75 citations · 369 across the 32 of their papers we have counts for
32 papers · 1 filter
A Fictitious Domain Formulation with Bubble Enrichment
Stefano Berrone, Lorenzo Neva, Stefano Scialò +1
The fictitious domain method offers a powerful alternative to circumvent complex mesh generation process by embedding the complex physical domain into a simpler, non-matching backg…
A 3D-1D Virtual Element Method for Modeling Root Water Uptake
Stefano Berrone, Stefano Ferraris, Denise Grappein +2
An optimization-based strategy is proposed for coupling three-dimensional and one-dimensional problems (3D-1D coupling) in the context of soil-root interaction simulations. This st…
The lowest-order Neural Approximated Virtual Element Method on polygonal elements
Stefano Berrone, Moreno Pintore, Gioana Teora
The lowest-order Neural Approximated Virtual Element Method on polygonal elements is proposed here. This method employs a neural network to locally approximate the Virtual Element…
A stabilized three fields formulation for Discrete Fracture Networks
Stefano Berrone, Silvia Bertoluzza, Stefano Scialò
We propose a hybridized domain decomposition formulation of the discrete fracture network model, allowing for independent discretization of the individual fractures. A natural norm…
3D Adaptive VEM with stabilization-free a posteriori error bounds
Stefano Berrone, Davide Fassino, Fabio Vicini
The present paper extends the theory of Adaptive Virtual Element Methods (AVEMs) to the three-dimensional meshes showing the possibility to bound the stabilization term by the resi…
Meshfree Variational Physics Informed Neural Networks (MF-VPINN): an adaptive training strategy
Stefano Berrone, Moreno Pintore
In this paper, we introduce a Meshfree Variational-Physics-Informed Neural Network. It is a Variational-Physics-Informed Neural Network that does not require the generation of the…
Mesh Optimization for the Virtual Element Method: How Small Can an Agglomerated Mesh Become?
Tommaso Sorgente, Stefano Berrone, Silvia Biasotti +3
We present an optimization procedure for generic polygonal or polyhedral meshes, tailored for the Virtual Element Method (VEM). Once the local quality of the mesh elements is analy…
Effective polygonal mesh generation and refinement for VEM
Stefano Berrone, Fabio Vicini
In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorit…
The lowest-order Neural Approximated Virtual Element Method
Stefano Berrone, Davide Oberto, Moreno Pintore +1
We introduce the Neural Approximated Virtual Element Method, a novel polygonal method that relies on neural networks to eliminate the need for projection and stabilization operator…
The Mixed Virtual Element Discretization for highly-anisotropic problems: the role of the boundary degrees of freedom
Stefano Berrone, Stefano Scialò, Gioana Teora
In this paper, we discuss the accuracy and the robustness of the mixed Virtual Element Methods when dealing with highly-anisotropic diffusion problems. In particular, we analyze th…
Orthogonal polynomial bases in the Mixed Virtual Element Method
Stefano Berrone, Stefano Scialò, Gioana Teora
The use of orthonormal polynomial bases has been found to be efficient in preventing ill-conditioning of the system matrix in the primal formulation of Virtual Element Methods (VEM…
Improving high-order VEM stability on badly-shaped elements
Stefano Berrone, Gioana Teora, Fabio Vicini
For the 2D and 3D Virtual Element Methods (VEM), a new approach to improve the conditioning of local and global matrices in the presence of badly-shaped polytopes is proposed. It d…
A first-order stabilization-free Virtual Element Method
Stefano Berrone, Andrea Borio, Francesca Marcon +1
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 mo…
Weak scalability of domain decomposition methods for discrete fracture networks
Stefano Berrone, Tommaso Vanzan
Discrete Fracture Networks (DFNs) are complex three-dimensional structures characterized by the intersections of planar polygonal fractures, and are used to model flows in fracture…
Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks
S. Berrone, C. Canuto, M. Pintore +1
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 Netw…
Mesh Quality Agglomeration algorithm for the Virtual Element Method applied to Discrete Fracture Networks
Tommaso Sorgente, Fabio Vicini, Stefano Berrone +3
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 Vi…
Solving PDEs by Variational Physics-Informed Neural Networks: an a posteriori error analysis
Stefano Berrone, Claudio Canuto, Moreno Pintore
We consider the discretization of elliptic boundary-value problems by variational physics-informed neural networks (VPINNs), in which test functions are continuous, piecewise linea…
A PDE-constrained optimization method for 3D-1D coupled problems with discontinuous solutions
Stefano Berrone, Denise Grappein, Stefano Scialò
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 contin…
Comparison of standard and stabilization free Virtual Elements on anisotropic elliptic problems
Stefano Berrone, Andrea Borio, Francesca Marcon
In this letter we compare the behaviour of standard Virtual Element Methods (VEM) and stabilization free Enlarged Enhancement Virtual Element Methods (EVEM) with the focus on s…
A new quality preserving polygonal mesh refinement algorithm for Virtual Element Methods
Stefano Berrone, Alessandro D'Auria
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 refi…
Agglomeration-based geometric multigrid schemes for the Virtual Element Method
Paola Francesca Antonietti, Stefano Berrone, Martina Busetto +1
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 syste…
Variational Physics Informed Neural Networks: the role of quadratures and test functions
Stefano Berrone, Claudio Canuto, Moreno Pintore
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…
Efficient partitioning and reordering of conforming virtual element discretizations for large scale Discrete Fracture Network flow parallel solvers
Stefano Berrone, Alice Raeli
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 efficien…
A gradient based resolution strategy for a PDE-constrained optimization approach for 3D-1D coupled problems
Stefano Berrone, Denise Grappein, Stefano Scialò +1
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 e…