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 1242 products
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22/2020 - 04/16/2020
Zeni, G.; Fontana, M.; Vantini, F.
Conformal Prediction: a Unified Review of Theory and New Challenges | Abstract | | In this work we provide a review of basic ideas and novel developments about Conformal Prediction - an innovative distribution-free, non-parametric forecasting method, based on minimal assumptions - that is able to yield in a very straightforward way predictions sets that are valid in a statistical sense also in in the finite sample case.
The in-depth discussion provided in the paper covers the theoretical underpinnings of Conformal Prediction, and then proceeds to list the more advanced developments and adaptations of the original idea.
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21/2020 - 04/16/2020
Benacchio, T.; Bonaventura, L.; Altenbernd, M.; Cantwell, C.D.; Düben, P.D.; Gillard, M.; Giraud, L.; Göddeke, D.; Raffin, E.; Teranishi, K.; Wedi, N.
Resilience and fault-tolerance in high-performance computing for numerical weather and climate prediction | Abstract | | Numerical weather and climate prediction rates as one of the scientific applications whose accuracy improvements greatly depend on the growth of the available computing power. As the number of cores in top computing facilities pushes into the millions, increasing average frequency of hardware and software failures forces users to review their algorithms and systems in order to protect simulations from breakdown. This report surveys approaches for fault-tolerance in numerical algorithms and system resilience in parallel simulations from the perspective of numerical weather and climate prediction systems. A selection of existing strategies is analyzed, featuring interpolation-restart and compressed checkpointing for the numerics, in-memory checkpointing, ULFM- and backup-based methods for the systems. Numerical examples showcase the performance of the techniques in addressing faults, with particular emphasis on iterative solvers for linear systems, a staple of atmospheric fluid flow solvers. The potential impact of these strategies is discussed in relation to current development of numerical weather prediction algorithms and systems towards the exascale. Trade-offs between performance, efficiency and effectiveness of resiliency strategies are analyzed and some recommendations outlined for future developments. |
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20/2020 - 04/16/2020
Almi, S.; Belz, S.; Micheletti, S.; Perotto, S.
A DIMENSION-REDUCTION MODEL FOR BRITTLE FRACTURES ON THIN SHELLS WITH MESH ADAPTIVITY | Abstract | | In this paper we derive a new two-dimensional brittle fracture
model for thin shells via dimension reduction, where the admissible displacements
are only normal to the shell surface. The main steps include to endow
the shell with a small thickness, to express the three-dimensional energy in
terms of the variational model of brittle fracture in linear elasticity, and to
study the ????-limit of the functional as the thickness tends to zero.
The numerical discretization is tackled by first approximating the fracture
through a phase field, following an Ambrosio-Tortorelli like approach, and then
resorting to an alternating minimization procedure, where the irreversibility
of the crack propagation is rigorously imposed via an inequality constraint.
The minimization is enriched with an anisotropic mesh adaptation driven by
an a posteriori error estimator, which allows us to sharply track the whole
crack path by optimizing the shape, the size, and the orientation of the mesh
elements.
Finally, the overall algorithm is successfully assessed on two Riemannian
settings and proves not to bias the crack propagation. |
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19/2020 - 03/12/2020
Stella, S.; Vergara, C.; Maines, M.; Catanzariti, D.; Africa, P.; Demattè, C.; Centonze, M.; Nobile, F.; Del Greco, M.; Quarteroni, A.
Integration of maps of activation times in computational cardiac electrophysiology | Abstract | | In this work we used the monodomain equation
in combination with the Bueno-Orovio ionic model for the prediction of the activation
times in cardiac electro-physiology. We considered four patients who suffered from Left
Bundle Branch Block (LBBB) and patient-specific maps of activation times obtained by inserting in the ventricles
electrodes located on catheters. We used activation maps acquired at the septum as input data for the model
and maps at the epicardial veins for the validation of the monodomain model
in the context of a normal excitation. In particular, a first set (half) of the latter
were used to estimate the conductivities of the patient and a second set (the remaining half) to compute
the errors of the numerical simulations. We found an excellent agreement between measures and numerical
results. Our validated
computational tool could be used to accurately predict activation times at the epicardial veins,
allowing to shorten the mapping procedure and reduce the exposition to radiations.
This could be of great interest for clinical applications, for example in the Cardiac Resynchronization
Therapy (CRT) where such mapping is commonly used to determine the best point of stimulus. |
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16/2020 - 03/05/2020
Paolucci, R.; Mazzieri, I.; Piunno, G.; Smerzini, C.; Vanini, M.; Ozcebe, A.G.
Earthquake ground motion modelling of induced seismicity in the Groningen gas field | Abstract | | A key element in the seismic hazard and risk assessment due to induced earthquakes in the Groningen gas field is a
ground motion model (GMM). Although significant efforts have been devoted to the construction of an empirical
GMM, there is a growing interest in reducing its uncertainty through data-driven approaches. In the framework of
the KEM research program launched by the Ministry of Economic Affairs and Climate Policy of the Netherlands,
the authors explored the use of 3D physics-based numerical approaches to characterize earthquake ground motion in
the Groningen area and to shed light on the potential impact of the specific geologic conditions, characterized by
irregular geologic interfaces and thick layers of soft deposits at ground surface. Within the wider scope of this
research, this paper is focused on the construction and validation of a large-scale ( 20 km × 20 km), heterogeneous
3D seismic wave propagation model for the Groningen area, based on the significant bulk of available geological,
geophysical, geotechnical and seismological data.
Results of physics-based numerical simulations are validated against the ground motion recordings of the Jan 8,
2018, ML 3.4 Zeerijp earthquake – the third largest event to date in the area. Taking advantage of suitable models of
slip time functions at the seismic source and of the detailed geophysical model, the numerical simulations are found
to reproduce accurately the observed features of ground motions at short epicentral distance (Repi < 10 km), in a
broad frequency range, up to about 10 Hz. To achieve this level of accuracy, the total number of degrees-of-freedom
was up to about 1 billion, implying taking advantage of high performance computing facilities. A sensitivity analysis
is also addressed to discuss the impact of key modeling assumptions, specifically, the role of 3D underground
geological features (“tunnel valleys”), the stochastic variability of shallow seismic velocities and the amplitude and
frequency dependence of the quality factor. Amongst others, results point out crucial aspects in deriving GMMs for
induced seismicity in Groningen, such as the magnitude and distance dependence of site amplification functions
associated with 3D wave propagation features, as opposed to the standard assumption of vertically propagating
plane waves. |
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18/2020 - 03/05/2020
Fumagalli, A.; Scotti, A.; Formaggia, L.
Performances of the mixed virtual element method on complex grids for underground flow | Abstract | | The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults, while the latter are connected to the properties of the rock matrix which might vary abruptly in space. The development of approximation schemes has recently focused on the overcoming of such difficulties with the objective of obtaining numerical schemes with good approximation properties. In this work we carry out a numerical study on the performances of the Mixed Virtual Element Method (MVEM) for the solution of a single-phase flow model in fractured porous media. This method is able to handle grid cells of polytopal type and treat hybrid dimensional problems. It has been proven to be robust with respect to the variation of the permeability field and of the shape of the elements. Our numerical experiments focus on two test cases that cover several of the aforementioned critical aspects. |
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17/2020 - 03/05/2020
Cerroni, D.; Formaggia, L.; Scotti, A.
A control problem approach to Coulomb's friction | Abstract | | In this work we present a formulation of Coulomb's friction in a fractured elastic body as a PDE control problem where the observed quantity is the tangential stress across an internal interface, while the control parameter is the slip i.e. the displacement jump across the interface. The cost function aims at minimizing the norm of a non-linear and not everywhere differentiable
complementarity function, written in terms of the tangential stress and the slip. The interesting point of this method is that gives rise to an iterative procedure where at each iteration we solve a problem with given slip at the interface, without resorting to the use of Lagrange multipliers.
We carry out a formal derivation of the method, with some preliminary results, and a numerical experiment to verify the efficacy of the technique.
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15/2020 - 02/22/2020
Fumagalli, I.; Fedele, M.; Vergara, C.; Dede', L.; Ippolito, S.; Nicolò, F.; Antona, C.; Scrofani, R.; Quarteroni, A.
An Image-based Computational Hemodynamics Study of the Systolic Anterior Motion of the Mitral Valve | Abstract | | Systolic Anterior Motion (SAM) of the mitral valve -- often associated to Hypertrophic Obstructive Cardiomyopathy (HOCM) -- is a cardiac pathology in which, during systole, a functional subaortic stenosis is induced by the mitral leaflets partially obstructing the outflow tract of the left ventricle. Its assessment by diagnostic tests is often difficult, possibly underestimating its severity and thus increasing the risk of sudden cardiac death. In the present work, the effects of SAM on the ventricular blood flow are investigated by means of Computational Fluid Dynamics (CFD) simulations. A novel image processing pipeline is set up to integrate cine-MRI data in the numerical model. Patient-specific geometry and motion of the left ventricle are accounted for by an Arbitrary Lagrangian-Eulerian approach, and the reconstructed mitral valve is immersed in the computational domain by means of a resistive method. Clinically relevant flow and pressure indicators are assessed for different degrees of SAM severity, in order to separate the effects of SAM from those of HOCM. Our numerical results and study provide preliminary indications that help better evaluating pathological condition and the design of its surgical treatment. |
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