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 1279 products
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110/2024 - 12/27/2024
Pederzoli, V.; Corti, M.; Riccobelli, D.; Antonietti, P.F.
A coupled mathematical and numerical model for protein spreading and tissue atrophy, applied to Alzheimer's disease | Abstract | | The aim of this paper is to introduce, analyse and test in practice a new mathematical model describing the interplay between biological tissue atrophy driven by pathogen diffusion, with applications to neurodegenerative disorders. This study introduces a novel mathematical and computational model comprising a Fisher-Kolmogorov equation for species diffusion coupled with an elasticity equation governing mass loss. These equations intertwine through a logistic law dictating the reduction of the medium's mass. One potential application of this model lies in understanding the onset and development of Alzheimer's disease. Here, the equations can describe the propagation of misfolded tau-proteins and the ensuing brain atrophy characteristic of the disease. To address numerically the inherited complexities, we propose a Polygonal Discontinuous Galerkin method on polygonal/polyhedral grids for spatial discretization, while time integration relies on the theta-method. We present the mathematical model, delving into its characteristics and propose discretization applied. Furthermore, convergence results are presented to validate the model, accompanied by simulations illustrating the application scenario of the onset of Alzheimer's disease. |
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107/2024 - 12/19/2024
Chen, J.; Ballini, E.; Micheletti, S.
Active Flow Control for Bluff Body under High Reynolds Number Turbulent Flow Conditions Using Deep Reinforcement Learning | Abstract | | This study employs Deep Reinforcement Learning (DRL) for active flow
control in a turbulent flow field of high Reynolds numbers at Re = 274000. That is, an agent is trained to obtain a control strategy that can reduce the drag of a cylinder while also minimizing the oscillations of the lift. Probes are placed only around the surface of the cylinder, and a Proximal Policy Optimization (PPO) agent controls nine zero-net mass flux jets on the downstream side of the cylinder. The trained PPO agent effectively reduces drag by 29% and decreases lift oscillations by 18% of amplitude, with the control effect demonstrating good repeatability. Control tests of this agent within the Reynolds number range of Re = 260000 to 288000 show the agent’s control strategy possesses a certain degree of robustness, with very similar drag reduction effects under different Reynolds numbers. Analysis using power spectral energy reveals that the agent learns specific flow frequencies in the flow field and effectively suppressesù low-frequency, large-scale structures. Graphically visualizing the policy, combined with pressure, vorticity, and turbulent kinetic energy contours, reveals the mechanism by which jets achieve drag reduction by influencing reattachment vortices. This study successfully implements robust active flow control in realistically significant high Reynolds number turbulent flows, minimizing time costs (using two-dimensional geometrical models and turbulence models) and maximally considering the feasibility of future experimental implementation. |
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106/2024 - 12/18/2024
Brunati, S.; Bucelli, M.; Piersanti, R.; Dede', L.; Vergara, C.
Coupled Eikonal problems to model cardiac reentries in Purkinje network and myocardium | Abstract | | We propose a novel partitioned scheme based on Eikonal equations to model the coupled propagation of the electrical signal in the His-Purkinje system and in the myocardium for cardiac electrophysiology. This scheme allows, for the first time in Eikonal-based modeling, to capture all possible signal reentries between the Purkinje network and the cardiac muscle that may occur under pathological conditions. As part of the proposed scheme, we introduce a new pseudo-time method for the Eikonal-diffusion problem in the myocardium, to correctly enforce electrical stimuli coming from the Purkinje network. We test our approach by performing numerical simulations of cardiac electrophysiology in a real biventricular geometry, under both pathological and therapeutic conditions, to demonstrate its flexibility, robustness, and accuracy. |
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105/2024 - 12/15/2024
Bartsch, J.; Barakat, A.A.; Buchwald, S.; Ciaramella, G.; Volkwein, S.; Weig, E.M.
Reconstructing the system coefficients for coupled harmonic oscillators | Abstract | | Physical models often contain unknown functions and relations. In order to gain more insights into the nature of physical processes, these unknown functions have to be identified or reconstructed. Mathematically, we can formulate this research question within the framework of inverse problems. In this work, we consider optimization techniques to solve the inverse problem using Tikhonov regularization and data from laboratory experiments. We propose an iterative strategy that eliminates the need for laboratory experiments. Our method is applied to identify the coupling and damping coefficients in a system of oscillators, ensuring an efficient and experiment-free approach. We present our results and compare them with those obtained from an alternative, purely experimental approach. By employing our proposed strategy, we demonstrate a significant reduction in the number of laboratory experiments required. |
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104/2024 - 12/07/2024
Cerrone, D.; Riccobelli, D.; Vitullo, P.; Ballarin, F.; Falco, J.; Acerbi, F.; Manzoni, A.; Zunino, P.; Ciarletta, P.
Patient-specific prediction of glioblastoma growth via reduced order modeling and neural networks | Abstract | | Glioblastoma (GBL) is one of the deadliest brain cancers in adults. The GBL cells invade the physical structures within the brain extracellular environment with patient-specific features. In this work, we propose a proof-of-concept for mathematical framework of precision oncology enabling rapid parameter estimation from neuroimaging data in clinical settings.
The proposed diffuse interface model of GBL growth is informed by neuroimaging data, periodically collected in a clinical study from diagnosis to surgery and adjuvant treatment. We build a robust and efficient computational pipeline to aid clinical decision-making based on integrating model reduction techniques and neural networks. Patient specificity is captured through the segmentation of the magnetic resonance imaging into a computational replica of the patient brain, mimicking the brain microstructure by incorporating also the diffusion tensor imaging data.
The full order model (FOM) is first discretized using the finite element method and later approximated by a reduced order model (ROM) adopting proper orthogonal decomposition (POD). Trained by clinical data, we finally use neural networks to map the parameter space of GBL evolution over time and to predict the patient-specific model parameters from the observed clinical evolution of the tumor mass. |
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103/2024 - 12/03/2024
Fois, M.; Gatti, F.; de Falco, C.; Formaggia, L.
A comparative analysis of mesh-based and particle-based numerical methods for landslide run-out simulations | Abstract | | Landslides are among the most dangerous natural disasters, with their unpredictability and potential for catastrophic human and economic losses exacerbated by climate change. Continuous monitoring and precise modeling of landslide-prone areas are crucial for effective risk management and mitigation. This study explores two distinct numerical simulation approaches: the mesh-based finite element model and the particle-based model. Both methods are analyzed for their ability to simulate landslide dynamics, focusing on their respective advantages in handling complex terrain, material interactions, and large deformations. A modified version of the second-order Taylor-Galerkin scheme and the depth-averaged Material Point Method are employed to model gravity-driven free surface flows, based on depth-integrated incompressible Navier-Stokes equations. The methods are rigorously tested against benchmarks and applied to a real-world scenario to assess their performance, strengths, and limitations. The results offer insights into selecting appropriate simulation techniques for landslide analysis, depending on specific modeling requirements and computational resources. |
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101/2024 - 11/29/2024
Bonetti, S.; Corti, M.
Unified discontinuous Galerkin analysis of a thermo/poro-viscoelasticity model | Abstract | | We present and analyze a discontinuous Galerkin method for the numerical modeling of a Kelvin-Voigt thermo/poro-viscoelastic problem. We present the derivation of the model, and we develop a stability analysis in the continuous setting that holds both for the full inertial and quasi-static problems and that is robust with respect to most of the physical parameters of the problem. For spatial discretization, we propose an arbitrary-order weighted symmetric interior penalty scheme that supports general polytopal grids and is robust with respect to strong heterogeneities in the model coefficients. For the semi-discrete problem, we prove the extension of the stability result demonstrated in the continuous setting. A wide set of numerical simulations is presented to assess the convergence and robustness properties of the proposed method. Moreover, we test the scheme with literature and physically sound test cases for proof-of-concept applications in the geophysical context. |
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102/2024 - 11/29/2024
Bucelli, M.
The lifex library version 2.0 | Abstract | | This article presents updates to lifex [Africa, SoftwareX (2022)], a C++ library for high-performance finite element simulations of multiphysics, multiscale and multidomain problems. In this release, we introduce an additional intergrid transfer method for non-matching multiphysics coupling on the same domain, significantly optimize nearest-neighbor point searches and interface coupling utilities, extend the support for 2D and mixed-dimensional problems, and provide improved facilities for input/output and simulation serialization and restart. These advancements also propagate to the previously released modules of lifex specifically designed for cardiac modeling and simulation, namely lifex-fiber [Africa et al., BMC Bioinformatics (2023)], lifex-ep [Africa et al., BMC Bioinformatics (2023)] and lifex-cfd [Africa et al., Computer Physics Communications (2024)]. The changes introduced in this release aim at consolidating lifex's position as a valuable and versatile tool for the simulation of multiphysics systems. |
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