75 citations · 304 across the 24 of their papers we have counts for
26 papers
A Virtual Element Method for elliptic problems on trimmed background meshes
L. Beirão da Veiga, C. Canuto, R. H. Nochetto +2
We consider a two-dimensional piecewise domain that cuts through a quasi-uniform fixed polygonal background mesh, for instance made of quadrilaterals. A simple procedure base…
Optimal Surrogate Boundary Selection and Scalability Studies for the Shifted Boundary Method on Octree Meshes
Cheng-Hau Yang, Kumar Saurabh, Guglielmo Scovazzi +3
The accurate and efficient simulation of Partial Differential Equations (PDEs) in and around arbitrarily defined geometries is critical for many application domains. Immersed bound…
New Feedback Control and Adaptive Evolve-Filter-Relax Regularization for the Navier-Stokes Equations in the Convection-Dominated Regime
Maria Strazzullo, Francesco Ballarin, Traian Iliescu +1
We propose, analyze, and investigate numerically a novel feedback control strategy for high Reynolds number flows. For both the continuous and the discrete (finite element) setting…
Higher-order adaptive virtual element methods with contraction properties
Claudio Canuto, Davide Fassino
The realization of a standard Adaptive Finite Element Method (AFEM) preserves the mesh conformity by performing a completion step in the refinement loop: in addition to elements ma…
Weighted reduced order methods for uncertainty quantification in computational fluid dynamics
Julien Genovese, Francesco Ballarin, Gianluigi Rozza +1
In this manuscript we propose and analyze weighted reduced order methods for stochastic Stokes and Navier-Stokes problems depending on random input data (such as forcing terms, phy…
Adaptive VEM for variable data: convergence and optimality
L. Beirão da Veiga, C. Canuto, R. H. Nochetto +2
We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization…
A posteriori error analysis and adaptivity for a VEM discretization of the Navier-Stokes equations
Claudio Canuto, Davide Rosso
We consider the Virtual Element method (VEM) introduced by Beirão da Veiga, Lovadina and Vacca in 2016 for the numerical solution of the steady, incompressible Navier-Stokes equati…
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…
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…
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…
Equilibrium analysis of an immersed rigid leaflet by the virtual element method
L. Beirão da Veiga, C. Canuto, R. H. Nochetto +1
We study, both theoretically and numerically, the equilibrium of a hinged rigid leaflet with an attached rotational spring, immersed in a stationary incompressible fluid within a r…
Analysis of the Shifted Boundary Method for the Poisson Problem in General Domains
Nabil M. Atallah, Claudio Canuto, Guglielmo Scovazzi
The shifted boundary method (SBM) is an approximate domain method for boundary value problems, in the broader class of unfitted/embedded/immersed methods. It has proven to be quite…
The Second-Generation Shifted Boundary Method and Its Numerical Analysis
Nabil M. Atallah, Claudio Canuto, Guglielmo Scovazzi
Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary valu…
Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method
Moreno Pintore, Federico Pichi, Martin Hess +2
The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities…
A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square
Claudio Canuto, Ricardo H. Nochetto, Rob Stevenson +1
Both practice and analysis of adaptive -FEMs and -FEMs raise the question what increment in the current polynomial degree guarantees a -independent reduction of the G…
On p-Robust Saturation for hp-AFEM
Claudio Canuto, Ricardo H. Nochetto, Rob Stevenson +1
We consider the standard adaptive finite element loop SOLVE, ESTIMATE, MARK, REFINE, with ESTIMATE being implemented using the -robust equilibrated flux estimator, and MARK bein…
A hybrid model for large neural network description
Anna Cattani, Sergio Solinas, Claudio Canuto
The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain a…
Convergence and Optimality of hp-AFEM
Claudio Canuto, Ricardo H. Nochetto, Rob Stevenson +1
We design and analyze an adaptive -finite element method (hp-AFEM) in dimensions . The algorithm consists of iterating two routines: hp-NEARBEST finds a near-best -a…
Contraction and optimality properties of an adaptive Legendre-Galerkin method: the multi-dimensional case
Claudio Canuto, Valeria Simoncini, Marco Verani
We analyze the theoretical properties of an adaptive Legendre-Galerkin method in the multidimensional case. After the recent investigations for Fourier-Galerkin methods in a period…
On the decay of the inverse of matrices that are sum of Kronecker products
Claudio Canuto, Valeria Simoncini, Marco Verani
Decay patterns of matrix inverses have recently attracted considerable interest, due to their relevance in numerical analysis, and in applications requiring matrix function approxi…
Legendre-Gauss-Lobatto grids and associated nested dyadic grids
Kolja Brix, Claudio Canuto, Wolfgang Dahmen
Legendre-Gauss-Lobatto (LGL) grids play a pivotal role in nodal spectral methods for the numerical solution of partial differential equations. They not only provide efficient high-…
The derivation of continuum limits of neuronal networks with gap-junction couplings
Claudio Canuto, Anna Cattani
We consider an idealized network, formed by N neurons individually described by the FitzHugh-Nagumo equations and connected by electrical synapses. The limit for N to infinity of t…
Multilevel Preconditioning of Discontinuous-Galerkin Spectral Element Methods, Part I: Geometrically Conforming Meshes
Kolja Brix, Martin Campos Pinto, Claudio Canuto +1
This paper is concerned with the design, analysis and implementation of preconditioning concepts for spectral Discontinuous Galerkin discretizations of elliptic boundary value prob…
Robust Preconditioners for DG-Discretizations with Arbitrary Polynomial Degrees
Kolja Brix, Claudio Canuto, Wolfgang Dahmen
Discontinuous Galerkin (DG) methods offer an enormous flexibility regarding local grid refinement and variation of polynomial degrees for a variety of different problem classes. Wi…