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 1249 products
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67/2022 - 10/19/2022
Alghamdi, M. M.; Boffi, D.; Bonizzoni, F.
A greedy MOR method for the tracking of eigensolutions to parametric elliptic PDEs | Abstract | | In this paper we introduce an algorithm based on a sparse grid adaptive refinement, for the approximation of the eigensolutions to parametric problems arising from elliptic partial differential equations. In particular, we are interested in detecting the crossing of the hypersurfaces describing the eigenvalues as a function of the parameters.
The a priori matching is followed by an a posteriori verification, driven by a suitably defined error indicator. At a given refinement level, a sparse grid approach is adopted for the construction of the grid of the next level, by using the marking given by the a
posteriori indicator.
Various numerical tests confirm the good performance of the scheme. |
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65/2022 - 10/05/2022
Dassi, F.; Fumagalli, A.; Mazzieri, I.; Vacca, G.
Mixed Virtual Element approximation of linear acoustic wave equation | Abstract | | We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time the semi-discrete problem we consider a classical theta-method scheme. We carry out the stability and convergence analysis in the energy norm for the semi-discrete problem showing optimal rate of convergence with respect to the mesh size. We further study the property of energy conservation for the fully-discrete system. Finally, we present some verification tests as well as engineering application of the method. |
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64/2022 - 10/05/2022
Massi, M.C., Dominoni, L., Ieva, F., Fiorito, G.
A Deep Survival EWAS approach estimating risk profile based on pre-diagnostic DNA methylation: an application to Breast Cancer time to diagnosis | Abstract | | Previous studies for cancer biomarker discovery based on pre-diagnostic blood DNA methylation profiles, either ignore the explicit modeling of the time to diagnosis (TTD) as in a survival analysis setting, or provide inconsistent results. This lack of consistency is likely due to the limitations of standard EWAS approaches, that model the effect of
DNAm at CpG sites on TTD independently. In this work, we argue that a global approach to estimate CpG sites effect profile is needed, and we claim that such approach should capture the complex (potentially non-linear) relationships interplaying between sites. To prove our concept, we develop a new Deep Learning-based approach assessing the relevance of individual CpG Islands (i.e., assigning a weight to each site) in determining TTD while modeling their combined effect in a survival analysis scenario.
The algorithm combines a tailored sampling procedure with DNAm sites agglomeration, deep non-linear survival modeling and SHapley Additive exPlanations (SHAP) values estimation to aid robustness of the derived effects profile. The proposed approach deal with the common complexities arising from epidemiological studies, such as small sample size, noise, and low signal-to-noise ratio of blood-derived DNAm. We apply our approach to a prospective case-control study on breast cancer nested in the EPIC Italy cohort and we perform weighted gene-set enrichment analyses to demonstrate the biological meaningfulness of the obtained results. We compared the results of Deep Survival EWAS with those of a traditional EWAS approach, demonstrating that our method performs better than the standard approach in identifying biologically relevant pathways. |
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63/2022 - 10/05/2022
Corti, M.; Antonietti, P.F.; Dede', L.; Quarteroni, A.
Numerical Modelling of the Brain Poromechanics by High-Order Discontinuous Galerkin Methods | Abstract | | We introduce and analyze a discontinuous Galerkin method for the numerical modelling of the equations of Multiple-Network Poroelastic Theory (MPET) in the dynamic formulation. The MPET model can comprehensively describe functional changes in the brain considering multiple scales of fluids. Concerning the spatial discretization, we employ a high-order discontinuous Galerkin method on polygonal and polyhedral grids and we derive stability and a priori error estimates. The temporal discretization is based on a coupling between a Newmark $beta$-method for the momentum equation and a $theta$-method for the pressure equations. After the presentation of some verification numerical tests, we perform a convergence analysis using an agglomerated mesh of a geometry of a brain slice. Finally we present a simulation in a three dimensional patient-specific brain reconstructed from magnetic resonance images. The model presented in this paper can be regarded as a preliminary attempt to model the perfusion in the brain. |
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66/2022 - 10/05/2022
Antonietti, P.F.; Liverani, L.; Pata, V.
Lack of superstable trajectories in linear viscoelasticity: A numerical approach | Abstract | | Given a positive operator $A$ on some Hilbert space,
and a nonnegative decreasing summable function $mu$,
we consider the abstract equation with memory
$$
ddot u(t)+ A u(t)- int_0^t mu(s)Au(t-s) ds=0
$$
modeling the dynamics of linearly viscoelastic solids.
The purpose of this work is to provide numerical evidence
of the fact that the energy
$$E(t)=Big(1-int_0^tmu(s)dsBig)|u(t)|^2_1+|dot u(t)|^2
+int_0^tmu(s)|u(t)-u(t-s)|^2_1ds,$$
of any nontrivial solution cannot decay faster than exponential,
no matter how fast might be the decay of the memory kernel $mu$.
This will be accomplished by simulating the integro-differential
equation for different choices of the memory kernel $mu$
and of the initial data. |
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62/2022 - 09/05/2022
Ciaramella, G.; Halpern, L.; Mechelli, L.
Convergence analysis and optimization of a Robin Schwarz waveform relaxation method for periodic parabolic optimal control problems | Abstract | | This paper is concerned with a novel convergence analysis of the
optimized Schwarz waveform relaxation method (OSWRM) for the
solution of optimal control problems governed by periodic parabolic
partial differential equations (PDEs). The new analysis is based on
Fourier-type technique applied to a semidiscrete in time form of the
optimality condition. This leads to a precise characterization of the
convergence factor of the method at the semidiscrete level. Using
this characterization, the optimal transmission condition parameter
is obtained at the semidiscrete level and its asymptotic behavior
as the time discretization converges to zero is analyzed in detail. |
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61/2022 - 09/05/2022
Gregorio, C.; Cappelletto, C.; Romani, S.; Stolfo, D.; Merlo, M.; Barbati, G.
Using marginal structural joint models to estimate the effect of a time-varying treatment on recurrent events and survival: An application on arrhythmogenic cardiomyopathy | Abstract | | In many clinical applications to evaluate the effect of a treatment, randomized control trials are difficult to carry out. On the other hand, clinical observational registries are often available and they contain longitudinal data regarding clinical parameters, drug therapies, and outcomes. In the past, much research has addressed causal methods to estimate treatment effects from observational studies. In the context of time-varying treatments, marginal structural models are often used. However, most analyses have focused on binary outcomes or time-to-the-first event analyses. The novelty of our approach is to combine the marginal structural methodology with the case where correlated recurrent events and survival are the outcomes of interest. Our work focuses on solving the nontrivial problem of defining the measures of effect, specifying the model for the time-dependent weights and the model to estimate the outcome, implementing them, and finally estimating the final treatment effects in this life-history setting. Our approach provides a strategy that allows obtaining treatment effect estimates both on the recurrent events and the survival with a clear causal and clinical interpretation. At the same time, the strategy we propose is based on flexible modeling choices such as the use of joint models to capture the correlation within events from the same subject and the specification of time-dependent treatment effects. The clinical problem which motivated our work is the evaluation of the treatment effect of beta-blockers in arrhythmogenic right ventricular cardiomyopathy (ARVC/D), and the dataset comes from the Trieste Heart Muscle Disease Registry. |
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60/2022 - 08/29/2022
Cortellessa, D.; Ferro, N.; Perotto, S.; Micheletti, S.
Enhancing level set-based topology optimization with anisotropic graded meshes | Abstract | | We propose a new algorithm for the design of topologically optimized lightweight structures, under a minimum compliance requirement. The new process enhances a standard level set formulation in terms of computational efficiency, thanks to the employment of a strategic computational mesh. We pursue a twofold goal, i.e., to deliver a final layout characterized by a smooth contour and reliable mechanical properties.
The smoothness of the optimized structure is ensured by the employment of an anisotropic adapted mesh, which sharply captures the material/void interface. A robust mechanical performance is guaranteed by a uniform tessellation of the internal part of the optimized configuration. A thorough numerical investigation corroborates the effectiveness of the proposed algorithm as a reliable and computationally affordable design tool, both in two- and three-dimensional contexts. |
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