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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44/2017 - 08/01/2017
Martino, A.; Ghiglietti, A.; Ieva, F.; Paganoni, A.M.
A k-means procedure based on a Mahalanobis type distance for clustering multivariate functional data | Abstract | | This paper proposes a clustering procedure for samples of multivariate functions in (L^2(I))^J, with J>=1. This method is based on a k-means algorithm in which the distance between the curves is measured with a metrics that generalizes the Mahalanobis distance in Hilbert spaces,
considering the correlation and the variability along all the components of the functional data. The proposed procedure has been studied in simulation and compared with the k-means based on other distances typically adopted for clustering multivariate functional data. In these simulations, it is shown that the k-means algorithm with the generalized Mahalanobis distance provides the best clustering performances, both in terms of mean and standard deviation of the number of misclassified curves. Finally, the proposed method has been applied to two real cases studies, concerning ECG signals and growth curves, where the results obtained in simulation are confirmed and strengthened. |
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43/2017 - 08/01/2017
Bottle, A.; Ventura, C.M.; Dharmarajan, K.; Aylin, P.; Ieva, F.; Paganoni, A.M.
Regional variation in hospitalisation and mortality in heart failure: comparison of England and Lombardy using multistate modelling | Abstract | | Heart failure (HF) is a common, serious chronic condition with high morbidity, hospitalisation and mortality. The healthcare systems of England and the northern Italian region of Lombardy share important similarities and have comprehensive hospital administrative databases linked to
the death register. We used them to compare admission for HF and mortality for patients between 2006 and 2012 (n = 37,185 for Lombardy, 234,719 for England) with multistate models. Despite close similarities in age, sex and common comorbidities of the two sets of patients, in Lombardy, HF admissions were longer and more frequent per patient than in England, but short- and medium-term mortality was much lower. English patients had more very short stays, but their very elderly also had longer stays than their Lombardy counterparts. Using a three-state model, the predicted total time spent in hospital showed large differences between the countries: women in England spent an average of 24 days if aged 65 at first admission and 19 days if aged 85; in Lombardy these figures were 68 and 27 days respectively. Eight-state models suggested disease progression that appeared similar in each country. Differences by region within England were
modest, with London patients spending more time in hospital and having lower mortality than the rest of England. Whilst clinical practice differences plausibly explain these patterns, we cannot confidently disentangle the impact of alternatives such as coding, casemix, and the availability and use of nonhospital settings. We need to better understand the links between rehospitalisation frequency and mortality. |
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42/2017 - 07/27/2017
Gower, AL, Shearer, T, Ciarletta P
A new restriction for initially stressed elastic solids | Abstract | | We introduce a fundamental restriction on the strain energy function
and stress tensor for initially stressed elastic solids. The restriction
applies to strain energy functions W that are explicit functions of the
elastic deformation gradient F and initial stress tau , i.e. W := W(F; tau ).
The restriction is a consequence of energy conservation and ensures
that the predicted stress and strain energy do not depend upon an
arbitrary choice of reference configuration. We call this restriction
initial stress reference independence (ISRI). It transpires that most
strain energy functions found in the literature do not satisfy ISRI,
and may therefore lead to unphysical behaviour, which we illustrate
via a simple example. To remedy this shortcoming we derive three
strain energy functions that do satisfy the restriction. We also show
that using initial strain (often from a virtual configuration) to model
initial stress leads to strain energy functions that automatically satisfy
ISRI. Finally, we reach the following important result: ISRI reduces
the number of unknowns in the linear stress tensor for initially stressed
solids. This new way of reducing the linear stress may open new
pathways for the non-destructive determination of initial stresses via
ultrasonic experiments, among others. |
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41/2017 - 07/26/2017
Beretta, E.; Micheletti, S.; Perotto, S.; Santacesaria, M.
Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT | Abstract | | In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to use a distributed shape derivative of a suitable cost functional with respect to movements of the partition. Numerical simulations showing the robustness and accuracy of the method are presented for simulated test cases in two dimensions. |
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39/2017 - 07/13/2017
Ciarletta, P.
Matched asymptotic solution for crease nucleation in soft solids | Abstract | | A soft solid subjected to a finite compression can suddenly develop sharp self-contacting folds at its free surface, also known as creases. This singular instability is of utmost importance in material science, since it can be positively used to fabricate objects with adaptive surface morphology at different length-scales. Creasing is physically different from other instabilities in elastic materials, like buckling or wrinkling. Indeed, it is a scale-free, fully nonlinear phenomenon displaying similar features as phase-transformations, but lacking an energy barrier. Despite recent experimental and numerical advances, the theoretical understanding of crease nucleation remains elusive, yet crucial for driving further progress in engineering applications.
This work solves the quest for a theoretical explanation of crease nucleation. Creasing is proved to occur after a global bifurcation allowing the co-existence of an affine outer deformation and an inner discontinuous solution with localised self-contact at the free surface. The most fundamental insight is the theoretical prediction of the crease nucleation threshold, in excellent agreement with experiments and numerical simulations. A matched asymptotic approximation is also provided within the intermediate region between the two co-existing inner and outer solutions. The near-field incremental problem becomes singular because of the surface self-contact, acting like the point-wise disturbance in the Oseen's correction for the 2D Stokes problem of the flow past a circle. Using Green's functions in the half-space, analytic expressions of the matching solution and the relative range of validity are derived, perfectly fitting the results of numerical simulations without any adjusting parameter. |
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38/2017 - 07/13/2017
Bonaventura, L.; Fernandez Nieto, E.; Garres Diaz, J.; Narbona Reina, G.;
Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization | Abstract | | We propose an extension of the discretization approaches for mul-
tilayer shallow water models, aimed at making them more
exible and
ecient for realistic applications to coastal
ows. A novel discretiza-
tion approach is proposed, in which the number of vertical layers and
their distribution are allowed to change in di erent regions of the com-
putational domain. Furthermore, semi-implicit schemes are employed
for the time discretization, leading to a signi cant eciency improve-
ment for subcritical regimes. We show that, in the typical regimes in
which the application of multilayer shallow water models is justi ed,
the resulting discretization does not introduce any major spurious fea-
ture and allows again to reduce substantially the computational cost
in areas with complex bathymetry. As an example of the potential of
the proposed technique, an application to a sediment transport prob-
lem is presented, showing a remarkable improvement with respect to
standard discretization approaches. |
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37/2017 - 07/13/2017
Formaggia, L.; Vergara, C.; Zonca, S.
Unfitted Extended Finite Elements for composite grids | Abstract | | We consider an Extended Finite Elements method to handle the case
of composite independent grids that lead to un tted meshes. We detail
the corresponding discrete formulation for the Poisson problem with dis-
continuous coecients. We also provide some technical details for the 3D
implementation. Finally, we provide some numerical examples with the aim
of showing the e ectiveness of the proposed formulation. |
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36/2017 - 07/09/2017
Koeppl, T.; Vidotto, E.; Wohlmuth, B.; Zunino, P.
Mathematical modelling, analysis and numerical approximation of second order elliptic problems with inclusions | Abstract | | Many biological and geological systems can be modelled as porous media with small inclusions. Vascularized tissue, roots embedded in soil or fractured rocks are examples of such systems. In these applicatons, tissue, soil or rocks are considered to be porous media, while blood vessels, roots or fractures form small inclusions. To model flow processes in thin inclusions, one-dimensional (1D) models of Darcy- or Poiseuille type have been used, whereas Darcy-equations of higher dimension have been considered for the flow processes within the porous matrix. A coupling between flow in the porous matrix and the inclusions can be achieved by setting suitable source terms for the corresponding models, where the source term of the higher-dimensional model is concentrated on the centre lines of the inclusions.
In this paper, we investigate an alternative coupling scheme. Here, the source term lives on the boundary of the inclusions. By doing so, we lift the dimension by one and thus increase the regularity of the solution. We show that this model can be derived from a full-dimensional model and the occurring modelling errors are estimated. Furthermore, we prove the well-posedness of the variational formulation and discuss the convergence behaviour of standard finite element methods with respect to this model. Our theoretical results are confirmed by numerical tests. Finally, we demonstrate how the new coupling concept can be used to simulate stationary flow through a capillary network embedded in a biological tissue. |
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