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 1253 products
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61/2023 - 08/04/2023
Afriaca, P.C.A; Piersanti, R.; Regazzoni, F.; Bucelli, M.; Salvador, M.; Fedele, M.; Pagani, S.; Dede', L.; Quarteroni, A.
lifex-ep: a robust and efficient software for cardiac electrophysiology simulations | Abstract | | Simulating the cardiac function requires the numerical solution of multi-physics and multi-scale mathematical models. This underscores the need for streamlined, accurate, and high-performance computational tools. Despite the dedicated endeavors of various research teams, comprehensive and user-friendly software programs for cardiac simulations, capable of accurately replicating both physiological and pathological conditions, are still in the process of achieving full maturity within the scientific community. This work introduces lifex-ep, a publicly available software for numerical simulations of the electrophysiology activity of the cardiac muscle, under both physiological and pathological conditions. lifex-ep employs the monodomain equation to model the heart’s electrical activity. It incorporates both phenomenological and second-generation ionic models. These models are discretized using the Finite Element method on tetrahedral or hexahedral meshes. Additionally, lifex-ep integrates the generation of myocardial fibers based on Laplace-Dirichlet Rule-Based Methods, previously released in Africa et al., 2023, within lifex-fiber. As an alternative, users can also choose to import myofibers from a file. This paper provides a concise overview of the mathematical models and numerical methods underlying lifex-ep, along with comprehensive
implementation details and instructions for users. lifex-ep features
exceptional parallel speedup, scaling efficiently when using up to thousands of cores, and its implementation has been verified against an established benchmark problem for computational electrophysiology. We
showcase the key features of lifex-ep through various idealized and
realistic simulations conducted in both physiological and pathological
scenarios. Furthermore, the software offers a user-friendly and flexible
interface, simplifying the setup of simulations using self-documenting
parameter files. lifex-ep provides easy access to cardiac electrophysiology simulations for a wide user community. It offers a computational tool that integrates models and accurate methods for simulating cardiac electrophysiology within a high-performance framework, while maintaining a user-friendly interface. lifex-ep represents a valuable tool for conducting in silico patient-specific simulations. |
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60/2023 - 08/02/2023
Negrini G.; Parolini N.; Verani M.
The Rhie-Chow stabilized Box Method for the Stokes problem | Abstract | | The Finite Volume method (FVM) is widely adopted in many different applications because of its built-in conservation properties, its ability to deal with arbitrary mesh and its computational efficiency. In this work, we consider the Rhie-Chow stabilized Box Method (RCBM) for the approximation of the Stokes problem. The Box Method (BM) is a piecewise linear Petrov-Galerkin formulation on the Voronoi dual mesh of a Delaunay triangulation, whereas the Rhie-Chow (RC) stabilization is a well known stabilization technique for FVM.
The first part of the paper provides a variational formulation of the RC stabilization and discusses the validity of crucial properties relevant for the well-posedeness and convergence of RCBM. Moreover, a numerical exploration of the convergence properties of the method on 2D and 3D test cases is presented. The last part of the paper considers the theoretically justification of the well-posedeness of RCBM and the experimentally observed convergence rates. This latter justification hinges upon suitable assumptions, whose validity is numerically explored. |
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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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