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 1239 products
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41/2022 - 06/14/2022
Arnone, A.; Ferraccioli, F.; Pigolotti, C.; Sangalli, L.M.
A roughness penalty approach to estimate densities over two-dimensional manifolds | Abstract | | An innovative nonparametric method for density estimation over general two-dimensional Riemannian manifolds is proposed. The method follows a functional data analysis approach, combining maximum likelihood estimation with a roughness penalty that involves a differential operator appropriately defined over the manifold domain, thus controlling the smoothness of the estimate. The proposed method can accurately handle point pattern data over complicated curved domains. Moreover, it is able to capture complex multimodal signals, with strongly localized and highly skewed modes, with varying directions and intensity of anisotropy. The estimation procedure exploits a discretization in finite element bases, enabling great flexibility on the spatial domain. The method is tested through simulation studies, showing the strengths of the proposed approach. Finally, the density estimation method is illustrated with an application to the distribution of earthquakes in the world. |
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40/2022 - 06/14/2022
Fumagalli, A.; Patacchini, F. S.
Well-posedness and variational numerical scheme for an adaptive model in highly heterogeneous porous media | Abstract | | Mathematical modeling of fluid flow in a porous medium is usually described by a continuity equation and a chosen constitutive law. The latter, depending on the problem at hand, may be a nonlinear relation between the fluid's pressure gradient and velocity. The actual shape of this relation is normally chosen at the outset of the problem, even though, in practice, the fluid may experience velocities outside of its range of applicability. We propose here an adaptive model, so that the most appropriate law is locally selected depending on the computed velocity. From the analytical point of view, we show well-posedness of the problem when the law is monotone in velocity and show existence in one space dimension otherwise. From the computational point of view, we present a new approach based on regularizing via mollification the underlying dissipation, i.e., the power lost by the fluid to the porous medium through drag. The resulting regularization is shown to converge to the original problem using $Gamma$-convergence on the dissipation in the monotone case. This approach gives rise to a variational numerical scheme which applies to very general problems and which we validate on three test cases. |
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39/2022 - 06/02/2022
Ferro, N.; Perotto, S.; Gavazzoni, M.
A new fluid-based strategy for the connection of non-matching lattice materials | Abstract | | We present a new algorithm for the design of the connection region between different lattice materials. We solve a Stokes-type topology optimization problem on a narrow morphing region to smoothly connect two different unit cells. The proposed procedure turns out to be effective and provides a local re-design of the materials, leading to a very mild modification of the mechanical behaviour characterizing the original lattices. The robustness of the algorithm is assessed in terms of sensitivity of the final layout to different parameters. Both the cases of Cartesian and non-Cartesian morphing regions are successfully investigated. |
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38/2022 - 05/31/2022
Burzacchi, A.; Landrò, M.; Vantini, S.
Object-oriented Classification of Road Pavement Type in Greater Maputo from Satellite Images | Abstract | | The information about pavement surface type is rarely available in road network databases of developing countries although it represents a cornerstone of the design of efficient mobility systems. This research develops an automatic classification algorithm for road pavement which makes use of satellite images to recognize road segment as paved or unpaved. The proposed methodology is based on an object-oriented approach, so that each road is classified by looking at the distribution of its pixels in the RGB space. The proposed approach is proven to be accurate, inexpensive, and readily replicable in other cities. |
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37/2022 - 05/31/2022
Boon, W. M.; Fumagalli, A.
A Reduced Basis Method for Darcy flow systems that ensures local mass conservation by using exact discrete complexes | Abstract | | A solution technique is proposed for flows in porous media that guarantees local conservation of mass. We first compute a flux field to balance the mass source and then exploit exact co-chain complexes to generate a solenoidal correction. A reduced basis method based on proper orthogonal decomposition is employed to construct the correction and we show that mass balance is ensured regardless of the quality of the reduced basis approximation. The method is directly applicable to mixed finite and virtual element methods, among other structure-preserving discretization techniques, and we present the extension to Darcy flow in fractured porous media. |
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36/2022 - 05/17/2022
Vaccaro, F.; Brivio, S.; Perotto, S.; Mauri, A.G.; Spiga, S.
Physics-based Compact Modelling of the Analog Dynamics of HfOx Resistive Memories | Abstract | | Resistive random access memories (RRAMs) constitute a class of memristive devices particularly appealing for bio-inspired computing schemes. In particular, the possibility of achieving analog control of the electrical conductivity of RRAM devices can be exploited to mimic the behaviour of biological synapses in neuromorphic systems. With a view to neuromorphic computing applications, it turns out to be crucial to guarantee some features, among which a detailed device characterization, a mathematical modelling comprehensive of all the key features of the device both in quasi-static and dynamic conditions, a description of the variability due to the inherently stochasticity of the processes involved in the switching transitions. In this paper, starting from experimental data, we provide a modelling and simulation framework to reproduce the operative analog behaviour of HfO$_x$-based RRAM devices under train of programming pulses both in the analog and binary operation mode. To this aim, we have calibrated
the model by using a single set of parameters for the quasi-static current-voltage characteristics as well as switching kinetics and device dynamics. The physics-based compact model here settled captures the difference between the SET and the RESET processes in the I-V characteristics, as well as the device memory window both for strong and weak programming conditions. Moreover, the model reproduces the correct slopes of the highly non-linear kinetics curves over several orders of magnitudes in time, and the dynamic device response including the inherent device variability.
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35/2022 - 05/17/2022
Perotto, S.; Bellini, G.; Ballarin, F.; Calò, K.; Mazzi, V.; Morbiducci, U.
Isogeometric hierarchical model reduction for advection-diffusion process simulation in microchannels | Abstract | | Microfluidics proved to be a key technology in various applications, allowing to reproduce large-scale laboratory settings
at a more sustainable small-scale. The current effort is focused on enhancing the mixing process of different passive species at the micro-scale, where a laminar flow regime damps turbulence effects. Chaotic advection is often used to improve mixing effects also at very low Reynolds numbers. In particular, we focus on passive micromixers, where chaotic advection is mainly achieved by properly selecting the geometry of microchannels. In such a context, reduced order modeling can play a role, especially in the design of new geometries.
In this chapter, we verify the reliability and the computational benefits lead by a Hierarchical Model (HiMod) reduction when modeling the transport of a passive scalar in an S-shaped microchannel. Such a geometric configuration provides an ideal setting where to apply a HiMod approximation, which exploits the presence of a leading dynamics to commute the original three-dimensional model into a system of one-dimensional coupled problems.
It can be proved that HiMod reduction guarantees a very good accuracy when compared with a high-fidelity model, despite a drastic reduction in terms of number of unknowns. |
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34/2022 - 05/17/2022
Antonietti, P.F.; Vacca, G.; Verani, M.
Virtual Element method for the Navier-Stokes equation coupled with the heat equation | Abstract | | We consider the Virtual Element discretization of the Navier-Stokes equations coupled with the heat equation where the viscosity depends on the temperature. We present the Virtual Element discretization of the coupled problem, show its well-posedness, and prove optimal error estimates. Numerical experiments which confirm the theoretical error bounds are also presented. |
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