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## Publications

Publications (102)

In this paper, we introduce a new Virtual Element Method (VEM) not requiring any stabilization term based on the usual enhanced first-order VEM space. The new method relies on a modified formulation of the discrete diffusion operator that ensures stability preserving all the properties of the differential operator.

In this paper we propose a primal C0-conforming virtual element discretization for the simulation of the two-phase flow of immiscible fluids in poro-fractured media modeled by means of a Discrete Fracture Network (DFN). The fractures are assumed to be made of the same isotropic rock type and to have the same width. The flexibility of the Virtual El...

Discrete Fracture Networks (DFNs) are complex three-dimensional structures characterized by the intersections of planar polygonal fractures, and are used to model flows in fractured media. Despite being suitable for Domain Decomposition (DD) techniques, there are relatively few works on the application of DD methods to DFNs. In this manuscript, we...

A new mathematical model and numerical approach are proposed for the simulation of fluid and chemical exchanges between a growing capillary network and the surrounding tissue, in the context of tumor-induced angiogenesis. Thanks to proper modeling assumptions the capillaries are reduced to their centerline: a well posed mathematical model is hence...

In this paper, we present and compare four methods to enforce Dirichlet boundary conditions in Physics-Informed Neural Networks (PINNs) and Variational Physics-Informed Neural Networks (VPINNs). Such conditions are usually imposed by adding penalization terms in the loss function and properly choosing the corresponding scaling coefficients; however...

We consider the discretization of elliptic boundary-value problems by variational physics-informed neural networks (VPINNs), in which test functions are continuous, piecewise linear functions on a triangulation of the domain. We define an a posteriori error estimator, made of a residual-type term, a loss-function term, and data oscillation terms. W...

Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first, adaptively refine a provided good quality polygonal mesh preserving quality, second, improve the quality of a coarse p...

In the present paper a new data-driven model is proposed to close and increase accuracy of Reynolds-averaged Navier-Stokes (RANS) equations. Among the variety of turbulent quantities, it has been decided to predict the divergence of the Reynolds Stress Tensor (RST). Recent literature works highlighted the potential of this choice. The key novelty o...

We propose a quality-based optimization strategy to reduce the total number of degrees of freedom associated to a discrete problem defined over a polygonal tessellation with the Virtual Element Method. The presented Quality Agglomeration algorithm relies only on the geometrical properties of the problem polygonal mesh, agglomerating groups of neigh...

In this work we analyze how quadrature rules of different precisions and piecewise polynomial test functions of different degrees affect the convergence rate of Variational Physics Informed Neural Networks (VPINN) with respect to mesh refinement, while solving elliptic boundary-value problems. Using a Petrov-Galerkin framework relying on an inf-sup...

In this letter we compare the behaviour of standard Virtual Element Methods (VEM) and stabilization free Enlarged Enhancement Virtual Element Methods (E2V EM) with the focus on some elliptic test problems whose solution and diffusivity tensor are characterized by anisotropies. Results show that the possibility to avoid an arbitrary stabilizing part...

Discrete Fracture Network models are largely used for large scale geological flow simulations in fractured media. For these complex simulations, it is worth investigating suitable numerical methods and tools for efficient parallel solutions on High Performance Computing systems. In this paper we propose and compare different partitioning strategies...

We consider the discretization of elliptic boundary-value problems by variational physics-informed neural networks (VPINNs), in which test functions are continuous, piecewise linear functions on a triangulation of the domain. We define an a posteriori error estimator, made of a residual-type term, a loss-function term, and data oscillation terms. W...

In the present paper a new data-driven model to close and increase accuracy of RANS equations is proposed. It is based on the direct approximation of the divergence of the Reynolds Stress Tensor (RST) through a Neural Network (NN). This choice is driven by the presence of the divergence of RST in the RANS equations. Furthermore, once this data-driv...

A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined function spaces a well posed 3D-1D problem is obtained from the original fully 3D problem and the solution is t...

In this work, we extend the formulation of the spatial-based graph convolutional networks with a new architecture, called the graph-informed neural network (GINN). This new architecture is specifically designed for regression tasks on graph-structured data that are not suitable for the well-known graph neural networks, such as the regression of fun...

In this letter we compare the behaviour of standard Virtual Element Methods (VEM) and stabilization free Enlarged Enhancement Virtual Element Methods (E$^2$VEM) with the focus on some elliptic test problems whose solution and diffusivity tensor are characterized by anisotropies. Results show that the possibility to avoid an arbitrary stabilizing pa...

A primal C⁰-conforming virtual element discretization for the approximation of the bidimensional two-phase flow of immiscible fluids in porous media using general polygonal meshes is discussed. This work investigates the potentialities of the Virtual Element Method (VEM) in solving this specific problem of immiscible fluids in porous media involvin...

In this paper we analyse the convergence properties of two-level, W-cycle and V-cycle agglomeration-based geometric multigrid schemes for the numerical solution of the linear system of equations stemming from the lowest order $C^0$-conforming Virtual Element discretization of two-dimensional second-order elliptic partial differential equations. The...

Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first, adaptively refine a provided good quality polygonal mesh preserving quality, second, improve the quality of a coarse p...

Coupled 3D-1D problems arise in many practical applications, in an attempt to reduce the computational burden in simulations where cylindrical inclusions with a small section are embedded in a much larger domain. Nonetheless the resolution of such problems can be non trivial, both from a mathematical and a geometrical standpoint. Indeed 3D-1D coupl...

In several applications concerning underground flow simulations in fractured media, the fractured rock matrix is modeled by means of the Discrete Fracture Network (DFN) model. The fractures are typically described through stochastic parameters sampled from known distributions. In this framework, it is worth considering the application of suitable c...

In this paper, a Virtual Element Method (VEM)-based approach is proposed for the simulation of flow in fractured porous media. The method is based on a robust meshing strategy, capable of producing conforming polyhedral meshes of intricate geometries and relies on the robustness of the VEM in handling distorted and elongated elements. Numerical tes...

In classic Reduced Basis (RB) framework, we propose a new technique for the offline greedy error analysis which relies on a residual-based a posteriori error estimator. This approach is as an alternative to classical a posteriori RB estimators, avoiding a discrete inf-sup lower bound estimate. We try to use less common ingredients of the RB framewo...

A new numerical approach is proposed for the simulation of coupled three-dimensional and one-dimensional elliptic equations (3D-1D coupling) arising from dimensionality reduction of 3D-3D problems with thin inclusions. The method is based on a well posed mathematical formulation and results in a numerical scheme with high flexibility in handling ge...

In the framework of flow simulations in Discrete Fracture Networks, we consider the problem of identifying possible backbones, namely preferential channels in the network. Backbones can indeed be fruitfully used to analyze clogging or leakage, relevant for example in waste storage problems, or to reduce the computational cost of simulations. With a...

In this work we analyze how Gaussian or Newton-Cotes quadrature rules of different precisions and piecewise polynomial test functions of different degrees affect the convergence rate of Variational Physics Informed Neural Networks (VPINN) with respect to mesh refinement, while solving elliptic boundary-value problems. Using a Petrov-Galerkin framew...

Simulation of fluid flow dynamics in fractured porous media is an important issue in several subsurface models. The intricate network generated by hundreds of fractures produces complex multi-scale geometries that can be modelled in different ways. In contrast to homogenization-based techniques, discrete fracture network (DFN) models explicitly rep...

Discrete Fracture Network models are largely used for very large scale geological flow simulations. For this reason numerical methods require an investigation of tools for efficient parallel solutions on High Performance Computing systems. In this paper we discuss and compare several partitioning and reordering strategies, that result to be highly...

Coupled 3D-1D problems arise in many practical applications, in an attempt to reduce the computational burden in simulations where cylindrical inclusions with a small section are embedded in a much larger domain. Nonetheless the resolution of such problems can be non trivial, both from a mathematical and a geometrical standpoint. Indeed 3D-1D coupl...

A new discretization approach is presented for the simulation of flow in complex poro-fractured media described by means of the Discrete Fracture and Matrix Model. The method is based on the numerical optimization of a properly defined cost-functional and allows to solve the problem without any constraint on mesh generation, thus overcoming one of...

The numerical simulation of phenomena such as subsurface fluid flow or rock deformations are based on geological models, where volumes are typically defined through stratigraphic surfaces and faults, which constitute the geometric constraints, and then discretized into blocks to which relevant petrophysical or stress-strain properties are assigned....

In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well and states new issues, here tackled, concerning good quality mesh elements and reliability of the simulations....

We introduce and analyse the first order Enlarged Enhancement Virtual Element Method (E$^2$VEM) for the Poisson problem. The method has the interesting property of allowing the definition of bilinear forms that do not require a stabilization term. We provide a proof of well-posedness and optimal order a priori error estimates. Numerical tests on co...

In this work, we investigate the sensitivity of a family of multi-task Deep Neural Networks (DNN) trained to predict fluxes through given Discrete Fracture Networks (DFNs), stochastically varying the fracture transmissivities. In particular, detailed performance and reliability analyses of more than two hundred Neural Networks (NN) are performed, t...

We derive an anisotropic a posteriori error estimate for the adaptive conforming virtual element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its approximation results to prove the reliability of the error indicator. We design and implement the corresponding a...

A new numerical approach is proposed for the simulation of coupled three-dimensional and one-dimensional elliptic equations (3D-1D coupling) arising from dimensionality reduction of 3D-3D problems with thin inclusions. The method is based on a well posed mathematical formulation and results in a numerical scheme with high robustness and flexibility...

We present a method combining multilevel Monte Carlo (MLMC) and a graph‐based primary subnetwork identification algorithm to provide estimates of the mean and variance of the distribution of first passage times in fracture media at significantly lower computational cost than standard Monte Carlo (MC) methods. Simulations of solute transport are per...

A new discretization approach is presented for the simulation of flow in complex poro-fractured media described by means of the Discrete Fracture and Matrix Model. The method is based on the numerical optimization of a properly defined cost-functional and allows to solve the problem without any constraint on mesh generation, thus overcoming one of...

We derive an anisotropic a posteriori error estimate for the adaptive conforming Virtual Element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its approximation results to prove the reliability of the error indicator. We design and implement the corresponding a...

A new numerical scheme is proposed for flow computation in complex discrete fracture networks. The method is based on a three-field formulation of the Darcy law for the description of the hydraulic head on the fractures and uses a cost functional to enforce the required coupling condition at fracture intersections. The resulting method can handle n...

In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well and states new issues, here tackled, concerning good quality mesh elements and reliability of the simulations....

A new approach for the flow simulation in very complex Discrete Fracture Networks (DFNs) based on PDE-constrained optimization has been recently proposed in Berrone et al. (2013, 2014) with the aim of improving robustness with respect to geometrical complexities. In Berrone et al. (2016) a rigorous derivation of “a posteriori” error estimates has b...

A new approach for flow simulation in very complex discrete fracture networks based on PDE-constrained optimization has been recently proposed in Berrone et al. (SIAM J Sci Comput 35(2):B487–B510, 2013b; J Comput Phys 256:838–853, 2014) with the aim of improving robustness with respect to geometrical complexities. This is an essential issue, in par...

Simulation of physical phenomena in networks of fractures is a challenging task, mainly as a consequence of the geometrical complexity of the resulting computational domains, typically characterized by a large number of interfaces, i.e. the intersections among the fractures. The use of numerical strategies that require a mesh conforming to the inte...

Two novel approaches are presented for dealing with three dimensional flow simulations in porous media with fractures: one method is based on the minimization of a cost functional to enforce matching conditions at the interfaces, thus allowing for non conforming grids at the interfaces; the other, instead, takes advantage of the new Virtual Element...

In recent years, the numerical treatment of boundary value problems with the help of polygonal and polyhedral discretization techniques has received a lot of attention within several disciplines. Due to the general element shapes an enormous flexibility is gained and can be exploited, for instance, in adaptive mesh refinement strategies. The Virtua...

In this note the issue of fluid flow computation in a Discrete Fracture-Matrix (DFM) model is addressed. In such a model, a network of percolative fractures delimits porous matrix blocks. Two frameworks are proposed for the coupling between the two media. First, a FEM–BEM technique is considered, in which finite elements on non-conforming grids are...

It is widely recognized that the prediction of transport of contaminants in a fractured rock mass requires models that preserve several distinctive features of the inner fracture network, like heterogeneity and directionality; in this respect, Discrete Fracture Networks (DFNs) play a significant role. The solution of the associated equations would...

We present the design, convergence analysis and numerical investigations of the nonconforming virtual element method with Streamline Upwind/Petrov-Galerkin (VEM-SUPG) stabilization for the numerical resolution of convection-diffusion-reaction problems in the convective-dominated regime. According to the virtual discretization approach, the bilinear...

We present the design, convergence analysis and numerical investigations of the nonconforming virtual element method with Streamline Upwind/Petrov–Galerkin (VEM-SUPG) stabilization for the numerical resolution of convection–diffusion–reaction problems in the convective-dominated regime.
According to the virtual discretization approach, the bilinear...

We consider the problem of uncertainty quantification analysis of the output of underground flow simulations. We consider in particular fractured media described via the discrete fracture network model; within this framework, we address the relevant case of networks in which the geometry of the fractures is described by stochastic parameters. In th...

We consider a Fictitious Domain formulation of an elliptic partial differential equation and approximate the resulting saddle-point system using an inexact preconditioned Uzawa iterative algorithm. Each iteration entails the approximation of an elliptic problems performed using adaptive finite element methods. We prove that the overall method conve...

In this paper we propose a modified construction for the polynomial basis on polygons used in the Virtual Element Method (VEM). This construction is alternative to the usual monomial basis used in the classical construction of the VEM and is designed in order to improve numerical stability. For badly shaped elements the construction of the projecti...

A novel approach for fully 3D flow simulations in porous media with immersed networks of fractures is presented. The method is based on the discrete fracture and matrix model, in which fractures are represented as two-dimensional objects in a three-dimensional porous matrix. The problem, written in primal formulation on both the fractures and the p...

A residual-based a posteriori error estimate for the Poisson problem with discontinuous diffusivity coefficient is derived in the case of a virtual element discretization. The error is measured considering a suitable polynomial projection of the discrete solution to prove an equivalence between the defined error and a computable residual based erro...

Among the major challenges in performing underground flow simulations in fractured media are geometrical complexities in the domain and uncertainty in the problem parameters, including the geometrical configuration. The Discrete Fracture Network (DFN) model is largely applied in order to properly account for the directionality of the flow in fractu...

This paper presents a new approach to the behavioral dynamics of human crowds. Macroscopic first order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional process by which walkers select their velocity direction. The present approach is applied to describe the...

We focus on the problem of performing underground flow simulations in fractured media. The medium is modelled by means of the so-called Discrete Fracture Network (DFN) model. Within this framework, we discuss about the use of the Virtual Element Method (VEM) in performing simulations, and about its role in facilitating the meshing process. DFN mode...

In the Fictitious Domain Method with Lagrange multiplier (FDM ) the physical domain is embedded into a simpler but larger domain called the fictitious domain. The partial differential equation is extended to the fictitious domain using a Lagrange multiplier to enforce the prescribed boundary conditions on the physical domain while all the other dat...

In the framework of the discretization of advection-diffusion problems by means of the Virtual Element Method, we consider stabilization issues. Herein, stabilization is pursued by adding a consistent SUPG-like term. For this approach we prove optimal rates of convergence. Numerical results clearly show the stabilizing effect of the method up to ve...

We focus on the simulation of underground flow in fractured media, modeled by means of Discrete Fracture Networks. Focusing on a new recent numerical approach proposed by the authors for tackling the problem avoiding mesh generation problems, we further improve the new family of methods making a step further towards effective simulations of large,...

A new approach for numerically solving flow in Discrete Fracture Networks (DFN) is developed in this work by means of the Virtual Element Method (VEM). Taking advantage of the features of the VEM, we obtain global conformity of all fracture meshes while preserving a fracture-independent meshing process. This new approach is based on a generalizatio...

Flows in fractured media have been modeled with many different approaches in order to get reliable and efficient simulations for many critical applications. The common issues to be tackled are the wide range of scales involved in the phenomenon, the complexity of the domain, and the huge computational cost. In this paper we introduce residual-based...

The most challenging issue in performing underground flow simulations in Discrete Fracture Networks (DFN) is to effectively tackle the geometrical difficulties of the problem. In this work we put forward a new application of the Virtual Element Method combined with the Mortar method for domain decomposition: we exploit the flexibility of the VEM in...

We consider the problem of underground flow simulations in fractured media. This is a large scale, heterogeneous multi-scale phenomenon involving very complex geological configurations. Within the Discrete Fracture Network (DFN) model, we focus on the resolution of the steady-state flow in large fracture networks. Exploiting the peculiarity of the...

We consider flows in fractured media, described by Discrete Fracture Network (DFN) models. We perform an Uncertainty Quantification analysis, assuming the fractures' transmissivity coefficients to be random variables. Two probability distributions (log-uniform and log-normal) are used within different laws that express the coefficients in terms of...

n this work, an efficient implementation of a zero-dimensional model is described for the estimation of key engine parameters for combustion control in compression-ignition engines. The direct problems of the estimation of the angle of 50% of fuel mass fraction burnt (MFB50) and of the Indicated Mean Effective Pressure (IMEP) are addressed as well...

Flows in fractured media have been modeled using many different approaches in order to get reliable and efficient simulations for many critical applications. The common issues to be tackled are the wide range of scales involved in the phenomenon, the complexity of the domain, and the huge computational cost. In the present paper we propose a parall...

This paper presents a new approach to behavioral-social dynamics of human
crowds. First order models are derived based on mass conservation at the
macroscopic scale, while methods of the kinetic theory are used to model the
decisional process by which walking individuals select their velocity
direction. Crowd heterogeneity is modeled by dividing th...

In this work, an optimization based approach presented in Berrone et al. (2013, 2014) [10–12] for Discrete Fracture Network simulations is coupled with the Virtual Element Method (VEM) for the space discretization of the underlying Darcy law. The great flexibility of the VEM in handling rather general polygonal elements allows, in a natural way, fo...

In recent papers [1,2] the authors introduced a new method for
simulating subsurface flow in a system of fractures based on a
PDE-constrained optimization reformulation, removing all difficulties
related to mesh generation and providing an easily parallel approach to
the problem. In this paper we further improve the method removing the
constraint o...

In this paper a numerical method for the simulation of the steady-state fluid flow in discrete fracture networks is described. It is based on the use of non-conforming meshes, enrichment functions and an optimization procedure. The meshing process is performed on each fracture independently of the other fractures, i.e. without geometrical conformit...

We investigate a new numerical approach for the computation of the three-dimensional flow in a discrete fracture network that does not require a conforming discretization of partial differential equations on complex three-dimensional systems of planar fractures. The discretization within each fracture is performed independently of the discretizatio...

Following the approach introduced by the authors in [SIAM J. Sci. Comput., 35, B487–B510 (2013; Zbl 1266.65188)], we consider the formulation of the problem of fluid flow in a system of fractures as a PDE constrained optimization problem, with discretization performed using suitable extended finite elements; the method allows independent meshes on...

The aim of the present paper is to investigate the viability of macroscopic traffic models for modeling and testing different traffic scenarios, in order to define the impact on air quality of different strategies for the reduction of traffic emissions. To this aim, we complement a well assessed traffic model on networks (Garavello and Piccoli (200...

We present a new marking strategy, named the conditional marking strategy, to be employed in the adaptive finite element approximation of distributed control constrained problems governed by second-order elliptic partial differential equations. The key feature of the conditional marking strategy is the possibility of dynamically choosing among sepa...

The flow past rectangular cylinders has been investigated by two different numerical techniques, an adaptive finite-element (AFEM) and a finite-volume method (FVM). A square and a rectangular cylinder with width-to-height equal to 5 are taken into account. 2D computations have been performed for different Reynolds numbers in order to consider diffe...

An integrated methodology evaluating the impact of the urban air pollution on human health is presented. From traffic emission data, background pollution level and meteorological data the pollutant concentration distribution within the street network is calculated by the urban scale dispersion model SIRANE and the potential health impact on populat...

In this paper we propose two error indicators aimed at estimating the space discretization error and the time discretization error for the unsteady Navier–Stokes equations. We define a space error indicator for evaluating the quality of the mesh and a time error indicator for evaluating the time discretization error. Moreover, we verify the reliabi...