The INTERNODES Method for Non-conforming Discretizations of PDEs

INTERNODES is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into two or several disjoint subdomains. It exploits two intergrid interpolation operators, one for transfering the Dirichlet trace across the interfaces, and the other for the Neumann trace. In this paper, in every subdomain the original problem is discretized by either the finite element method (FEM) or the spectral element method (SEM or hp-FEM), using a priori non-matching grids and piecewise polynomials of different degrees. Other discretization methods, however, can be used. INTERNODES can also be applied to heterogeneous or multiphysics problems, that is, problems that feature different differential operators inside adjacent subdomains. For instance, in this paper we apply the INTERNODES method to a Stokes- Darcy coupled problem that models the filtration of fluids in porous media. Our results highlight the flexibility of the method as well as its optimal rate of convergence with respect to the grid size and the polynomial degree.

Optimized numerical solutions of SIRDVW multiage model controlling SARS-CoV-2 vaccine roll out:An application to the Italian scenario

In the context of SARS-CoV-2 pandemic,mathematical modelling has played a funda-mental role for making forecasts,simulating scenarios and evaluating the impact of pre-ventive political,social and pharmaceutical measures.Optimal control theory represents a useful mathematical tool to plan the vaccination campaign aimed at eradicating the pandemic as fast as possible.The aim of this work is to explore the optimal prioritisation order for planning vaccination campaigns able to achieve specific goals,as the reduction of the amount of infected,deceased and hospitalized in a given time frame,among age classes.For this purpose,we introduce an age stratified SIR-like epidemic compartmental model settled in an abstract framework for modelling two-doses vaccination campaigns and conceived with the description of COVID19 disease.Compared to other recent works,our model incorporates all stages of the COVID-19 disease,including death or recovery,without accounting for additional specific compartments that would increase computa-tional complexity and that are not relevant for our purposes.Moreover,we introduce an optimal control framework where the model is the state problem while the vaccine doses administered are the control variables.An extensive campaign of numerical tests,featured in the Italian scenario and calibrated on available data from Dipartimento di Protezione Civile Italiana,proves that the presented framework can be a valuable tool to support the planning of vaccination campaigns.Indeed,in each considered scenario,our optimization framework guarantees noticeable improvements in terms of reducing deceased,infected or hospitalized individuals with respect to the baseline vaccination policy.

Modelling the COVID-19 epidemic and the vaccination campaign in Italy by the SUIHTER model

Several epidemiological models have been proposed to study the evolution of COVID-19 pandemic.In this paper,we propose an extension of the SUIHTER model,to analyse the COVID-19 spreading in Italy,which accounts for the vaccination campaign and the presence of new variants when they become dominant.In particular,the specific features of the variants(e.g.their increased transmission rate)and vaccines(e.g.their efficacy to prevent transmission,hospitalization and death)are modeled,based on clinical evidence.The new model is validated comparing its near-future forecast capabilities with other epidemiological models and exploring different scenario analyses.

Isogeometric Analysis of a Phase Field Model for Darcy Flows with Discontinuous Data

The authors consider a phase field model for Darcy flows with discontinuous data in porous media;specifically,they adopt the Hele-Shaw-Cahn-Hillard equations of[Lee,Lowengrub,Goodman,Physics of Fluids,2002]to model flows in the Hele-Shaw cell through a phase field formulation which incorporates discontinuities of physical data,namely density and viscosity,across interfaces.For the spatial approximation of the problem,the authors use NURBS—based isogeometric analysis in the framework of the Galerkin method,a computational framework which is particularly advantageous for the solution of high order partial differential equations and phase field problems which exhibit sharp but smooth interfaces.In this paper,the authors verify through numerical tests the sharp interface limit of the phase field model which in fact leads to an internal discontinuity interface problem;finally,they show the efficiency of isogeometric analysis for the numerical approximation of the model by solving a benchmark problem,the so-called"rising bubble"problem.

Partitioned and Monolithic Algorithms for the Numerical Solution of Cardiac Fluid-Structure Interaction

We reviewand compare different fluid-structure interaction(FSI)numerical methods in the context of heart modeling,aiming at assessing their computational efficiency for cardiac numerical simulations and selecting the most appropriate method for heart FSI.Blood dynamics within the human heart is characterized by active muscular action,during both contraction and relaxation phases of the heartbeat.The efficient solution of the FSI problem in this context is challenging,due to the added-mass effect(caused by the comparable densities of fluid and solid,typical of biomechanics)and to the complexity,nonlinearity and anisotropy of cardiac consitutive laws.In this work,we review existing numerical coupling schemes for FSI in the two classes of strongly-coupled partitioned and monolithic schemes.The schemes are compared on numerical tests that mimic the flow regime characterizing the heartbeat in a human ventricle,during both systole and diastole.Active mechanics is treated in both the active stress and active strain frameworks.Computational costs suggest the use of a monolithic method.We employ it to simulate a full heartbeat of a human ventricle,showing how it allows to efficiently obtain physiologically meaningful results.

心血管数学

在本文中，我们将介绍描述循环系统中血液流动的一些基本微分（方程）模型．我们将对以下问题进行评述：这些模型的数学性质、它们的意义以及在给出实际和准确的数值模拟方面的局限性，还有它们对更好地理解心血管的病理生理学的贡献。