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 1287 products
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34/2018 - 06/03/2018
Laurino, F.; Coclite, A.; Tiozzo, A.; Decuzzi, P.; Zunino, P.;
A muliscale computational approach for the interaction of functionalized nanoparticles with the miscrovasculature | Abstract | | There is a pressing need in nanomedicine of quantitative predictive tools for the design of nanocostructs for therapeutic and imaging applications. The advance nano-fabrication technologies can control a large spectrum of design parameters of such constructs, which in turn affect their performance in treatments. However, tuning such parameters by means of a trial and error approach based on animal experiments is expensive and impractical. For this reason, computational models are emerging as complementary tools to guide the design and optimization of nano-based therapies.
This work addresses this need, in the particular case of nanoparticles designed to be delivered in the vascular system and interact with the microvasculature. In particular, we develop a sophisticated multiscale and multiphysics computational model that is able to describe blood flow in the microvasculature combined with the detailed description of particle interaction with the wall on the basis of physically sound mechanistic approach. The model is then applied to simulate particle delivery to a representative portion of a tumor, with the aim to compare the distribution and accumulation of particles for different design parameters such as the deformability of the particle, the number and the strength of ligands distributed on the particle surface. |
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32/2018 - 06/03/2018
Dal Santo, N.; Deparis, S.; Manzoni, A.; Quarteroni, A.
An algebraic least squares reduced basis method for the solution of nonaffinely parametrized Stokes equations | Abstract | | In this paper we propose a new, purely algebraic, Petrov-Galerkin reduced basis (RB) method to solve the parametrized Stokes equations, where parameters serve to identify the (variable) domain geometry. Our method is obtained as an algebraic least squares reduced basis (aLS-RB) method, and improves the existing RB methods for Stokes equations in several directions. First of all, it does not require to enrich the velocity space, as often done when dealing with a velocity-pressure formulation, relying on a Petrov-Galerkin RB method rather than on a Galerkin RB (G-RB) method. Then, it exploits a suitable approximation of the matrix-norm in the definition of the (global) supremizing operator. The proposed method also provides a fully automated procedure to assemble and solve the RB problem, able to treat any kind of parametrization, and we rigorously prove the stability of the resulting aLS-RB problem (in the sense of a suitable inf-sup condition). Next, we introduce a coarse aLSRB (caLSRB) method, which is obtained by employing an approximated RB test space, and further improves the efficiency of the aLSRB method both offline and online. We provide numerical comparisons between the proposed methods and the current state-of-art G-RB methods. The new approach results in a more convenient option both during the offline and the online stage of computation, as shown by the numerical results. |
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31/2018 - 05/28/2018
Quarteroni, A.
The role of statistics in the era of big data: A computational scientist’ perspective | Abstract | | In their modern implementation, computational models based on first principles from Physics can dramatically benefit from the recent explosion of Data Science. In fact, these two branches of applied mathematics can virtuously interplay, and at a large extent they already do. |
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30/2018 - 05/12/2018
Ieva, F.; Palma, F.; Romo, J.
Bootstrap-based Inference for Dependence in Multivariate Functional Data | Abstract | | In this work, we propose a bootstrap based inferential framework for quantifying dependency among families of multivariate curves.We start from the notion of Spearman index and Spearman Matrix to provide pointwise estimates of dependency among families of (multivariate) curves, enabling
the analysis of the pattern of dependence among the components of a multivariate functional dataset. Moreover, a suitable inferential framework for the Spearman index and matrix is proposed, making use of a testing procedure based on adjusted confidence intervals for the Spearman index. An additional bootstrap based test for the matrices, enabling the detection of significant differencies in the patterns of dependency among components in different families of multivariate curves is provided. We apply these procedures to a real case study, where two populations of electrocardiographic signals from healthy and unhealthy patients are compared. All the codes are embedded in a suitable R-package, namely raohd. The inferential tools presented in this work represent, to the best of our knowledge, the first systematic attempt to investigate dependency in the (multivariate) functional setting. |
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29/2018 - 05/01/2018
Manzoni, A; Bonomi, D.; Quarteroni, A.
Reduced order modeling for cardiac electrophysiology and mechanics: new methodologies, challenges & perspectives | Abstract | | Reduced-order modeling techniques enable a remarkable speed up in the solution of the parametrized electromechanical model for heart dynamics. Being able to rapidly approximate the solution of this problem allows to investigate the impact of significant model parameters querying the parameter-to-solution map in a very inexpensive way. The construction of reduced-order approximations for cardiac electromechanics faces several challenges from both modeling and computational viewpoints, because of the multiscale nature of the problem, the need of coupling different physics, and the nonlinearities involved. Our approach relies on the reduced basis method for parametrized PDEs. This technique performs a Galerkin projection onto low-dimensional spaces built from a set of snapshots of the high-fidelity problem by the Proper Orthogonal Decomposition technique. Snapshots are obtained for different values of the parameters and computed, e.g., by the finite element method. Then, suitable hyper-reduction techniques, in particular the Discrete Empirical Interpolation Method and its matrix version, are called into play to efficiently handle nonlinear and parameter-dependent terms. In this work we show how a fast and reliable approximation of both the electrical and the mechanical model can be achieved by developing two separate reduced order models where the interaction of the cardiac electrophysiology system with the contractile muscle tissue, as well as the sub-cellular activation-contraction mechanism, are included. Open challenges and possible perspectives are finally outlined. |
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28/2018 - 04/26/2018
Gerbi, A.; Dede', L.; Quarteroni, A.
Segregated algorithms for the numerical simulation of cardiac electromechanics in the left human ventricle | Abstract | | In this paper, we propose and numerically assess three segregated algorithms for the numerical solution of the coupled electromechanics problem for the left human ventricle. We split the coupled problem into its core mathematical models and we proceed to their numerical approximation. Space and time discretizations of the core problems are carried out by means of the Finite Element Method and Backward Differentiation Formulas, respectively. In our mathematical model, electrophysiology is represented
by the monodomain equation while the Holzapfel-Ogden strain energy function is used for the passive characterization of tissue mechanics. A transmurally variable active strain model is used for the active deformation of the fibers of the myocardium to couple the electrophysiology and the mechanics in the framework of the active strain model. In this work we focus on the numerical strategy to deal with the solution of the coupled model, which is based on novel segregated algorithms that we propose. These also allow using different time discretization schemes for the core submodels, thus leading to the formulation of staggered algorithms, a feature that we sistematically exploit to increase the overall efficiency of the computational procedure. We assess the accuracy of these segregated algorithms, measured by means of numerical tests, which exhibit at least first order of accuracy. We take advantage of the efficiency of the segregated schemes to solve, in an High Performance Computing framework, the cardiac electromechanics problem for the human left ventricle, for both idealized and subject-specific configurations. |
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27/2018 - 04/24/2018
Antonietti, P.F.; Verani, M.; Vergara, C.; Zonca, S.
Numerical solution of fluid-structure interaction problems by means of a high order Discontinuous Galerkin method on polygonal grids
| Abstract | | We consider the two-dimensional numerical approximation of the fluid-structure interaction problem over unfitted fluid and structure meshes.
In particular, we consider a method where the fluid mesh is on the background and fixed, apart at the interface with the moving immersed structure, that cuts the fluid mesh elements generating polygons of arbitrary shape. The new idea of this work is to handle the discretization on such polygons by using the Discontinuous Galerkin method on polyhedral grids (PolyDG), which has been recently developed for different differential equations and here adapted for the first time to an heterogeneous problem. We prove a stability result of the proposed semi-discrete formulation and discuss how to deal with the partial or total covering of a fluid mesh element due to the structure movement.
We finally present some numerical results with the aim of showing the effectiveness of the proposed method. |
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26/2018 - 04/24/2018
Vergara, C.; Zonca, S.
Extended Finite Elements method for fluid-structure interaction with an immersed thick non-linear structure | Abstract | | We consider an Extended Finite Element method to
solve fluid-structure interaction problems in the case of an immersed thick
structure described by non-linear finite elasticity. This method, that belongs to the family of the Cut Finite Element methods, allows to consider unfitted meshes for the fluid and solid domains by maintaining the fluid mesh fixed in time as the solid moves. We review the state of the art about the numerical methods for fluid-structure interaction problems and we present an overview of the Cut Finite Element methods. We describe the numerical discretization proposed here to handle the case of a thick immersed structure with size comparable or smaller than the fluid mesh element size in the case of non-linear finite elasticity. Finally, we present some three-dimensional numerical results of the proposed method. |
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