Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1237 prodotti
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70/2024 - 16/09/2024
Panzeri, L.; Fumagalli, A.; Longoni, L.; Papini, M.; Diego, A.
Sensitivity analysis with a 3D mixed-dimensional code for DC geoelectrical investigations of landfills: synthetic tests | Abstract | | Electrical resistivity tomography is a suitable technique for non-invasive monitoring of municipal solid waste landfills, but accurate sensitivity analysis is necessary to evaluate the effectiveness and reliability of geoelectrical investigations and to properly design data acquisition. Commonly, a thin high-resistivity membrane in placed underneath the waste to prevent leachate leakage. In the construction of a numerical framework for sensitivity computation, taking into account the actual dimensions of the electrodes and, in particular, of the membrane, can lead to extremely high computational costs. In this work, we present a novel approach for numerically computing sensitivity effectively by adopting a mixed-dimensional framework, where the membrane is approximated as a 2D object and the electrodes as 1D objects. The code is first validated against analytical expressions for simple 4-electrode arrays and a homogeneous medium. It is then tested in simplified landfill models, where a 2D box-shaped liner separates the landfill body from the surrounding media, and 48 electrodes are used. The results show that electrodes arranged linearly along both sides of the perimeter edges of the box-shaped liner are promising for detecting liner damage, with sensitivity increasing by 2-3 orders of magnitude, even for damage as small as one-sixth of the electrode spacing in diameter. Good results are also obtained when simulating an electrical connection between the landfill and the surrounding media that is not due to liner damage. The next steps involve evaluating the minimum number of configurations needed to achieve suitable sensitivity with a manageable field effort and validating the modeling results with downscaled laboratory tests. |
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64/2024 - 13/09/2024
Cavazzutti, M.; Arnone, E.; Ferraccioli, F.; Galimberti, C.; Finos, L.; Sangalli, L.M.
Sign-Flip inference for spatial regression with differential regularization | Abstract | | We address the problem of performing inference on the linear and nonlinear terms of a semiparametric
spatial regression model with differential regularization. For the linear term, we propose a new resampling procedure, based on (partial) sign-flipping of an appropriate transformation of the residuals of the model. The proposed resampling scheme can mitigate the bias effect, induced by the differential regularization. We prove that the proposed test is asymptotically exact. Moreover, we show by simulation studies that it enjoys very good control of Type-I error also in small sample scenarios, differently from parametric alternatives. Furthermore, we show that the proposed test has higher power with respect to recently proposed nonparametric tests on the linear term of semiparametric regression models with differential regularization. Concerning the nonlinear term, we develop three different inference approaches: a parametric test, and two nonparametric alternatives. The nonparametric tests are based on a sign-flip approach. One of these tests is proved to be asymptotically exact, while the other is proved to be exact also for finite samples. Simulation
studies highlight the very good control of Type-I error of the nonparametric approaches, while retaining high power. |
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65/2024 - 13/09/2024
Possenti, L.; Vitullo, P.; Cicchetti, A.; Zunino, P.; Rancati, T.
Modeling Hypoxia Induced Radiation Resistance and the Impact of Radiation Sources | Abstract | | Hypoxia contributes significantly to resistance in radiotherapy. Our research rigorously examines the influence of microvascular morphology on radiotherapy outcome, specifically focusing on how microvasculature shapes hypoxia within the microenvironment and affects resistance to a standard treatment regimen (30 X 2 Gy).
Our computational modeling extends to the effects of different radiation sources. For photons and protons, our analysis establishes a clear correlation between hypoxic volume distribution and treatment effectiveness, with vascular density and regularity playing a crucial role in treatment success.
On the contrary, carbon ions exhibit distinct effectiveness, even in areas of intense hypoxia and poor vascularization. This finding points to the potential of carbon-based hadron therapy in overcoming hypoxia-induced resistance to RT.
Considering that the spatial scale analyzed in this study is closely aligned with that of imaging data voxels, we also address the implications of these findings in a clinical context envisioning the possibility of detecting subvoxel hypoxia. |
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63/2024 - 12/09/2024
Vitullo, P.; Franco, N.R.; Zunino, P.
Deep learning enhanced cost-aware multi-fidelity uncertainty quantification of a computational model for radiotherapy | Abstract | | Forward uncertainty quantification (UQ) for partial differential equations is a many-query task that requires a significant number of model evaluations. The objective of this work is to mitigate the computational cost of UQ for a 3D-1D multiscale computational model of microcirculation. To this purpose, we present a deep learning enhanced multi-fidelity Monte Carlo (DL-MFMC) method that integrates the information of a multiscale full-order model (FOM) with that coming from a deep learning enhanced non-intrusive projection-based reduced order model (ROM). The latter is constructed by leveraging on proper orthogonal decomposition (POD) and mesh-informed neural networks (previously developed by the authors and co-workers), integrating diverse architectures that approximate POD coefficients while introducing fine-scale corrections for the microstructures. The DL-MFMC approach provides a robust estimator of specific quantities of interest and their associated uncertainties, with optimal management of computational resources. In particular, the computational budget is efficiently divided between training and sampling, ensuring a reliable estimation process suitably exploiting the ROM speed-up. Here, we apply the DL-MFMC technique to accelerate the estimation of biophysical quantities regarding oxygen transfer and radiotherapy outcomes. Compared to classical Monte Carlo methods, the proposed approach shows remarkable speed-ups and a substantial reduction of the overall computational cost. |
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62/2024 - 09/09/2024
Roknian, A.A.; Scotti, A.; Fumagalli, A.
Free convection in fractured porous media: a numerical study | Abstract | | The objective of this study is to better understand the influence of fractures on the possibility of free convection in porous media. To this aim, we introduce a mathematical model for density driven flow in the presence of fractures, and the corresponding numerical approximation. In addition to the direct numerical solution of the problem we propose and implement a novel method for the assessment of convective stability through the eigenvalue analysis of the linearized numerical problem. The new method is shown to be in agreement with existing literature cases both in simple and complex fracture configurations. With respect to direct simulation in time, the results of the eigenvalue method lack information about the strength of convection and the steady state solution, they however provide detailed (quantitative) information about the behavior of the solution near the initial equilibrium condition. Furthermore, not having to solve a time-dependent problem makes the method computationally very efficient. Finally, the question of how the porous matrix interacts with the fracture network to enable free convection is examined: the porous matrix is shown to be of key importance in enabling convection for complex fracture networks, making stability criteria based on the fracture network alone somewhat limited in applicability. |
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59/2024 - 07/09/2024
Carbonaro, D.; Ferro, N.; Mezzadri, F.; Gallo, D.; Audenino, A.; Perotto, S.; Morbiducci, U.; Chiastra, C.
Easy-to-use formulations based on the homogenization theory for vascular stent design and mechanical characterization | Abstract | | Vascular stents are scaffolding structures implanted in the vessels of patients with obstructive disease. Stents are typically designed as cylindrical lattice structures characterized by the periodic repetition of unit cells. Their design, including geometry and material characteristics, influences their mechanical performance and, consequently, the clinical outcomes. Computational Optimization frameworks have proven to be effective in assisting the design phase of vascular stents, facilitating the achievement of enhanced mechanical performances. However,
the reliance on time-consuming simulations and the challenge of automating the design process limit the number of design evaluations and reduce Optimization efficiency. In this context, a rapid and automated method for the mechanical characterization of vascular stents is presented, taking the stent geometry, conceived as the periodic repetition of a unit cell, and material as input and providing the mechanical response of the stent as output.
Vascular stents were assumed to be thin-walled hollow cylinders sharing the same macroscopic geometrical characteristics as the cylindrical lattice structure but composed of an anisotropic homogenized material. Homogenization theory was applied to average the microscopic inhomogeneities at the stent unit cell level into a homogenized material at the macroscale, enabling the calculation of the associated homogenized material tensor. Analytical formulations were derived to relate the stent mechanical behavior to the homogenized stiffness tensor, considering linear elastic theory for thin-walled hollow cylinders and three loading scenarios of relevance for vascular stents: radial crimping; axial traction; torsion. Validation was conducted by
comparing the derived analytical formulations with results obtained from finite element analyses on typical stent designs.
Homogenized stiffness tensors were computed for the unit cells of three stent designs, revealing insights into their mechanical performance, including whether they exhibit auxetic behavior. The derived analytical formulations were successfully validated with finite element analyses, yielding low relative differences in the computed values of foreshortening, radial, axial and torsional stiffnesses for all three stents.
The proposed method offers a rapid, fully automated procedure that facilitates the assessment of the mechanical behavior of vascular stents and is suitable for effective integration into computational optimization frameworks. |
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60/2024 - 07/09/2024
Temellini, E.; Ferro, N.; Stabile, G.; Delgado Avila, E.; Chacon Rebollo, T.; Perotto, S.
Space - time mesh adaptation for the VMS - Smagorinsky modeling of high Reynolds number flows | Abstract | | Traditional methods, such as Reynolds-Averaged Navier-Stokes (RANS) equations and Large Eddy Simulations (LES), provide consolidated tools for the numerical approximation of high Reynolds number flows in a wide range of applications - from green energy to industrial design. In general, RANS modeling is practical when the main interest is the time-averaged flow behavior. LES equations offer detailed insights into flow dynamics and a more accurate solution, but the high computational demand necessitates innovative strategies to reduce costs while maintaining precision. In this study, we enhance the Variational MultiScale (VMS)-Smagorinsky LES model by relying on an adaptive discretization strategy in both space and time, driven by a recovery-based a posteriori error analysis. We assess the effectiveness of the approach in capturing flow characteristics across a wide range of Reynolds numbers through benchmark tests. |
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61/2024 - 07/09/2024
Speroni, G.; Ferro, N.
A novel metric - based mesh adaptation algorithm for 3D periodic domains | Abstract | | We present a novel metric-based mesh adaptation algorithm, named 3DPAMA, to be employed for discretization of three-dimensional periodic domains. The proposed method - based on mathematically rigorous assumptions - utilizes established techniques for unconstrained mesh adaptation and resorts to localized manipulations on the external boundary of the mesh. In particular, the scheme comprises four steps: (i) a non-periodic initial mesh adaptation, (ii) the splitting of the obtained volumetric grid into interior and exterior tessellations, (iii) minimal local operations to yield a periodic external surface, and (iv) the assembly of the final adapted grids. To demonstrate the robustness, efficacy, and flexibility of the proposed methodology, 3DPAMA algorithm is employed in a continuous finite element setting to tackle test cases established in the literature as well as challenging scenarios that involve various periodic requirements, domain geometries, and metric fields. Finally, 3DPAMA is employed in a practical use case where mesh adaptation is tightly coupled with the solution of a time-dependent partial differential equation. |
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