73 citations · 364 across the 42 of their papers we have counts for
45 papers
Tensor Networks for Solving Realistic Time-independent Boltzmann Neutron Transport Equation
Duc P. Truong, Mario I. Ortega, Ismael Boureima +3
Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultr…
A -conforming arbitrary-order two-dimensional virtual element method for the fourth-order phase-field equation
Dibyendu Adak, Gianmarco Manzini, Hashem M. Mourad +2
We present a two-dimensional conforming virtual element method for the fourth-order phase-field equation. Our proposed numerical approach to the solution of this high-order phase-f…
High-order finite element method for atomic structure calculations
Ondřej Čertík, John E. Pask, Isuru Fernando +5
We introduce \texttt{featom}, an open source code that implements a high-order finite element solver for the radial Schrödinger, Dirac, and Kohn-Sham equations. The formulation acc…
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…
A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method
Lampros Svolos, Hashem M. Mourad, Gianmarco Manzini +1
Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure u…
The Virtual Element Method for the 3D Resistive Magnetohydrodynamic model
Lourenço Beirão da Veiga, Franco Dassi, Gianmarco Manzini +1
We present a four-field Virtual Element discretization for the time-dependent resistive Magnetohydrodynamics equations in three space dimensions, focusing on the semi-discrete form…
Conforming virtual element approximations of the two-dimensional Stokes problem
Gianmarco Manzini, Annamaria Mazzia
The virtual element method (VEM) is a Galerkin approximation method that extends the finite element method to polytopal meshes. In this paper, we present two different conforming v…
On arbitrarily regular conforming virtual element methods for elliptic partial differential equations
Paola Francesca Antonietti, Gianmarco Manzini, Simone Scacchi +1
The Virtual Element Method (VEM) is a very effective framework to design numerical approximations with high global regularity to the solutions of elliptic partial differential equa…
A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem
Gianmarco Manzini, Annamaria Mazzia
The Virtual Element Method (VEM) is a Galerkin approximation method that extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we present a conforming formula…
Polyhedral Mesh Quality Indicator for the Virtual Element Method
Tommaso Sorgente, Silvia Biasotti, Gianmarco Manzini +1
We present the design of a mesh quality indicator that can predict the behavior of the Virtual Element Method (VEM) on a given mesh family or finite sequence of polyhedral meshes (…
Extended virtual element method for two-dimensional linear elastic fracture
Elena Benvenuti, Andrea Chiozzi, Gianmarco Manzini +1
In this paper, we propose an eXtended Virtual Element Method (X-VEM) for two-dimensional linear elastic fracture. This approach, which is an extension of the standard Virtual Eleme…
Energy-conserving explicit and implicit time integration methods for the multi-dimensional Hermite-DG discretization of the Vlasov-Maxwell equations
Cecilia Pagliantini, Gianmarco Manzini, Oleksandr Koshkarov +2
We study the conservation properties of the Hermite-discontinuous Galerkin (Hermite-DG) approximation of the Vlasov-Maxwell equations. In this semi-discrete formulation, the total…
Virtual element approximation of two-dimensional parabolic variational inequalities
Dibyendu Adak, Gianmarco Manzini, Sundararajan Natarajan
We design a virtual element method for the numerical treatment of the two-dimensional parabolic variational inequality problem on unstructured polygonal meshes. Due to the expected…
Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces
Elena Bachini, Gianmarco Manzini, Mario Putti
We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial diffe…
The virtual element method for the coupled system of magneto-hydrodynamics
Sebastian Naranjo-Alvarez, Vrushali Bokil, Vitaliy Gyrya +1
In this work, we review the framework of the Virtual Element Method (VEM) for a model in magneto-hydrodynamics (MHD), that incorporates a coupling between electromagnetics and flui…
A review on arbitrarily regular conforming virtual element methods for elliptic partial differential equations
Paola Francesca Antonietti, Gianmarco Manzini, Simone Scacchi +1
The Virtual Element Method is well suited to the formulation of arbitrarily regular Galerkin approximations of elliptic partial differential equations of order , for any inte…
A decision-making machine learning approach in Hermite spectral approximations of partial differential equations
Lorella Fatone, Daniele Funaro, Gianmarco Manzini
The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains, are strongly affected by the amp…
Stabilization of the nonconforming virtual element method
Silvia Bertoluzza, Gianmarco Manzini, Micol Pennacchio +1
We address the issue of designing robust stabilization terms for the nonconforming virtual element method. To this end, we transfer the problem of defining the stabilizing bilinear…
VEM and the Mesh
Tommaso Sorgente, Daniele Prada, Daniela Cabiddu +6
In this work we report some results, obtained within the framework of the ERC Project CHANGE, on the impact on the performance of the virtual element method of the shape of the pol…
Stability and conservation properties of Hermite-based approximations of the Vlasov-Poisson system
Daniele Funaro, Gianmarco Manzini
Spectral approximation based on Hermite-Fourier expansion of the Vlasov-Poisson model for a collisionless plasma in the electro-static limit is provided, by including high-order ar…
The role of mesh quality and mesh quality indicators in the Virtual Element Method
Tommaso Sorgente, Silvia Biasotti, Gianmarco Manzini +1
Since its introduction, the Virtual Element Method (VEM) was shown to be able to deal with a large variety of polygons, while achieving good convergence rates. The regularity assum…
The conforming virtual element method for polyharmonic and elastodynamics problems: a review
Paola Francesca Antonietti, Gianmarco Manzini, Ilario Mazzieri +2
In this paper, we review recent results on the conforming virtual element approximation of polyharmonic and elastodynamics problems. The structure and the content of this review is…
Virtual elements for Maxwell's equations
L. Beirão da Veiga, F. Dassi, G. Manzini +1
We present a low order virtual element discretization for time dependent Maxwell's equations, which allow for the use of general polyhedral meshes. Both the semi- and fully-discret…
The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations
Oleksandr Koshkarov, Gianmarco Manzini, Gian Luca Delzanno +2
We discuss the development, analysis, implementation, and numerical assessment of a spectral method for the numerical simulation of the three-dimensional Vlasov-Maxwell equations.…