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 1238 products
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37/2016 - 10/12/2016
Tugnoli, M; Abbà, A. ; Bonaventura, L.; Restelli, M.
A locally p-adaptive approach for Large Eddy Simulation of compressible flows in a DG framework | Abstract | | We investigate the possibility of reducing the computational burden of LES models by employing local polynomial degree adaptivity in the framework of a high order DG method. A novel degree adaptation technique especially featured to be effective for LES applications is proposed and its effectiveness is compared to that of other criteria already employed in the literature. The resulting locally adaptive approach allows to achieve significant reductions in computational cost of representative LES computations. |
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36/2016 - 10/12/2016
Mancini, L.; Paganoni, A.M.
Marked Point Process models for the admissions of heart failured patients | Abstract | | The aim of this paper is to model the stochastic process of hospitalizations with Marked Point Processes. We examine the longitudinal dataset including the admissions of heart failured patients to Lombardia hospitals on a follow-up period of six years since January 1st, 2006. We analyse four separate groups of patients, which we call HF groups, according to their diagnoses-codes contained in the SDO (dimission hospital discharge form) of their first hospitalizations.
The statistical model links the temporal trend of hospitalization (the ground process) with the length of stay (the mark) at each event. Instead of framing our application in the more theoretical context of the counting measures and processes, we make use of the conditional intensity function, a parametric approach which leads us to deal with Hawkes processes.
Hypotheses are made on the mark concerning its distribution as well as
its independence or dependence with the ground process. Independence is
better to model and give us significant results while dependence is harder
to be dealt with due to computational and modeling issues.
Finally, we provide a general framework for modeling longitudinal data with
a MPP as of methods for statistical inference and suggest a specific model
for our topic, validating it through a goodness of fit technique. |
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33/2016 - 10/06/2016
Antonietti, P. F.; Ferroni, A.; Mazzieri, I.; Quarteroni, A.
hp-version discontinuous Galerkin approximations of the elastodynamics equation | Abstract | | In this paper we extend the results contained in [Antonietti, Ayuso de Dios, Mazzieri, Quarteroni, J. Sci. Comput., 2016] and consider the problem of approximating the elastodynamics equation by means of hp-version discontinuous Galerkin methods. For the resulting semi-discretized schemes we derive stability bounds as well as hp error estimates in a suitable energy norm. Our theoretical estimates are verified through three dimensions numerical experiments. |
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35/2016 - 10/06/2016
Zonca, S.; Formaggia, L.; Vergara, C.
An unfitted formulation for the interaction of an incompressible fluid with a thick structure via an XFEM/DG approach | Abstract | | A numerical procedure that combines an Extended Finite Element (XFEM) formulation and a Discontinuous Galerkin technique is presented, with the final aim of providing an effective tool for the simulation of three-dimensional fluid-structure interaction problems where the structure undergoes large displacements. In this work we consider thick structures immersed in a fluid domain and we focus on the description of the numerical models and on the techniques used to deal with the issues related to the implementation of XFEM in this context. Numerical results are provided to show the effectiveness of the approach. |
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34/2016 - 10/06/2016
Menafoglio, A.; Secchi, P.
Statistical analysis of complex and spatially dependent data: a review of Object Oriented Spatial Statistics | Abstract | | We review recent advances in Object Oriented Spatial Statistics, a system of ideas, algorithms and methods that allows the analysis of high dimensional and complex data when their spatial dependence is an important issue. At the intersection of different disciplines -- including mathematics, statistics, computer science and engineering -- Object Oriented Spatial Statistics provides the right perspective to address key problems in varied contexts, from Earth and life sciences to urban planning. We illustrate a few paradigmatic methods applied to problems of prediction, classification and smoothing, giving emphasis to the key ideas Object Oriented Spatial Statistics relies upon. |
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32/2016 - 09/30/2016
Tarabelloni, N.; Schenone, E.; Collin, A.; Ieva, F.; Paganoni, A.M.; Gerbeau, J.-F.
Statistical Assessment and Calibration of Numerical ECG Models | Abstract | | Objective: Because of the inter-subject variability of ECGs in a healthy
population, it is not straightforward to assess the quality of synthetic ECGs
produced by deterministic mathematical models. We propose a statistical method
to address this question.
Methods: We use a dataset of 1588 healthy, real ECGs and we introduce a way to
calibrate the deterministic model so that its output fits the dataset. Our
approach is based on the concepts of spatial quantiles and spatial depths. These
notions are convenient to manipulate functional data since they provide a
non-parametric way to measure the discrepancy of the model output with a
distribution of data.
Results: The method is successfully applied to two very different models: a
phenomenological model based on ordinary differential equations, and a complex
biophysical model based on partial differential equations set on a
three-dimensional geometry of the heart and the torso. We show in particular
that the proposed calibration strategy allows us to improve the quality of the
ECG obtained with the biophysical model.
Significance: The proposed methodology is to our knowledge the first attempt to
assess the quality of synthetic ECGs with quantitative statistical arguments.
More generally it can be applied to other situations where a deterministic model
produces a functional output that has to be compared with a population of
measurements containing inter-subject variability. |
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31/2016 - 09/09/2016
Antonietti, P.F.; Merlet, B.; Morgan, P.; Verani, M.
Convergence to equilibrium for a second-order time semi-discretization of the Cahn-Hilliard equation | Abstract | | We consider a second-order two-step time semi-discretization of the Cahn-Hilliard equation with an analytic nonlinearity. The time-step is chosen small enough so that the pseudo-energy associated with the discretization is non-increasing at every time iteration. We prove that the sequence generated by the scheme converges to a steady state as time tends to infinity. We also obtain convergence rates in the energy norm. The proof is based on the Lojasiewicz-Simon inequality. |
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30/2016 - 09/09/2016
Abramowicz, K.; Häger, C.; Pini, A.; Schelin, L.; Sjöstedt de Luna, S.; Vantini, S.
Nonparametric inference for functional-on-scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament | Abstract | | Motivated by the analysis of the dependence of knee movement patterns during functional tasks on subject-speci c covariates, we introduce a distribution-free procedure for testing a functional-on-scalar linear model with fixed e ects. The procedure does not only test the global hypothesis on all the domain, but also selects the intervals where statistically signi ficant e ects are detected. We prove that the proposed tests are provided with an asymptotic control of the interval-wise error rate, i.e., the
probability of falsely rejecting any interval of true null hypotheses. The procedure is applied to one-leg hop data from a study on anterior cruciate ligament injury. We compare knee kinematics of three groups of individuals (two injured groups with di erent treatments, and one group of healthy controls), taking individual-speci c covariates into account. |
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