comorbidity Patterns in Heart Failure Patients using Administrative Data | Abstract | | Background: Congestive Heart Failure (HF) is a widespread chronic disease characterized by a very high incidence in elder people. The high mortality and readmission rate of HF strongly depends on the complicated morbidity scenario often characterising it.
Methods: Data were retrieved from the healthcare administrative datawarehouse of Lombardy, the most populated regional district in Italy. Network analysis techniques and community detection algorithms are applied to comorbidities registered in hospital discharge papers of HF patients, in 7 cohorts between 2006 and 2012.
Results: The relevance network indexes applied to the 7 cohorts identified death, ipertension, arrythmia, renal and pulmonary diseases as the most relevant nodes related to HF, in terms of prevalence and closeness/strenght of the relationship. Moreover, 3 clusters of nodes have been identified in all the cohorts, i.e. those related to cancer, lung diseases and heart/circulation related problems.
Conclusions: Network analysis can be a useful tool in epidemiologic framework when relational data are the objective of the investigation, since it allows to visualize and make inference on patterns of association among nodes (here HF comorbidities) by means of both qualitative indexes and clustering techniques. |
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06/2018 - 01/23/2018
Antonietti, P.F.; Mazzieri, I.
High-order Discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes | Abstract | | We propose and analyze a Discontinuous Galerkin Finite Element Method for the approximate solution of wave propagation problems modeled by the elastodynamics equations on computational meshes made by polygonal or polyhedral elements. We analyze the well posedness of the resulting formulation, prove a-priori hp--version error estimates, and present a dispersion analysis, showing that polygonal meshes behaves as classical simplicial/quadrilateral grids in terms of dispersion properties. The theoretical estimates are then validated through two-dimensional numerical computations carried out on both benchmark as well as real test cases |
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05/2018 - 01/16/2018
Pagani, S.; Manzoni, A.; Quarteroni, A.
Numerical approximation of parametrized problems in cardiac electrophysiology by a local reduced basis method | Abstract | | The efficient solution of coupled PDEs/ODEs problems arising in cardiac electrophysiology
is of key importance whenever interested to study the electrical behavior of the tissue for several instances of relevant physical and/or geometrical parameters. This poses significant challenges to reduced order modeling (ROM) techniques - such as the reduced basis method - traditionally employed when dealing with the repeated solution of parameter dependent differential equations. Indeed, the nonlinear nature of the problem, the presence of moving fronts in the solution, and the high sensitivity of this latter to parameter variations, make the application of standard ROM techniques very problematic. In this paper we propose a local ROM built through a k-means clustering in the state space of the snapshots for both the solution and the nonlinear term. Several comparisons among alternative local ROMs on a benchmark test case show the effectivity of the proposed approach. Finally, the application to a parametrized problem set on an idealized left-ventricle geometry shows the capability of the proposed ROM to face complex problems. |
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04/2018 - 01/13/2018
Ekin, T.; Ieva, F.; Ruggeri, F.; Soyer, R.
Statistical Medical Fraud Assessment: Exposition to an Emerging Field | Abstract | | Health care expenditures constitute a significant portion of governmental budgets.
The percentage of fraud, waste and abuse within that spending has increased
over years. This paper introduces the emerging area of statistical medical fraud assessment, which becomes crucial to handle the increasing size and complexity of the medical programs. An overview of fraud types and detection is followed by the description of medical claims data. The utilization of sampling, overpayment estimation and data mining methods in medical fraud assessment are presented. Recent unsupervised methods are illustrated with real world data. Finally, the paper introduces potential future research areas such as integrated decision making approaches and
Bayesian methods, and concludes with an overall discussion. The main goal of this exposition is to increase awareness about this important area among a broader audience of statisticians. |
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03/2018 - 01/13/2018
Antonietti, P. F.; Houston, P.; Pennesi, G.
Fast numerical integration on polytopic meshes with applications to discontinuous Galerkin finite element methods | Abstract | | In this paper we present efficient quadrature rules for the numerical approximation of integrals of polynomial functions over general polygonal/polyhedral elements that do not require an explicit construction of a sub-tessellation into triangular/tetrahedral elements. The method is based on successive application of Stokes' theorem; thereby, the underlying integral may be evaluated using only the values of the integrand at the vertices of the polytopic domain, and hence leads to an exact cubature rule whose quadrature points are the vertices of the polytope. We demonstrate the capabilities of the proposed approach by efficiently computing the stiffness and mass matrices arising from $hp$-version symmetric interior penalty discontinuous Galerkin discretizations of second-order elliptic partial differential equations. |
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01/2018 - 01/03/2018
Berrone, S.; Bonito, A.; Stevenson, R.; Verani, M.
An optimal adaptive Fictitious Domain Method | Abstract | | We consider a Fictitious Domain formulation of an elliptic partial differential equation and approximate the resulting saddle-point system using an inexact preconditioned Uzawa iterative algorithm.
Each iteration entails the approximation of an elliptic problems performed using adaptive finite element methods. We prove that the overall method converges with the best possible rate and illustrate numerically our theoretical findings. |
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