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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59/2023 - 08/01/2023
Corti, M.; Bonizzoni, F.; Antonietti, P.F.
Structure Preserving Polytopal Discontinuous Galerkin Methods for the Numerical Modeling of Neurodegenerative Diseases | Abstract | | Many neurodegenerative diseases are connected to the spreading of misfolded prionic proteins. In this paper, we analyse the process of misfolding and spreading of both alpha-synuclein and Amyloid-beta, related to Parkinson's and Alzheimer's diseases, respectively. We introduce and analyze a positivity-preserving numerical method for the discretization of the Fisher-Kolmogorov equation, modelling accumulation and spreading of prionic proteins. The proposed approximation method is based on the discontinuous Galerkin method on polygonal and polyhedral grids for space discretization and on theta-method time integration scheme. We prove the existence of the discrete solution and a convergence result where the Implicit Euler scheme is employed for time integration. We show that the proposed approach is structure-preserving, in the sense that it guaranteed that the discrete solution is non-negative, a feature that is of paramount importance in practical application. The numerical verification of our numerical model is performed both using a manufactured solution and considering wavefront propagation in two-dimensional polygonal grids. Next, we present a simulation of alpha-synuclein spreading in a two-dimensional brain slice in the sagittal plane. The polygonal mesh for this simulation is agglomerated maintaining the distinction of white and grey matter, taking advantage of the flexibility of PolyDG methods in the mesh construction. Finally, we simulate the spreading of Amyloid-beta in a patient-specific setting by using a three-dimensional geometry reconstructed from magnetic resonance images and an initial condition reconstructed from positron emission tomography. Our numerical simulations confirm that the proposed method is able to capture the evolution of Parkinson's and Alzheimer's diseases. |
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57/2023 - 07/24/2023
Regazzoni, F.
An optimally convergent Fictitious Domain method for interface problems | Abstract | | We introduce a novel Fictitious Domain (FD) unfitted method for interface problems that achieves optimal convergence without the need for adaptive mesh refinements nor enrichments of the Finite Element spaces. The key aspect of the proposed method is that it extends the solution into the fictitious domain in a way that ensures high global regularity. Continuity of the solution across the interface is enforced through a boundary Lagrange multiplier. The subdomains coupling, however, is not achieved by means of the duality pairing with the Lagrange multiplier, but through an $L^2$ product with the $H^1$ Riesz representative of the latter, thus avoiding gradient jumps across the interface. Thanks to the enhanced regularity, the proposed method attains an increase, with respect to standard FD methods, of up to one order of convergence in energy norm. The Finite Element formulation of the method is presented, followed by its analysis. Numerical tests demonstrate its effectiveness. |
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58/2023 - 07/24/2023
Montino Pelagi, G.; Baggiano, A.; Regazzoni, F.; Fusini, L.; Alì, M.; Pontone, G.; Valbusa, G.; Vergara, C.
Personalized pressure conditions and calibration for a predictive computational model of coronary and myocardial blood flow | Abstract | | Purpose: predictive modeling of hyperemic coronary and myocardial blood flow (MBF) greatly support diagnosis and prognostic stratification of patients suffering from coronary artery disease (CAD). In this work, we propose a novel strategy, using only readily available clinical data, to build personalized inlet conditions for coronary and MBF models and to achieve an effective calibration for their predictive application to real clinical cases. Methods: experimental data are used to build personalized pressure waveforms at the aortic root, representative of the hyperemic state and adapted to surrogate the systolic contraction, to be used in computational fluid-dynamics analyses. Model calibration to simulate hyperemic flow is performed in a “blinded” way, not requiring any additional exam. Coronary and myocardial flow simulations are performed in eight patients with different clinical conditions to predict FFR and MBF. Results: realistic pressure waveform are recovered for all the patients. Consistent pressure distribution, blood velocities in the large arteries, and distribution of MBF in the healthy myocardium are obtained. FFR results show great accuracy with a per-vessel sensitivity and specificity of 100% according to clinical threshold values. Mean MBF shows good agreement with values from stress-CTP, with lower values in patients with diagnosed perfusion defects. Conclusion: the proposed methodology allows us to quantitatively predict FFR and MBF, by the exclusive use of standard measures easily obtainable in a clinical context. This represents a fundamental step to avoid catheter-based exams and stress tests in CAD diagnosis. |
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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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