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 1152 products
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55/2023 - 07/12/2023
Orlando, G; Barbante, P.F.; Bonaventura, L.
On the evolution equations of interfacial variables in two-phase flows | Abstract | | Many physical situations are characterized by interfaces with a non trivial shape so that relevant geometric features, such as interfacial area, curvature or unit normal vector, can be used as main indicators of the topology of the interface. We analyze the evolution equations for a set of geometrical quantities that characterize the interface
in two-phase flows. Several analytical relations for the interfacial area density are reviewed and presented, clarifying the physical significance of the different quantities involved and specifying the hypotheses under which each transport equation is valid. Moreover, evolution equations for the unit normal vector and for the curvature are analyzed. The impact of different formulations is then assessed in numerical simulations of rising bubble benchmarks. |
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54/2023 - 07/10/2023
Orlando, G.
An implicit DG solver for incompressible two-phase flows with an artificial compressibility formulation | Abstract | | We propose an implicit Discontinuous Galerkin (DG) discretization for incompressible two-phase flows using an artificial compressibility formulation. Conservative level set (CLS) method is employed in combination with a reinitialization procedure to capture the moving interface. A projection method based on the L-stable TR-BDF2 method is adopted for the time discretization of the Navier-Stokes equations and of the level set method. Adaptive Mesh Refinement (AMR) is employed to enhance the resolution in correspondence of the interface between the two fluids. The effectiveness of the proposed approach is shown in a number of classical benchmarks, such as the Rayleigh-Taylor instability and the rising bubble test case, for which a specific analysis on the influence of different choices of the mixture viscosity is carried out. |
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53/2023 - 06/19/2023
Rossi, A.; Cappozzo, A.; Ieva, F.
Functional Boxplot Inflation Factor adjustment through Robust Covariance Estimators | Abstract | | The accurate identification of anomalous curves in functional data analysis (FDA) is of utmost importance to ensure reliable inference and unbiased estimation of parameters. However, detecting outliers within the infinite-dimensional space that encompasses such data can be challenging. In order to address this issue, we present a novel approach that involves adjusting the fence inflation factor in the functional boxplot, a widely utilized tool in FDA, through simulation-based methods. Our proposed adjustment method revolves around controlling the proportion of observations considered anomalous within outlier-free replications of the original data. To accomplish this, state-of-the-art robust estimators of location and scatter are employed. In our study, we compare the performance of multivariate procedures, which are suitable for addressing the challenges posed by the "small N, large P" problems, and functional operators for implementing the tuning process. A simulation study and a real-data example showcase the validity of our proposal. |
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52/2023 - 06/02/2023
Antonietti, P.F.; Botti, M.; Mazzieri, I.
A space-time discontinuous Galerkin method for coupled poroelasticity-elasticity problems | Abstract | | This work is concerned with the analysis of a space-time finite element discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical discretization of wave propagation in coupled poroelastic-elastic media. The mathematical model consists of the low-frequency Biot's equations in the poroelastic medium and the elastodynamics equation for the elastic one.
To realize the coupling, suitable transmission conditions on the interface between the two domains are (weakly) embedded in the formulation.
The proposed PolydG discretization in space is then coupled with a dG time integration scheme, resulting in a full space-time dG discretization.
We present the stability analysis for both the continuous and the semidiscrete formulations, and we derive error estimates for the semidiscrete formulation in a suitable energy norm.
The method is applied to a wide set of numerical test cases to verify the theoretical bounds. Examples of physical interest are also presented to investigate the capability of the proposed method in relevant geophysical scenarios. |
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51/2023 - 06/02/2023
Bucelli, M.; Regazzoni, F.; Dede', L.; Quarteroni, A.
Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: application to cardiac electromechanics | Abstract | | The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Function (RBF) interpolation with Singular Value Decomposition (SVD) to preserve the positivity of the determinant of the deformation gradient tensor. The method involves decomposing the evaluations of the tensor at the quadrature nodes of the source mesh into rotation matrices and diagonal matrices of singular values; computing the RBF interpolation of the quaternion representation of rotation matrices and the singular value logarithms; reassembling the deformation gradient tensors at quadrature nodes of the destination mesh, to be used in the assembly of the electrophysiology model equations. The proposed method overcomes limitations of existing interpolation methods, including nested intergrid interpolation and RBF interpolation of the displacement field, that may lead to the loss of physical meaningfulness of the mathematical formulation and then to solver failures at the algebraic level, due to negative determinant values. Furthermore, the proposed method enables the transfer of solution variables between finite element spaces of different degrees and shapes and without stringent conformity requirements between different meshes, thus enhancing the flexibility and accuracy of electromechanical simulations. We show numerical results confirming that the proposed method enables the transfer of the deformation gradient tensor, allowing to successfully run simulations in cases where existing methods fail. This work provides an efficient and robust method for the intergrid transfer of the deformation gradient tensor, thus enabling independent tailoring of mesh discretizations to the particular characteristics of the individual physical components concurring to the of the multiphysics model. |
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49/2023 - 05/24/2023
Ieva, F.; Ronzulli, M.; Romo, J.; Paganoni, A.M.
A Spearman Dependence Matrix for Multivariate Functional Data | Abstract | | We propose a nonparametric inferential framework for quantifying dependence
among two families of multivariate functional data. We generalize the notion of
Spearman correlation coefficient to situations where the observations are curves generated
by a stochastic processes. In particular, several properties of the Spearman
index are illustrated emphasizing the importance of having a consistent estimator of
the index of the original processes. We use the notion of Spearman index to define
the Spearman matrix, a mathematical object expressing the pattern of dependence
among the components of a multivariate functional dataset. Finally, the notion of
Spearman matrix is exploited to analyze two different populations of multivariate
curves (specifically, Electrocardiographic signals of healthy and unhealthy people),
in order to test if the pattern of dependence between the components is statistically
different in the two cases. |
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48/2023 - 05/23/2023
Renzi, F.; Vergara, C.; Fedele, M.; Giambruno, V.; Quarteroni, A.; Puppini, G.; Luciani, G.B.
Accurate and Efficient 3D Reconstruction of Right Heart Shape and Motion from Multi-Series Cine-MRI | Abstract | | The accurate reconstruction of the right heart geometry and motion from time-resolved
medical images enhances diagnostic tools based on image visualization as well as the
analysis of cardiac blood dynamics through computational methods. Due to the peculiarity
of the right heart morphology and motion, commonly used segmentation and/or
reconstruction techniques, which only employ Short-Axis cine-MRI, lack accuracy in
relevant regions of the right heart, like the ventricular base and the outflow tract. Moreover,
the reconstruction procedure is time-consuming and, in the case of the generation
of computational domains, requires a lot of manual intervention.
This paper presents a new method for the accurate and efficient reconstruction of the
right heart geometry and motion from time-resolved MRI. In particular, the proposed
method makes use of surface morphing to merge information coming from multi-series
cine-MRI (such as Short/Long-Axis and 2/3/4 Chambers acquisitions) and to reconstruct
important cardiac features. It also automatically provides the complete cardiac
contraction and relaxation motion by exploiting a suitable image registration technique.
The method is applied both to a healthy and a pathological (tetralogy of Fallot) case,
and yelds more accurate results than standard procedures. The proposed method is also
employed to provide significant input for computational fluid dynamics. The corresponding
numerical results demonstrate the reliability of our approach in the computation
of clinically relevant blood dynamics quantities. |
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45/2023 - 05/21/2023
Gironi, P.; Petraro, L.; Santoni, S.; Dede', L.; Colosimo, B.M.
A Computational Model of Cell Viability and Proliferation of Extrusion-based 3D Bioprinted Constructs During Tissue Maturation Process | Abstract | | 3D bioprinting is a novel promising solution for living tissue fabrication, with several potential advantages in many different applicative sectors. However, the implementation of complex vascular networks remains among the limiting factors for the production of complex tissues and for bioprinting scale-up. In this work, a physics-based computational model is presented to describe nutrients diffusion and consumption phenomena in bioprinted constructs. The model - a system of Partial Differential Equations that is approximated by means of the Finite Element method - allows for the description of cell viability and proliferation, and it can be easily adapted to different cell types, densities, biomaterials and 3D printed geometries, thus allowing a preassessment of cell viability within the bioprinted construct. The experimental validation is performed on bioprinted specimens to assess the ability of the model to predict changes in cell viability. The proposed model constitutes a proof of concept of digital twinning of biofabricated constructs that can be suitably included in the basic toolkit for tissue bioprinting. |
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