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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09/2022 - 02/22/2022
Corti, M.; Zingaro, A.; Dede', L.; Quarteroni, A.
Impact of Atrial Fibrillation on Left Atrium Haemodynamics: A Computational Fluid Dynamics Study | Abstract | | We analyze left atrium haemodynamics, highlighting differences among healthy individuals and patients affected by atrial fibrillation. The computational study is based on patient-specific geometries of the left atria to simulate blood flow dynamics. We devise a novel procedure aimed at recovering the boundary conditions for the 3D haemodynamics simulations, particularly useful in absence of specific ones provided by clinical measurements. With this aim, we introduce a parametric definition of the atria displacement, and we employ a closed-loop lumped parameter model of the whole cardiocirculatory system conveniently tuned on the basis of the patient characteristics. We evaluate a number of fluid dynamics indicators for the atrial haemodynamics, validating our numerical results in terms of several clinical measurements; we investigate the impact of geometrical and clinical features on the risk of thrombosis. To analyse the correlation of thrombus formation with atrial fibrillation, coherently with the medical evidence, we propose a novel indicator, which we call age stasis and that arises from the combination of Eulerian and Lagrangian quantities. This indicator identifies regions where the slow flow cannot rinse the chamber properly, accumulating stale blood particles and creating optimal conditions for clot formation.
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08/2022 - 02/02/2022
Gobat, G.; Opreni, A.; Fresca, S.; Manzoni, A.; Frangi, A.
Reduced order modeling of nonlinear microstructures through Proper Orthogonal Decomposition | Abstract | | We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of nonlinearity, associated to the large displacements of the devices, leads to polynomial terms up to cubic order that are reduced through exact projection onto a low dimensional subspace spanned by the Proper Orthogonal Modes (POMs). On the contrary, electrostatic nonlinearities are modeled resorting to precomputed manifolds in terms of the amplitudes of the electrically active POMs. We extensively test the reliability of the assumed linear trial space in challenging applications focusing on resonators, micromirrors and arches also displaying internal resonances. We discuss several options to generate the matrix of snapshots using both classical time marching schemes and more advanced Harmonic Balance (HB) approaches. Furthermore, we propose a comparison between the periodic orbits computed with POD and the invariant manifold approximated with Direct Normal Form approaches, further stressing the reliability of the technique and its remarkable predictive capabilities, e.g., in terms of estimation of the frequency response function of selected output quantities of interest |
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07/2022 - 02/02/2022
Sinigaglia, C.; Quadrelli, D.E.; Manzoni, A.; Braghin, F.
Fast active thermal cloaking through PDE-constrained optimization and reduced-order modeling | Abstract | | In this paper we show how to efficiently achieve thermal cloaking from a computational standpoint in several virtual scenarios by controlling a distribution of active heat sources. We frame this problem in the setting of PDE-constrained optimization, where the reference field is the solution of the time-dependent heat equation in the absence of the object to cloak. The optimal control problem then aims at actuating the space-time control field so that the thermal field outside the obstacle is indistinguishable from the reference field. In particular, we consider multiple scenarios where material’s thermal diffusivity, source intensity and obstacle’s temperature are allowed to vary within a user-defined range. To tackle the thermal cloaking problem in a rapid and reliable way, we rely on a parametrized reduced order model built through the reduced basis method, thus entailing huge computational speedups compared to high-fidelity, full-order model exploiting the finite element method while dealing both with complex target shapes and disconnected control domains. |
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06/2022 - 02/02/2022
Pozzi, G.; Grammatica, B.; Chaabane, L.; Catucci, M.; Mondino, A.; Zunino, P.; Ciarletta, P.
T cell therapy against cancer: a predictive diffuse-interface mathematical model informed by pre-clinical studies | Abstract | | T cell therapy has become a new therapeutic opportunity against solid cancers. Predicting T cell behaviour and efficacy would help therapy optimization and clinical implementation. In this work, we model responsiveness of mouse prostate adenocarcinoma to T cell-based therapies. The mathematical model is based on a Cahn-Hilliard diffuse interface description of the tumour, coupled with Keller-Segel type equations describing immune components dynamics. The model is fed by pre-clinical magnetic resonance imaging data describing anatomical features of prostate adenocarcinoma developed in the context of the Transgenic Adenocarcinoma of the Mouse Prostate model. We perform computational simulations based on the finite element method to describe tumor growth dynamics in relation to local T cells concentrations. We report that when we include in the model the possibility to activate tumor-associated vessels and by that increase the number of T cells within the tumor mass, the model predicts higher therapeutic effects (tumor regression) shortly after therapy administration. The simulated results are found in agreement with reported experimental data. Thus, this diffuse-interface mathematical model well predicts T cell behavior in vivo and represents a proof-of-concept for the role such predictive strategies may play in optimization of immunotherapy against cancer. |
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05/2022 - 01/14/2022
Aspri, A; Beretta, E.; Cavaterra, C.; Rocca, E.; Verani, M.
Identification of cavities and inclusions in linear elasticity with a phase-field approach | Abstract | | In this paper we deal with the inverse problem of the shape reconstruction of cavities and inclusions embedded in a linear elastic isotropic medium from boundary displacement's measurements. For this goal, we consider a constrained minimization problem involving a boundary quadratic misfit functional with a regularization term that penalizes the perimeter of the cavity or inclusion to be identified.
Then using a phase field approach we derive a robust algorithm for the reconstruction of elastic inclusions and of cavities modelled as inclusions with a very small elasticity tensor. |
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04/2022 - 01/11/2022
Africa, P.C.; Piersanti, R.; Fedele, M.; Dede', L.; Quarteroni, A.
lifex - heart module: a high-performance simulator for the cardiac function | Abstract | | Modeling the whole cardiac function involves several complex multi-
physics and multi-scale phenomena that are highly computationally
demanding, which makes calling for simpler yet accurate, high-performance computational tools still a paramount challenge to be addressed. Despite all the efforts made by several research groups worldwide, no software has progressed as a standard reference tool for whole-heart fully-coupled cardiac simulations in the scientific community yet.
In this work we present the first publicly released package of the
heart module of lifex, a high-performance solver for multi-physics
and multi-scale problems, aimed at cardiac applications.
The goal of lifex is twofold. On the one side, it aims at making
in silico experiments easily reproducible and accessible to the wider
public, targeting also users with a background in medicine or bioengineering, thanks to an extensive documentation and user guide.
On the other hand, being conceived as an academic research library,
lifex can be exploited by scientific computing experts to explore new
modeling and numerical methodologies within a robust development
framework.
lifex has been developed with a modular structure and will be
released bundled in different modules/packages. This initial release
includes a generator for myocardial fibers based on Laplace-Dirichlet-
Rule-Based-Methods (LDRBMs). This report comes with an extensive technical and mathematical documentation to welcome new users to
the core structure of a prototypical lifex application and to provide
them with a possible approach to include the generated cardiac fibers
into more sophisticated computational pipelines. |
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03/2022 - 01/09/2022
Giacomini, M.; Perotto, S.
Anisotropic mesh adaptation for region-based segmentation accounting for image spatial information | Abstract | | A finite element-based image segmentation strategy enhanced by an anisotropic mesh adaptation procedure is presented. The methodology relies on a split Bregman algorithm for the minimisation of a region-based energy functional and on an anisotropic recovery-based error estimate to drive mesh adaptation. More precisely, a Bayesian energy functional is considered to account for image spatial information, ensuring that the methodology is able to identify inhomogeneous spatial patterns in complex images.
In addition, the anisotropic mesh adaptation guarantees a sharp detection of the interface between background and foreground of the image, with a reduced number of degrees of freedom.
The resulting split-adapt Bregman algorithm is tested on a set of real images showing the accuracy and robustness of the method, even in the presence of Gaussian, salt and pepper and speckle noise. |
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02/2022 - 01/09/2022
Antonietti, P.F.; Scacchi, S.; Vacca, G.; Verani, M.
$C^1$-VEM for some variants of the Cahn-Hilliard equation: a numerical exploration | Abstract | | We consider the $C^1$-Virtual Element Method (VEM) for the conforming numerical approximation of some variants of the Cahn-Hilliard equation on polygonal meshes. In particular, we focus on the discretization of the advective Cahn-Hilliard problem and the Cahn-Hilliard inpainting problem. We present the numerical approximation and several numerical results to assess the efficacy of the proposed methodology.
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