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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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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28/2023 - 03/24/2023
Zingaro, A.; Vergara, C.; Dede', L.; Regazzoni, F.; Quarteroni, A.
A comprehensive mathematical model for myocardial perfusion | Abstract | | We present a novel mathematical model that simulates myocardial blood perfusion by embedding multiscale and multiphysics features. Our model incorporates cardiac electrophysiology, active and passive mechanics, hemodynamics, reduced valve modeling, and a multicompartment Darcy model of perfusion . We consider a fully coupled electromechanical model of the left heart that provides input for a fully coupled Navier-Stokes - Darcy Model for myocardial perfusion. The fluid dynamics problem is modeled in a left heart geometry that includes large epicardial coronaries, while the multicompartment Darcy model is set in a biventricular domain. Using a realistic and detailed cardiac geometry, our simulations demonstrate the accuracy of our model in describing cardiac perfusion, including myocardial blood flow maps. Additionally, we investigate the impact of a regurgitant aortic valve on myocardial perfusion, and our results indicate a reduction in myocardial perfusion due to blood flow taken away by the left ventricle during diastole. To the best of our knowledge, our work represents the first instance where electromechanics, hemodynamics, and perfusion are integrated into a single computational framework. |
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27/2023 - 03/22/2023
Beirao da Vega, L.; Canuto, C.; Nochetto, R.H.; Vacca, G.; Verani, M.
Adaptive VEM for variable data: convergence and optimality | Abstract | | We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization-free a posteriori error estimators recently derived in [8]. The crucial property, that also plays a central role in this paper, is that the stabilization term can be made arbitrarily small relative to the a posteriori error estimators upon increasing the stabilization parameter. Our AVEM concatenates two modules, GALERKIN and DATA. The former deals with piecewise constant data and is shown in [8] to be a contraction between consecutive iterates. The latter approximates general data by piecewise constants to a desired accuracy. AVEM is shown to be convergent and quasi-optimal, in terms of error decay versus degrees of freedom, for solutions and data belonging to appropriate approximation classes. Numerical experiments illustrate the interplay between these two modules and provide computational evidence of optimality |
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26/2023 - 03/18/2023
Artoni, A.; Antonietti, P.F.; Corradi, R.; Mazzieri, I.; Parolini, N.; Rocchi, D.; Schito P.; Semeraro, F.F.;
AeroSPEED: a high order acoustic solver for aeroacoustic applications | Abstract | | We propose AeroSPEED, a solver based on the Spectral Element Method (SEM) that solves the aeroacoustic Lighthill's wave equation. First, the fluid solution is computed employing a cell centered Finite Volume method. Then, AeroSPEED maps the sound source coming from the flow solution onto the acoustic grid, where finally the Lighthill's wave equation is solved.
An ad-hoc projection strategy is adopted to apply the flow source term in the acoustic solver.
A model problem with a manufactured solution and the Noise Box test case are used as benchmark for the acoustic problem. We studied the noise generated by the complex flow field around tandem cylinders as a relevant aeroacoustic application. AeroSPEED is an effective and accurate solver for both acoustics and aeroacoustic problems. |
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25/2023 - 03/16/2023
Bonetti, S.; Botti, M.; Mazzieri, I.; Antonietti, P.F.
Numerical modelling of wave propagation phenomena in thermo-poroelastic media via discontinuous Galerkin methods | Abstract | | We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids.
Stability analysis and hp-version error estimates in suitable energy norms are derived for the semi-discrete problem. The fully-discrete scheme is then obtained based on employing an implicit Newmark-$beta$ time integration scheme. A wide set of numerical simulations is reported, both for the verification of the theoretical estimates and for examples of physical interest. A comparison with the results of the poroelastic model is provided too, highlighting the differences between the predictive capabilities of the two models. |
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