The hybrid high-order method for polytopal meshes

DA Di Pietro, J Droniou - Number 19 in Modeling, Simulation and …, 2020 - Springer
Originally introduced in [146, 158], Hybrid High-Order (HHO) methods provide a framework
for the discretisation of models based on Partial Differential Equations (PDEs) with features …

hp-version discontinuous Galerkin methods on polygonal and polyhedral meshes

A Cangiani, EH Georgoulis… - Mathematical Models and …, 2014 - World Scientific
An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical
solution of second-order elliptic partial differential equations on general computational …

Numerical modeling of seismic waves by discontinuous spectral element methods

PF Antonietti, A Ferroni, I Mazzieri… - ESAIM: Proceedings …, 2018 - esaim-proc.org
We present a comprehensive review of Discontinuous Galerkin Spectral Element (DGSE)
methods on hybrid hexahedral/tetrahedral grids for the numerical modeling of the ground …

High–order discontinuous Galerkin methods on polyhedral grids for geophysical applications: seismic wave propagation and fractured reservoir simulations

PF Antonietti, C Facciolà, P Houston, I Mazzieri… - Polyhedral methods in …, 2021 - Springer
We present a comprehensive review of the current development of discontinuous Galerkin
methods on polytopic grids (PolyDG) methods for geophysical applications, addressing as …

Ill‐conditioning in the virtual element method: Stabilizations and bases

L Mascotto - Numerical Methods for Partial Differential …, 2018 - Wiley Online Library
In this article, we investigate the behavior of the condition number of the stiffness matrix
resulting from the approximation of a 2D Poisson problem by means of the virtual element …

Numerical modeling of the brain poromechanics by high-order discontinuous Galerkin methods

M Corti, PF Antonietti, L Dede'… - … Models and Methods in …, 2023 - World Scientific
We introduce and analyze a discontinuous Galerkin method for the numerical modeling of
the equations of Multiple-Network Poroelastic Theory (MPET) in the dynamic formulation …

Agglomeration of polygonal grids using graph neural networks with applications to multigrid solvers

PF Antonietti, N Farenga, E Manuzzi, G Martinelli… - … & Mathematics with …, 2024 - Elsevier
Agglomeration-based strategies are important both within adaptive refinement algorithms
and to construct scalable multilevel algebraic solvers. In order to automatically perform …

Discontinuous Galerkin approximation of flows in fractured porous media on polytopic grids

PF Antonietti, C Facciola, A Russo, M Verani - SIAM Journal on Scientific …, 2019 - SIAM
We present a numerical approximation of Darcy's flow through a fractured porous medium
which employs discontinuous Galerkin methods on polytopic grids. For simplicity, we …

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics …

R Saye - Journal of Computational Physics, 2017 - Elsevier
In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG)
framework is developed for fluid interface dynamics, facilitating precise computation of …

[HTML][HTML] Polytopal discontinuous Galerkin discretization of brain multiphysics flow dynamics

I Fumagalli, M Corti, N Parolini, PF Antonietti - Journal of Computational …, 2024 - Elsevier
A comprehensive mathematical model of the multiphysics flow of blood and Cerebrospinal
Fluid (CSF) in the brain can be expressed as the coupling of a poromechanics system and …