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 1268 products
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53/2021 - 08/03/2021
Ciaramella, G.; Mechelli, L.
On the effect of boundary conditions on the scalability of Schwarz methods | Abstract | | In contrast with classical Schwarz theory, recent results have shown that for special domain geometries,
one-level Schwarz methods can be scalable. This property has been proved for the Laplace equation and external
Dirichlet boundary conditions. Much less is known if mixed boundary conditions are considered.
This short manuscript focuses on the convergence and scalability analysis of one-level parallel Schwarz method
and optimized Schwarz method for several different external configurations of boundary conditions, i.e.,
mixed Dirichlet, Neumann and Robin conditions. |
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52/2021 - 08/03/2021
Ciaramella, G.; Mechelli, L.
An overlapping waveform-relaxation preconditioner for economic optimal control problems with state constraints | Abstract | | In this work, a class of parabolic economic optimal control problems is considered.
These problems are characterized by pointwise state constraints regularized by a parameter,
which transforms the pure state constraints in mixed control-state ones.
However, the convergence of classical (semismooth) Newton methods deteriorates
for decreasing values of the regularization parameter. To tackle this problem, a nonlinear
preconditioner is introduced. This is based on an overlapping optimized waveform-relaxation method
characterized by Robin transmission conditions. Numerical experiments show that appropriate
choices of the overlap and of the Robin parameter lead to a preconditioned Newton method with a robust convergence
against the state constraints regularization parameter. |
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51/2021 - 08/03/2021
Ciaramella, G.; Kwok, F.; Mueller, G.
Nonlinear optimized Schwarz preconditioner for elliptic optimal control problems | Abstract | | We introduce a domain decomposition-based nonlinear preconditioned iteration for solving nonlinear, nonsmooth elliptic optimal control problems, with a nonlinear reaction term, $L^1$ regularization and box constraints on the control function. The method is obtained by applying semismooth Newton to the fixed-point equation of the parallel optimized Schwarz iteration. As a proof of concept, numerical experiments are performed on two subdomains, as well as on a multi-subdomain test case. The results show that it is possible to obtain substantial improvements in robustness and efficiency with the
new method, relative to semismooth Newton applied directly to the full optimization problem, provided appropriate Robin parameters and a good continuation strategy are chosen. |
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50/2021 - 08/03/2021
Ciaramella, G.; Vanzan, T.
On the asymptotic optimality of spectral coarse spaces | Abstract | | This paper is concerned with the asymptotic optimality of
spectral coarse spaces for two-level iterative methods. Spectral coarse spaces, namely coarse spaces obtained as the span of the slowest modes of the used one-level smoother, are known to be very efficient and, in some cases, optimal.
However, the results of this paper show that spectral coarse spaces do not necessarily minimize the asymptotic contraction factor of a two-level iterative method.
Moreover, the presented numerical experiments show that there exist coarse spaces that are asymptotically more efficient and lead to preconditioned systems with improved conditioning
properties. |
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49/2021 - 07/21/2021
Rea, F.; Savaré, L; Franchi, M.; Corrao, G; Mancia, G
Adherence to Treatment by Initial Antihypertensive Mono and Combination Therapies | Abstract | | BACKGROUND
Aim of our study was to compare adherence to antihypertensive drug
therapy between newly treated patients in whom monotherapy or a
2-drug single-pill combination (SPC) was initially dispensed.
METHODS
The 63,448 residents of Lombardy Region (Italy), aged 40–80 years,
who were newly treated with antihypertensive drugs during 2016,
were identified and followed for 1 year after the first prescription. The
outcome of interest was adherence to drug therapy that was measured
according to the “proportion of days covered” (PDC) criterion, i.e.,
the ratio between the number of days in which the drug was available
and the days of follow-up. Patients who had a PDC >75% and
<25% were defined as highly and poorly adherent to drug therapy,
respectively. Log-binomial regression models were fitted to compare
the propensity to treatment adherence between the initial therapeutic
strategies, after adjusting for baseline demographic and clinical
covariates.
RESULTS
About 46% and 17% of patients showed high and poor adherence, respectively.
Compared with patients under initial monotherapy (85%),
those who were initially treated with a SPC (15%) had higher propensity
to be highly adherent and a lower propensity to be poorly adherent
to antihypertensive treatment (risk ratio: 1.18, 95% confidence interval
1.16–1.21; 0.42, 0.39–0.45, respectively). This was the case regardless the
sex, the age, the patient clinical status, and with almost any type of SPC.
CONCLUSIONS
In a real-life setting, patients who were initially prescribed a 2-drug
SPC exhibited more frequently a good adherence to antihypertensive
treatment than those starting with a single drug.
Author Laura Savarè is currently affiliated to MOX-Politecnico di Milano |
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48/2021 - 07/17/2021
Riccobelli, D.
Active elasticity drives the formation of periodic beading in damaged axons | Abstract | | In several pathological conditions, such as coronavirus infections, multiple sclerosis, Alzheimer's and Parkinson's diseases, the physiological shape of axons is altered and a periodic sequence of bulges appears. Experimental evidences suggest that such morphological changes are caused by the disruption of the microtubules composing the cytoskeleton of the axon. In this paper, we develop a mathematical model of damaged axons based on the theory of continuum mechanics and nonlinear elasticity. The axon is described as a cylinder composed of an inner passive part, called axoplasm, and an outer active cortex, composed mainly of F-actin and able to contract thanks to myosin-II motors. Through a linear stability analysis we show that, as the shear modulus of the axoplasm diminishes due to the disruption of the cytoskeleton, the active contraction of the cortex makes the cylindrical configuration unstable to axisymmetric perturbations, leading to a beading pattern. Finally, the non-linear evolution of the bifurcated branches is investigated through finite element simulations. |
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47/2021 - 07/17/2021
Orlando, G; Della Rocca, A; Barbante, P. F.; Bonaventura, L.; Parolini, N.
An efficient and accurate implicit DG solver for the incompressible Navier-Stokes equations | Abstract | | We propose an efficient, accurate and robust implicit solver for the incompressible Navier-Stokes equations, based on a DG spatial discretization and on the TR-BDF2 method for time discretization. The effectiveness of the method is demonstrated in a number of classical benchmarks, which highlight its superior efficiency with respect to other widely used implicit approaches. The parallel implementation of the proposed method in the framework of the deal.II software package allows for accurate and efficient adaptive simulations in complex geometries, which makes the proposed solver attractive for large scale industrial applications. |
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46/2021 - 07/02/2021
Diquigiovanni, J.; Fontana, M.; Vantini, F.
Conformal Prediction Bandsfor Multivariate Functional Data | Abstract | | Motivated by the pressing request of methods able to create prediction sets in ageneral regression framework for a multivariate functional response and pushed bynew methodological advancements in non-parametric prediction for functional data,we propose a set of conformal predictors that produce finite-sample either validor exact multivariate simultaneous prediction bands under the mild assumption ofexchangeable regression pairs. The fact that the prediction bands can be built aroundany regression estimator and that can be easily found in closed form yields a verywidely usable method, which is fairly straightforward to implement. In addition,we first introduce and then describe a specific conformal predictor that guaranteesan asymptotic result in terms of efficiency and inducing prediction bands able tomodulate their width based on the local behavior and magnitude of the functionaldata. The method is investigated and analyzed through a simulation study and areal-world application in the field of urban mobility. |
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