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 1268 products
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09/2023 - 02/10/2023
Buchwald, S.; Ciaramella, G.; Salomon, J.
Gauss-Newton oriented greedy algorithms for the reconstruction of operators in nonlinear dynamics | Abstract | | This paper is devoted to the development and convergence analysis of greedy reconstruction algorithms based on the strategy presented in [Y. Maday and J. Salomon, Joint Proceedings of the 48th IEEE Conference on
Decision and Control and the 28th Chinese Control Conference, 2009, pp. 375--379]. These procedures allow the design of a sequence of control functions that ease the
identification of unknown operators in nonlinear dynamical systems.
The original strategy of greedy reconstruction algorithms is based on an offline/online
decomposition of the reconstruction process and on an ansatz for the unknown operator obtained by an a priori chosen set of linearly independent matrices. In the previous work [S. Buchwald, G. Ciaramella and J. Salomon, SIAM J. Control Optim., 59(6), pp. 4511-4537], convergence results were obtained in the case of linear identification problems. We tackle here the more general case of nonlinear systems. More precisely, we show that the controls obtained with the greedy algorithm on the corresponding linearized system lead to the local convergence of the classical Gauss-Newton method applied to the online nonlinear identification problem. We then extend this result to the controls obtained on nonlinear systems where a local convergence result is also obtained. The main convergence results are obtained for the reconstruction of drift operators in linear and bilinear dynamical systems. |
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08/2023 - 02/07/2023
Bonizzoni, F.; Hu, K.; Kanschat, G.; Sap, D.
Discrete tensor product BGG sequences: splines and finite elements | Abstract | | In this paper, we provide a systematic discretization of the
Bernstein-Gelfand-Gelfand (BGG) diagrams and complexes over cubical
meshes of arbitrary dimension via the use of tensor-product structures of one-dimensional piecewise-polynomial spaces, such as spline and finite element spaces. We demonstrate the construction of the Hessian, the elasticity, and divdiv complexes as examples for our construction. |
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07/2023 - 02/06/2023
Garcia-Contreras, G.; Còrcoles, J.; Ruiz-Cruz, J.A.; Oldoni, M; Gentili, G.G.; Micheletti, S.; Perotto, S.
Advanced Modeling of Rectangular Waveguide Devices with Smooth Profi les by Hierarchical Model Reduction | Abstract | | We present a new method for the analysis of smoothly varying tapers, transitions and fi lters in rectangular waveguides. With this aim, we apply a Hierarchical Model (HiMod) reduction to the vector Helmholtz equation. We exploit a suitable coordinate transformation and, successively, we use the waveguide modes as a basis for the HiMod expansion. We show that accurate results can be obtained with an impressive speed-up factor when compared with standard commercial codes based on a three-dimensional fi nite element discretization. |
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06/2023 - 02/06/2023
Artoni, A.; Antonietti, P. F.; Mazzieri, I.; Parolini, N.; Rocchi, D.
A segregated finite volume - spectral element method for aeroacoustic problems | Abstract | | We propose a segregated Finite Volume (FV) - Spectral Element Method (SEM) for modelling aeroacoustic phenomena based on the Lighthill's acoustic analogy. First the fluid solution is computed employing a FV method. Then, the sound source term is projected onto the acoustic grid and the inhomogeneous Lighthill's wave equation is solved employing the SEM. The novel projection method computes offline the intersections between the acoustic and the fluid grids in order to preserve the accuracy. The proposed intersection algorithm is shown to be robust, scalable and able to efficiently compute the geometric intersection of arbitrary polyhedral elements.
We then analyse the properties of the projection error and we numerically assess the obtained theoretical estimates. Finally, we address two relevant aeroacoustic benchmarks, namely the corotating vortex pair and the noise induced by a laminar flow around a squared cylinder, to demonstrate in practice the effectiveness of the proposed approach. The flow computations are performed with OpenFOAM , an open-source finite volume library, while the inhomogeneous Lighthill's wave equation is solved with SPEED, an open-source spectral element library. |
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05/2023 - 01/14/2023
Fumagalli, I.; Vergara, C.
Novel approaches for the numerical solution of fluid-structure interaction in the aorta | Abstract | | The aorta is the artery that undergoes the most deformation during the heartbeat. This is associated with the strong Fluid-Structure Interaction (FSI) occurring between the blood flow and the aortic wall. Moreover, also the dynamics of the aortic valve is the result of a FSI process. In this work, we describe the mathematical formulation of both vascular and valve FSI problems and we review the most recent numerical strategies for their solution. Concerning vascular FSI, we consider a moving-domain approach encompassing an arbitrary Lagrangian-Eulerian formulation of the fluid equations, which is the most employed framework in hemodynamics applications. In this context, we provide a systematic description and comparison of different algorithms for the coupling between the fluid and the structure model. In terms of valve FSI, we report a survey on the different numerical methods for the treatment of surfaces immersed and moving in a fluid, with particular focus on unfitted methods, which are the most established for cardiac valve modeling, and the more recent promising family of Cut Finite Elements methods.
Aiming to point out the main difficulties specifically related to aortic FSI simulation in a patient-specific context, we also review strategies for the imposition of boundary conditions, the recovery of a zero-pressure configuration of the vessel wall, and the calibration and validation of computational models against clinical data. |
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04/2023 - 01/10/2023
Quarteroni, A.; Dede’, L.; Regazzoni, F.; Vergara, C.
A mathematical model of the human heart suitable to address clinical problems | Abstract | | In this paper, we present a mathematical model capable of simulating
the human cardiac function. We review the basic equations of the
model, their coupling, the numerical approach for the computer solution of this mathematical model, and a few examples of application to specific problems of clinical interest. |
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03/2023 - 01/05/2023
Africa, P.C.; Perotto, S.; de Falco, C.
Scalable Recovery-based Adaptation on Quadtree Meshes for Advection-Diffusion-Reaction Problems | Abstract | | We propose a mesh adaptation procedure for Cartesian quadtree meshes, to discretize scalar advection-diffusion-reaction problems.
The adaptation process is
driven by a recovery-based a posteriori estimator for the L^2-norm of the discretization error, based on suitable higher order approximations of both the solution and the associated gradient. In particular, a metric-based approach exploits the information furnished by the estimator to iteratively predict the new adapted mesh.
The new mesh adaptation algorithm is successfully assessed on different configurations, and turns out to perform well also when dealing with discontinuities in the data as well as in the presence of internal layers not
aligned with the Cartesian directions.
A cross-comparison with a standard
estimate--mark--refine approach and with other adaptive strategies available in the literature shows the remarkable accuracy and parallel scalability
of the proposed approach. |
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02/2023 - 01/05/2023
Boon, W. M.; Fumagalli, A.; Scotti, A.
Mixed and multipoint finite element methods for rotation-based poroelasticity | Abstract | | This work proposes a mixed finite element method for the Biot poroelasticity equations that employs the lowest-order Raviart-Thomas finite element space for the solid displacement and piecewise constants for the fluid pressure. The method is based on the formulation of linearized elasticity as a weighted vector Laplace problem. By introducing the solid rotation and fluid flux as auxiliary variables, we form a four-field formulation of the Biot system, which is discretized using conforming mixed finite element spaces. The auxiliary variables are subsequently removed from the system in a local hybridization technique to obtain a multipoint rotation-flux mixed finite element method. Stability and convergence of the four-field and multipoint mixed finite element methods are shown in terms of weighted norms, which additionally leads to parameter-robust preconditioners. Numerical experiments confirm the theoretical results. |
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