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 1251 products
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38/2023 - 04/29/2023
Africa, P. C.; Fumagalli, I.; Bucelli, M.; Zingaro, A.; Fedele, M.; Dede', L.; Quarteroni, A.
lifex-cfd: an open-source computational fluid dynamics solver for cardiovascular applications | Abstract | | Computational fluid dynamics (CFD) is an important tool for the simulation of the cardiovascular function and
dysfunction. Due to the complexity of the anatomy, the transitional regime of blood flow in the heart, and the
strong mutual influence between the flow and the physical processes involved in the heart function, the development of accurate and efficient CFD solvers for cardiovascular flows is still a challenging task. In this paper we
present lifex-cfd: an open-source CFD solver for cardiovascular simulations based on the lifex finite element
library, written in modern C++ and exploiting distributed memory parallelism. We model blood flow in both
physiological and pathological conditions via the incompressible Navier-Stokes equations, accounting for moving
cardiac valves, moving domains, and transition-to-turbulence regimes. In this paper, we provide an overview of
the underlying mathematical formulation, numerical discretization, implementation details and instructions for
use of lifex-cfd. The code has been verified through rigorous convergence analyses, and we show its almost
ideal parallel speedup. We demonstrate the accuracy and reliability of the numerical methods implemented
through a series of idealized and patient-specific vascular and cardiac simulations, in different physiological flow
regimes. The lifex-cfd source code is available under the LGPLv3 license, to ensure its accessibility and
transparency to the scientific community, and to facilitate collaboration and further developments. |
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37/2023 - 04/29/2023
Regazzoni, F.; Pagani, S.; Salvador, M.; Dede’, L.; Quarteroni, A.
Latent Dynamics Networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes | Abstract | | Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to yield predictions through the numerical approximation of high-dimensional systems of differential equations, thus calling for large-scale parallel computing platforms and requiring large computational costs. Data-driven approaches, instead, enable the description of systems evolution in low-dimensional latent spaces, by leveraging dimensionality reduction and deep learning algorithms. We propose a novel architecture, named Latent Dynamics Network (LDNet), which is able to discover low-dimensional intrinsic dynamics of possibly non-Markovian dynamical systems, thus predicting the time evolution of space-dependent fields in response to external inputs. Unlike popular approaches, in which the latent representation of the solution manifold is learned by means of auto-encoders that map a high-dimensional discretization of the system state into itself, LDNets automatically discover a low-dimensional manifold while learning the latent dynamics, without ever operating in the high-dimensional space. Furthermore, LDNets are meshless algorithms that do not reconstruct the output on a predetermined grid of points, but rather at any point of the domain, thus enabling weight-sharing across query-points. These features make LDNets lightweight and easy-to-train, with excellent accuracy and generalization properties, even in time-extrapolation regimes. We validate our method on several test cases and we show that, for a challenging highly-nonlinear problem, LDNets outperform state-of-the-art methods in terms of accuracy (normalized error 5 times smaller), by employing a dramatically smaller number of trainable parameters (more than 10 times fewer). |
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35/2023 - 04/23/2023
Ferrari, L.; Manzi, G.; Micheletti, A.; Nicolussi, F.; Salini, S.
Pandemic Data Quality Modelling: A Bayesian Approach | Abstract | | When pandemics like COVID-19 spread around the world, the rapidly evolving situation compels officials and executives to take prompt decisions and adapt policies depending on the current state of the disease. In this context, it is crucial for policymakers to have always a firm grasp on what is the current state of the pandemic, and to envision how the number of infections and possible deaths is going to evolve over the next weeks. However, as in many other situations involving compulsory registration of sensitive data from multiple collectors, cases might be reported with errors, often with delays deferring an up-to-date view of the state of things. Errors in collecting new cases affect the overall mortality, resulting in excess deaths reported by official statistics only months later. In this paper, we provide tools for evaluating the quality of pandemic mortality data. We accomplish this through a Bayesian approach accounting for the excess mortality pandemics might bring with respect to the normal level of mortality in the population. |
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34/2023 - 04/23/2023
Caldana, M.; Antonietti, P. F.; Dede', L.
A Deep Learning algorithm to accelerate Algebraic Multigrid methods in Finite Element solvers of 3D elliptic PDEs | Abstract | | Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most severe limitation of AMG methods is the dependence on parameters that require to be fine-tuned. In particular, the strong threshold parameter is the most relevant since it stands at the basis of the construction of successively coarser grids needed by the AMG methods. We introduce a novel Deep Learning algorithm that minimizes the computational cost of the AMG method when used as a finite element solver. We show that our algorithm requires minimal changes to any existing code. The proposed Artificial Neural Network (ANN) tunes the value of the strong threshold parameter by interpreting the sparse matrix of the linear system as a black-and-white image and exploiting a pooling operator to transform it into a small multi-channel image. We experimentally prove that the pooling successfully reduces the computational cost of processing a large sparse matrix and preserves the features needed for the regression task at hand. We train the proposed algorithm on a large dataset containing problems with a highly heterogeneous diffusion coefficient defined in different three-dimensional geometries and discretized with unstructured grids and linear elasticity problems with a highly heterogeneous Young's modulus. When tested on problems with coefficients or geometries not present in the training dataset, our approach reduces the computational time by up to 30%. |
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32/2023 - 04/15/2023
Gambarini, M.; Ciaramella, G.; Miglio, E.; Vanzan, T.
Robust optimization of control parameters for WEC arrays using stochastic methods | Abstract | | This work presents a new computational optimization framework for the robust control of parks of Wave Energy Converters (WEC) in irregular waves. The power of WEC parks is maximized with respect to the individual control damping and stiffness coefficients of each device. The results are robust with respect to the incident wave direction, which is treated as a random variable. Hydrodynamic properties are computed using the linear potential model, and the dynamics of the system is computed in the frequency domain. A slamming constraint is enforced to ensure that the results are physically realistic. We show that the stochastic optimization problem is well posed. Two optimization approaches for dealing with stochasticity are then considered: stochastic approximation and sample average approximation. The outcomes of the above mentioned methods in terms of accuracy and computational time are presented.
The results of the optimization for complex and realistic array configurations of possible engineering interest are then discussed. Results of extensive numerical experiments demonstrate the efficiency of the proposed computational framework.
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31/2023 - 04/12/2023
Orlando, G.
Assessing ChatGPT for coding finite element methods | Abstract | | ChatGPT is a language model trained by OpenAI to follow an instruction in a prompt and to provide a detailed response. We investigate the capabilities of ChatGPT to generate codes which implement the finite element method. The Finite element method (FEM) is a popular technique for the numerical solution of partial differential equations (PDEs). More specifically, we analyze the codes generated for two open source platforms: deal.II, a C++ software library, and FEniCS, for which we focus on its Python interface. We consider as benchmark problems the Poisson equation and a linear advection problem. The outcomes suggest that ChatGPT can be employed as initial building block to write finite element codes, but certain limitations and failures, which require further improvement of the machine learning model and a human supervision, are still present. |
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30/2023 - 04/03/2023
Antonietti, P. F.; Bonizzoni, F.; Verani, M.
A DG-VEM method for the dissipative wave equation | Abstract | | A novel space-time discretization for the (linear) scalar-valued dissipative wave equation is presented. It is a structured approach, namely, the discretization space is obtained tensorizing the Virtual Element (VE) discretization in space with the Discontinuous Galerkin (DG) method in time. As such, it combines the advantages of both the VE and the DG methods. The proposed scheme is implicit and it is proved to be unconditionally stable and accurate in space and time. |
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29/2023 - 03/24/2023
Carbonaro, D.; Mezzadri, F.; Ferro, N.; De Nisco, G.; Audenino, A.L.; Gallo, D.; Chiastra, C.; Morbiducci, U.; Perotto, S.
Design of innovative self-expandable femoral stents using inverse homogenization topology optimization | Abstract | | In this study, we propose a novel computational framework for designing innovative self-expandable femoral stents. First, a two-dimensional stent unit cell is designed by inverse homogenization topology optimization. In particular, the unit cell is optimized in terms of contact area with the target of matching prescribed mechanical properties. The topology optimization is enriched by an anisotropic mesh adaptation strategy, enabling a time- and cost-effective procedure that promotes original layouts. Successively, the optimized stent unit cell is periodically repeated on a hollow cylindrical surface to construct the corresponding three-dimensional device. Finally, structural mechanics and computational fluid dynamics simulations are carried out to verify the performance of the newly-designed stent.
The proposed workflow is being tested through the design of five proof-of-concept stents. These devices are compared through specific performance evaluations, which include the assessments of the minimum requirement for usability, namely the ability to be crimped into a catheter, and the quantification of the radial force, the foreshortening, the structural integrity and the induced blood flow disturbances. |
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