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 1249 products
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79/2020 - 11/25/2020
Regazzoni, F.; Salvador, M.; Africa, P.c.; Fedele, M.; Dede', L.; Quarteroni, A.
A cardiac electromechanics model coupled with a lumped parameters model for closed-loop blood circulation. Part I: model derivation | Abstract | | We propose an integrated electromechanical model of the human heart, with focus on the left ventricle, wherein biophysically detailed models describe the different physical phenomena concurring to the cardiac function. We model the subcellular generation of active force by means of an Artificial Neural Network, which is trained by a suitable Machine Learning algorithm from a collection of pre-computed numerical simulations of a biophysically detailed, yet computational demanding, high-fidelity model. To provide physiologically meaningful results, we couple the 3D electromechanical model with a closed-loop 0D (lumped parameters) model describing the blood circulation in the whole cardiovascular network. We prove that the 3D-0D coupling of the two models is compliant with the principle of energy conservation, which is achieved in virtue of energy-consistent boundary conditions that account for the interaction among cardiac chambers within the computational domain, pericardium and surrounding tissue. We thus derive an overall balance of mechanical energy for the 3D-0D model. This provides a quantitative insight into the energy utilization, dissipation and transfer among the different compartments of the cardiovascular network and during different stages of the heartbeat. In virtue of this new model and the energy balance, we propose a new validation tool of heart energy usage against relationships used in the daily clinical practice. Finally, we provide a mathematical formulation of an inverse problem aimed at recovering the reference configuration of one or multiple cardiac chambers, starting from the stressed configuration acquired from medical imaging. This is fundamental to correctly initialize electromechanical simulations. Numerical methods and simulations of the 3D-0D model will be detailed in Part II. |
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78/2020 - 11/25/2020
Regazzoni, F.; Salvador, M.; Africa, P.c.; Fedele, M.; Dede', L.; Quarteroni, A.
A cardiac electromechanics model coupled with a lumped parameters model for closed-loop blood circulation. Part II: numerical approximation | Abstract | | In the framework of accurate and efficient segregated schemes for 3D cardiac electromechanics and 0D cardiovascular models, we propose here a novel numerical approach to address the coupled 3D-0D problem introduced in Part I of this two-part series of papers. We combine implicit-explicit schemes to solve the different cardiac models in a multiphysics setting. We properly separate and manage the different time and space scales related to cardiac electromechanics and blood circulation. We employ a flexible and scalable intergrid transfer operator that enables to interpolate Finite Element functions among different meshes and, possibly, among different Finite Element spaces. We propose a numerical method to couple the 3D electromechanical model and the 0D circulation model in a numerically stable manner within a fully segregated fashion. No adaptations are required through the different phases of the heartbeat. We also propose a robust algorithm to reconstruct the stress-free reference configuration. Due to the computational cost associated with the numerical solution of this inverse problem, the reference configuration recovery algorithm comes along with a novel projection technique to precisely recover the unloaded geometry from a coarser representation of the computational domain. We show the convergence property of our numerical schemes by performing an accuracy study through grid refinement. To prove the biophysical accuracy of our computational model, we also address different scenarios of clinical interest in our numerical simulations by varying preload, afterload and contractility. Indeed, we simulate physiologically relevant behaviors and we reproduce meaningful results in the context of cardiac function. |
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77/2020 - 11/22/2020
Parolini, N.; Ardenghi, G.;Dede’, L.; Quarteroni, A.
A Mathematical Dashboard for the Analysis of Italian COVID-19 Epidemic Data | Abstract | | A data analysis of the COVID-19 epidemic is proposed on the basis of the dashboard publicly accessible at http://www.epimox.polimi.it that focuses on the characterization of the first and second epidemic outbreaks in Italy. The scope of this tool, which provides an immediate appreciation of the past epidemic development together with its current trends, is to foster a deeper interpretation of available data as well as to provide a hint on the near future evolution of the most relevant epidemic indicators. |
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75/2020 - 11/19/2020
F. Dassi; A. Fumagalli; D. Losapio; S. Scialò; A. Scotti; G. Vacca
The mixed virtual element method for grids with curved interfaces | Abstract | | In many applications the accurate representation of the computational domain is a key factor to obtain reliable and effective numerical solutions. Curved interfaces, which might be internal, related to physical data, or portions of the physical boundary, are often met in real applications. However, they are often approximated leading to a geometrical error that might become dominant and deteriorate the quality of the results. Underground problems often involve the motion of fluids where the fundamental governing equation is the Darcy law. High quality velocity fields are of paramount importance for the successful subsequent coupling with other physical phenomena such as transport. The virtual element method, as solution scheme, is known to be applicable in problems whose discretizations requires cells of general shape, and the mixed formulation is here preferred to obtain accurate velocity fields. To overcome the issues associated to the complex geometries and, at the same time, retaining the quality of the solutions, we present here the virtual element method to solve the Darcy problem, in mixed form, in presence of curved interfaces in two and three dimensions. The numerical scheme is presented in detail explaining the discrete setting with a focus on the treatment of curved interfaces. Examples, inspired from industrial applications, are presented showing the validity of the proposed approach. |
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76/2020 - 11/19/2020
Centofanti, F.; Lepore, A.; Menafoglio, A.; Palumbo, B.; Vantini, S.
Functional Regression Control Chart | Abstract | | The modern development of data acquisition technologies in many industrial processes is facilitating the collection of quality characteristics that are apt to be modelled as functions, which are usually referred to as pro les. At the same time, measurements of concurrent variables, which are related to the quality characteristic profiles, are often available in a functional form as well, and usually referred to as covariates. In order to adjust the monitoring of the quality characteristic pro les by the effect of this additional information, a new functional control chart is elaborated on the residuals obtained from a function-on-function linear regression of the quality characteristic profile on the functional covariates.
Furthermore, by means of a Monte Carlo simulation study, the performance of the proposed control chart are compared with those of other charts proposed in the literature. Eventually, a real-case study in the shipping industry is presented with the purpose of monitoring ship fuel consumption and thus, CO2 emissions from a Ro-Pax ship, with particular regard to detecting CO2 emission reduction after a specific energy efficiency initiative. |
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74/2020 - 11/09/2020
Formaggia, L; Fumagalli, A.; Scotti, A.
A multi-layer reactive transport model for fractured porous media | Abstract | | An accurate modeling of reactive flows in fractured porous media is a key ingredient to obtain reliable numerical simulations of several industrial and environmental applications. For some values of the physical parameters we can observe the formation of a narrow region or layer around the fractures where chemical reactions are focused. Here the transported solute may precipitate and form a salt, or vice-versa. This phenomenon has been observed and reported in real outcrops. By changing its physical properties this layer might substantially alter the global flow response of the system and thus the actual transport of solute: the problem is thus non-linear and fully coupled. The aim of this work is to propose a new mathematical model for reactive flow in fractured porous media, by approximating both the fracture and these surrounding layers via a reduced model. In particular, our main goal is to describe the layer thickness evolution with a new mathematical model, and compare it to a fully resolved equidimensional model for validation. As concerns numerical approximation we extend an operator splitting scheme in time to solve sequentially, at each time step, each physical process thus avoiding the need for a non-linear monolithic solver, which might be challenging due to the non-smoothness of the reaction rate. We consider bi- and tridimensional numerical test cases to asses the accuracy and benefit of the proposed model in realistic scenarios. |
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73/2020 - 11/07/2020
Bennati, L.; Vergara, C.; Domanin, M.; Trimarchi, S.; Malloggi, C.; Silani, V.; Parati, G.; Casana, R.
A computational fluid structure interaction study for carotids with different atherosclerotic plaques | Abstract | | Atherosclerosis is a systemic disease that leads to accumulation of deposits, known as atherosclerotic plaques, within the walls of the carotids. In particular, three types of plaque can be distinguished: soft, fibrous and calcific. Most of the computational studies who investigated the interplay between the plaque and the blood flow on patient-specific geometries, used non standard medical images to directly delineate and segment the plaque and its components. However these techniques are not so widely available in the clinical practice. In this context the aim of our work was twofold: i) to propose a new geometric tool that allowed to reconstruct a plausible plaque in the carotids from standard images and ii) to perform 3D FSI simulations where we compared some fluid-dynamic and structural quantities among 15 patients characterized by different typologies of plaque. Our results highlighted that both the morphology and the mechanical properties of different plaque components play a crucial role in determining the vulnerability of the plaque. |
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72/2020 - 11/07/2020
Belli E.; Vantini S.
Measure Inducing Classification and Regression Trees for Functional Data | Abstract | | We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing generalization error while retaining the interpretability of a tree. This is achieved by learning a weighted functional L2 space by means of constrained convex optimization, which is then used to extract multiple weighted integral features from the input functions, in order to determine the binary split for each internal node of the tree. The approach is designed to manage multiple functional inputs and/or outputs, by defining suitable splitting rules and loss functions that can depend on the specific problem and can also be combined with scalar and categorical data, as the tree is grown with the original greedy CART algorithm. We focus on the case of scalar-valued functional inputs defined on unidimensional domains and illustrate the effectiveness of our method in both classification and regression tasks, through a simulation study and four real world applications. |
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