Fluid-structure interaction modeling of artery aneurysms with steady-state configurations

This paper addresses numerical simulations of fluid-structure interaction (FSI) problems involving artery aneurysms, focusing on steady-state configurations. Both the fluid flow and the hyperelastic material are incompressible. A monolithic formulation for the FSI problem is considered, where the deformation of the fluid domain is taken into account according to an Arbitrary Lagrangian Eulerian (ALE) scheme. The numerical algorithm is a Newton-Krylov method combined with geometric multigrid preconditioner and smoothing based on domain decomposition. The system is modeled using a specific equation shuffling that aims at improving the row pivoting. Due to the complexity of the operators, the exact Jacobian matrix is evaluated using automatic differentiation tools. We describe benchmark settings which shall help to test and compare different numerical methods and code implementations for the FSI problem in hemodynamics. The configurations consist of realistic artery aneurysms. A case of endovascular stent implantation on a cerebral aneurysm is also presented. Hybrid meshes are employed in such configurations. We show numerical results for the described aneurysm geometries for steady-state boundary conditions. Parallel implementation is also addressed

Un approccio geometrico ai sistemi di equazioni differenziali

Vengono trattati tre diversi tipi di sistemi di equazioni differenziali utilizzando nozioni di tipo geometrico come le funzioni di matrici, le matrici costituenti e i fasci di matrici singolari

I motori di ricerca: algoritmi a confronto e sperimentazione in una classe di scuola superiore.

Tesi interdisciplinare che coniuga due importanti ambiti della Matematica: il Calcolo Numerico e la Didattica della Matematica. Alcuni algoritmi utilizzati per il web information retrieval sono stati introdotti all'interno di due classi di scuola superiore avvalendosi del programma di calcolo Matlab

Fluid-structure interaction modeling of artery aneurysms with steady-state configurations

This paper addresses numerical simulations of fluid-structure interaction (FSI) problems involving artery aneurysms, focusing on steady-state configurations. Both the fluid flow and the hyperelastic material are incompressible. A monolithic formulation for the FSI problem is considered, where the deformation of the fluid domain is taken into account according to an Arbitrary Lagrangian Eulerian (ALE) scheme. The numerical algorithm is a Newton-Krylov method combined with geometric multigrid preconditioner and smoothing based on domain decomposition. The system is modeled using a specific equation shuffling that aims at improving the row pivoting. Due to the complexity of the operators, the exact Jacobian matrix is evaluated using automatic differentiation tools. We describe benchmark settings which shall help to test and compare different numerical methods and code implementations for the FSI problem in hemodynamics. The configurations consist of realistic artery aneurysms. A case of endovascular stent implantation on a cerebral aneurysm is also presented. Hybrid meshes are employed in such configurations. We show numerical results for the described aneurysm geometries for steady-state boundary conditions. Parallel implementation is also addressed

Mathematical Modeling and Robustness Analysis to Unravel COVID-19 Transmission Dynamics: The Italy Case

This study started from the request of providing predictions on hospitalization and Intensive Care Unit (ICU) rates that are caused by COVID-19 for the Umbria region in Italy. To this purpose, we propose the application of a computational framework to a SEIR-type (Susceptible, Exposed, Infected, Removed) epidemiological model describing the different stages of COVID-19 infection. The model discriminates between asymptomatic and symptomatic cases and it takes into account possible intervention measures in order to reduce the probability of transmission. As case studies, we analyze not only the epidemic situation in Umbria but also in Italy, in order to capture the evolution of the pandemic at a national level. First of all, we estimate model parameters through a Bayesian calibration method, called Conditional Robust Calibration (CRC), while using the official COVID-19 data of the Italian Civil Protection. Subsequently, Conditional Robustness Analysis (CRA) on the calibrated model is carried out in order to quantify the influence of epidemiological and intervention parameters on the hospitalization rates. The proposed pipeline properly describes the COVID-19 spread during the lock-down phase. It also reveals the underestimation of new positive cases and the need of promptly isolating asymptomatic and presymptomatic cases. The results emphasize the importance of the lock-down timeliness and provide accurate predictions on the current evolution of the pandemic