Silvia Bertoluzza

Research Director

Research Activity

Numerical Method for the solution of PDEs
  • Polytopal Discretization Methods (Discontinuous galerkin, Virtual Elements)
  • Domain decomposition
  • Fictitious Domain methods
  • Stabilization of unstable numerical methods
  • Wavelet methods
Other interests
  • Image compression
  • Image registration

Preprints

  • S. Bertoluzza, M. Pennacchio, D. Prada, Weakly imposed Dirichlet boundary conditions for 2D and 3D Virtual Elements, arxiv.org/abs/2112.15039, 2021.
  • S. Bertoluzza, M. Manzini, M. Pennacchio, D. Prada,Stabilization of the Nonconforming Virtual Element Method, arxiv.org/abs/2103.03742, 2021, to appear on Computers and Mathematics with Applications
  • S. Bertoluzza, E. Burman, C. He, An a posteriori error estimate of the outer normal derivative using dual weights, arxiv.org/abs/2008.07690, 2020, to appear on SIAM J. Numer. Anal.
  • S. Bertoluzza, I. Perugia, D. Prada, A p-robust Polygonal Discontinuous Galerkin Method with Minus One Stabilization, arxiv.org/abs/2012.11276, 2020, to appear on Mathematical Models and Methods in Applied Sciences
  • S. Bertoluzza, Algebraic representation of dual scalar products and stabilization of saddle point problems, arxiv.org/abs/1906.01296, 2019, to appear on Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.


Projects

PRIN 2017 - 201744KLJL_003

CHANGE

IHP

TMR Network

Analisi numerica e calcolo scientifico

GNCS Giovani ricercatori 2016

INdAM

TECHEDGE

Numerical Methods for PDE'S

FIRB CASHMA


Publications

2022, Journal article
A theoretical and numerical analysis of a Dirichlet-Neumann domain decomposition method for diffusion problems in heterogeneous media
A. Viguerie, S. Bertoluzza, A. Veneziani, and F. Auricchio
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing...

CNR@People | DOI: 10.1016/j.apnum.2021.11.012
2021, Journal article
A polygonal discontinuous Galerkin method with minus one stabilisation
S. Bertoluzza and D. Prada
We propose a discontinuous Galerkin method for the Poisson equation on polygonal tessel- lations in two dimensions, stabilized by penalizing, locally in each element K, a residual term involving the f...

CNR@People | DOI: 10.1051/m2an/2020059
2021, Journal article
Benchmarking the geometrical robustness of a Virtual Element Poisson solver
M.Attene,S. Biasotti, S. Bertoluzza, D. Cabiddu, M. Livesu, G. Patanè, M. Pennacchio, D. Prada, and M. Spagnuolo
Polytopal Element Methods (PEM) allow us solving differential equations on generalpolygonal and polyhedral grids, potentially offering great flexibility to meshgeneration algorithms. Differently from ...

CNR@People | DOI: 10.1016/j.matcom.2021.07.018
2020, Journal article
A Fat boundary-type method for localized nonhomogeneous material problems
A. Viguerie, S. Bertoluzza, and F. Auricchio
Problems with localized nonhomogeneous material properties arise frequently in many applications and are a well-known source of difficulty in numerical simulations. In certain applications (including ...

CNR@People | DOI: 10.1016/j.cma.2020.112983
2020, Journal article
FETI-DP for the Three Dimensional Virtual Element Method
S. Bertoluzza, M. Pennacchio, and D. Prada
We deal with the finite element tearing and interconnecting dual primal precon- ditioner for elliptic problems discretized by the virtual element method. We extend the result of [S. Bertoluzza, M. Pen...

CNR@People | DOI: 10.1137/18M1233303
2020, Journal article
The virtual element method for a minimal surface problem
P.F. Antonietti, S. Bertoluzza, D. Prada, and M. Verani
In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing the area of a surfac...

CNR@People | DOI: 10.1007/s10092-020-00388-0
2020, Journal article
Wavelets and convolution quadrature for the efficient solution of a 2D space-time BIE for the wave equation
S. Bertoluzza, S. Falletta, and L. Scuderi
We consider a wave propagation problem in 2D, reformulated in terms of a Boundary In- tegral Equation (BIE) in the space-time domain. For its solution, we propose a numeri- cal scheme based on a convo...

CNR@People | DOI: 10.1016/j.amc.2019.124726
2019, Journal article
FEM Solution of exterior elliptic problems with weakly enforced integral non reflecting boundary conditions
S. Bertoluzza and S. Falletta
We consider a coupling of finite element (FEM) and boundary element (BEM) methods for the solution of the Poisson equation in unbounded domains. We propose a numerical method that approximates the sol...

CNR@People | DOI: 10.1007/s10915-019-01048-4
2019, Journal article
High order VEM on curved domains
S. Bertoluzza, M. Pennacchio, and D. Prada
We deal with the virtual element method (VEM) for solving the Poisson equation on a domain $Omega$ with curved boundaries. Given a polygonal approximation $Omega_h$ of the domain $Omega$, the standa...

CNR@People | DOI: 10.4171/RLM/853
2018, Journal article
A new class of wavelet-based metrics for image similarity assessment
M.G. Albanesi, R. Amadeo, S. Bertoluzza, and G. Maggi
In this paper, we propose a new class of image similarity metrics based on a wavelet decomposition. By suitably combining weighted contributions of the different dyadic frequency bands, we define a cl...

CNR@People | DOI: 10.1007/s10851-017-0745-1
2018, Journal article
Local error analysis for the Stokes equations with a punctual source term
S. Bertoluzza, A. Decoene, L. Lacouture, and S. Martin
The solution of the Stokes problem with a punctual force in source term is not H(1)xL(2) and therefore the approximation by a finite element method is suboptimal. In the case of Poisson problem with a...

CNR@People | DOI: 10.1007/s00211-018-0976-0
2018, Journal article
Local error estimates of the finite element method for an elliptic problem with a Dirac source term
S. Bertoluzza, A. Decoene, L. Lacouture, and S. Martin
The solutions of elliptic problems with a Dirac measure right-hand side are not H1 in dimension d ? {2, 3} and therefore the convergence of the finite element solutions is suboptimal in the L2-norm. I...

CNR@People | DOI: 10.1002/num.22186
2017, Journal article
A new construction of boundary interpolating wavelets for fourth order problems
S. Bertoluzza and V. Perrier
In this article we introduce a new mixed Lagrange-Hermite interpolating wavelet family on the interval, to deal with two types (Dirichlet and Neumann) of boundary conditions. As this construction is a...

CNR@People | DOI: 10.1007/s10440-017-0110-9
2017, Journal article
BDDC and FETI-DP for the virtual element method
S. Bertoluzza, M. Pennacchio, and D. Prada
We build and analyze balancing domain decomposition by constraint and finite element tearing and interconnecting dual primal preconditioners for elliptic problems discretized by the virtual element me...

CNR@People | DOI: 10.1007/s10092-017-0242-3
2017, Journal article
Boundary conditions involving pressure for the Stokes problem and applications in computational hemodynamics
S. Bertoluzza, V. Chabannes, C. Prud'homme, and M. Szopos
Pressure driven flows typically occur in hydraulic networks, e.g. oil ducts, water supply, biological flows, microfluidic channels etc. However, Stokes and Navier-Stokes problems are most often studie...

CNR@People | DOI: 10.1016/j.cma.2017.04.024
2016, Journal article
A conservative slide line method for cell-centered semi-lagrangian and ALE schemes in 2D
S. Bertoluzza, S. Del Pino, and E. Labourasse
In this paper, we propose a new cell-center method to treat sliding of compressible fluid domains. We describe at first the theoretical framework based on [S. Del Pino, C. R. Acad. Sci. Paris, Ser. I ...

CNR@People | DOI: 10.1051/m2an/2015037
2016, Journal article
Analysis of a mesh dependent stabilization for the three fields domain decomposition method
S. Bertoluzza
We consider a stabilized version of the three fields domain decomposition method in the finite element framework, by a variant of the stabilization proposed in [2]. Under fairly general conditions on ...

CNR@People | DOI: 10.1007/s00211-015-0742-5
2016, Journal article
Substructuring preconditioners for h-p Mortar FEM
S. Bertoluzza, M. Pennacchio, C. Prud'homme, and A. Samake
We build and analyze a substructuring preconditioner for the Mortar method, applied to elliptic problems, in the h-p finite element framework. Particular attention is given to the construction of the ...

CNR@People | DOI: 10.1051/m2an/2015065
2015, Journal article
Substructuring preconditioners for an h-p domain decomposition method with interior penalty mortaring
P. F. Antonietti, B. Ayuso de Dios, S. Bertoluzza, and M. Pennacchio
We propose and study an iterative substructuring method for an h-p Nitsche-type discretization, following the original approach introduced in Bramble et al. Math. Comp. 47(175):103-134, (1986) for con...

CNR@People | DOI: 10.1007/s10092-014-0117-9
2011, Journal article
A wavelet collocation approach for the analysis of laminated shells
A.J.M. Ferreira, L.M. Castro, and S. Bertoluzza
The static deformations and the natural frequencies of doubly-curved composite shells are computed by the first-order theory of Donnell. A meshless method based on wavelet collocation is used for disc...

CNR@People | DOI: 10.1016/j.compositesb.2010.06.003
2011, Journal article
Analysis of plates on Winkler foundation by wavelet collocation
A.J.M. Ferreira, L.M. Castro, and S. Bertoluzza
N/A

CNR@People | DOI: 10.1007/s11012-010-9341-9
2011, Journal article
Analysis of some injection bounds for Sobolev spaces by wavelet decomposition
S. Bertoluzza and S. Falletta
We consider the Sobolev spaces Hs(?) and and the Besov spaces , where ? is a sufficiently regular (see Lemma 2) subdomain of R2. It is well known that for the values of s?[0,1/2) the two Sobolev spac...

CNR@People | DOI: 10.1016/j.crma.2011.02.015
2011, Journal article
Analysis of the fully discrete fat boundary method
S. Bertoluzza, M. Ismail, and B. Maury
The Fat Boundary Method is a method of the Fictitious Domain class, which was proposed to solve elliptic problems in complex geometries with non-conforming meshes. It has been designed to recover opti...

CNR@People | DOI: 10.1007/s00211-010-0317-4
2011, Journal article
Buckling analysis of laminated plates by wavelets
A.J.M. Ferreira, L.M. Castro, C.M. Roque, J.N. Reddy, and S. Bertoluzza
This paper addresses, for the first time, the buckling analysis of isotropic and laminated plates that are subjected to partial inplane edge loads by a first-order shear deformation theory. The numeri...

CNR@People | DOI: 10.1016/j.compstruc.2011.01.007
2010, Journal article
A wavelet collocation method for the static analysis of sandwich plates using a layerwise theory
L.M.S. Castro, A.J.M. Ferreira, S. Bertoluzza, R.C. Batra, and J.N. Reddy
A study of bending deformations of sandwich plates using a layerwise theory of laminated or sandwich plates is presented. The analysis is based on a wavelet collocation technique to produce highly acc...

CNR@People | DOI: 10.1016/j.compstruct.2010.01.021
2009, Journal article
A high order collocation method for the static and vibration analysis of composite plates using a first-order theory
Ferreira A.J.M., Castro L.M.S., Bertoluzza S.
A study of static deformations and free vibrations of shear flexible isotropic and laminated compositeplates with a first-order shear deformation theory is presented. The analysis is based on collocat...

CNR@People | DOI: 10.1016/j.compstruct.2008.09.006
2008, Journal article
Efficient design of residual-based stabilization techniques for three fields domain decomposition method
S. Bertoluzza, S. Falletta, and G. Manzini
We consider a class of residual-based stabilization schemes (including the one usingwavelets) for the three fields formulation of domain decomposition of elliptic boundaryvalue problems. These schemes...

CNR@People
2007, Journal article
Analysis of substructuring preconditioners for mortar methods in an abstract framework
S. Bertoluzza and M. Pennacchio
A class of preconditioners for the linear system arising from the discretization by the mortar method is studied. We focus on the substructuring approach already applied by Achdou et al. [Y. Achdou, Y...

CNR@People | DOI: 10.1016/j.aml.2006.02.029
2007, Journal article
The method of mothers for non-overlapping non-matching DDM
Bertoluzza S., Brezzi F., Sangalli G.
In this paper we introduce a variant of the three-field formulation where we use only two sets of variables. Considering, to fix the ideas, the Poisson equationwith homogeneous Dirichlet boundary cond...

CNR@People | DOI: 10.1007/s00211-007-0090-1
2006, Journal article
Local boundary estimates for the Lagrange multiplier discretization of a Dirichlet boundary value problem with application to domain decomposition
Bertoluzza S.
We give an estimate on the error resulting from approximatingthe outer normal derivative of the solution of a second-order partial differentialequation with the Lagrange multiplier obtained in using t...

CNR@People | DOI: 10.1007/s10092-006-0115-7
2005, Journal article
Recent developments in wavelet methods for the solution of PDE's
Bertoluzza S.
N/A

CNR@People
2005, Journal article
Subgrid modeling for convection-diffusion-reaction in one space dimension using a Haar multiresolution analysis
Hoffman J., Johnson C., Bertoluzza S.
In this paper we propose and study a subgrid model for linear convection-diffusion-reaction equations with fractal rough coefficients. The subgrid model is based on scale extrapolation of a modeling r...

CNR@People | DOI: 10.1016/j.cma.2003.08.016
2004, Journal article
Preconditioning the mortar method by substructuring: the high order case
S. Bertoluzza and M. Pennacchio
We analyze a class of preconditioners for the mortar method, based on substructuring. After splitting in a suitable way the degrees of freedom in interior, edge and vertex, we study the performance of...

CNR@People | DOI: 10.1002/anac.200410008
2004, Journal article
Substructuring preconditioners for the three fields domain decomposition methods
Bertoluzza S.
We study a class of preconditioners based on substructuring, forthe discrete Steklov-Poincare operator arising in the three fields formulation ofdomain decomposition in two dimensions. Under extremely...

CNR@People
2004, Journal article
The wavelet mortar method in the adaptive framework
Bertoluzza S., Piquemal A.S.
N/A

CNR@People
2003, Journal article
A non-linear Richardson algorithm for the solution of elliptic PDE's
Bertoluzza S.(1), Mazet S.(2), Verani M.(3)
We prove convergence of a computable adaptive wavelet algorithm for the solution of elliptic PDE's, which combines Richardson type iterations with non linear projection steps.

CNR@People
2003, Journal article
Analysis of a stabilized three-fields domain decomposition method
Bertoluzza, S.(1)
In this paper we prove that, for suitable choices of the bilinear form involved in the stabilization procedure, the stabilized three fields domain decomposition method proposed in the paper "Wave...

CNR@People
2003, Journal article
Building wavelets on ] 0,1 [ at large scales
Bertoluzza S.(1), Falletta S.(2)
We present a new approach to the construction of orthonormal wavelets on the interval which allows to overcome the ''non interacting boundaries'' restriction of existing constructions, and therefore t...

CNR@People
2003, Journal article
Convergence of a non-linear wavelet algorithm for the solution of PDE's.
Bertoluzza S., Verani M.
We prove convergence of an adaptive wavelet algorithm for the solution of elliptic PDE's, which combines Richardson type iterations with non linear projection steps.

CNR@People
2009, Book
Numerical solutions of partial differential equations
Bertoluzza S., Falletta S., Russo G., Shu C.-W.
N/A

CNR@People
2012, Essay or book chapter
Adaptive wavelet methods
S. Bertoluzza
Wavelet bases, initially introduced as a tool for signal and image processing, have rapidly obtained recognition in many different application fields. In this lecture notes we will describe some of th...

CNR@People | DOI: 10.1007/978-3-642-24079-9_1
2009, Essay or book chapter
Wavelets and partial differential equations
Bertoluzza S., Falletta S.
N/A

CNR@People
2020, Conference proceedings
Geometry description and mesh construction from medical imaging
M. G. Carlino, P. Ricka, M. Phan, S. Bertoluzza, M. Pennacchio, G. Patane' and M. Spagnuolo
We present a new method for defining and meshing patient-specfic domains from medicalimages. Our approach is based on an atlas image segmentation technique, and relies on the modularregistration algor...

CNR@People | DOI: 10.1051/proc/202067010
2019, Conference proceedings
FETI-DP preconditioners for the virtual element method on general 2D meshes
D. Prada, S. Bertoluzza, M. Pennacchio, and M. Livesu
We analyze the performance of a state-of-the-art domain decomposition approach, the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) method (Toselli and Widlund, Domain decomposition m...

CNR@People | DOI: 10.1007/978-3-319-96415-7_12
2017, Meeting abstracts
Patient-specific virtual simulator of tissue perfusion in the lamina cribrosa
L. Sala, C. Prud'homme, D. Prada, F. Salerni, C. Trophime, V. Chabannes, M. Szopos, R. Repetto, S. Bertoluzza, R. Sacco, A. Harris, and G. Guidoboni
Purpose Improper perfusion of the lamina cribrosa (LC) may lead to severe alterations of the visual function. LC perfusion parameters are difficult to estimate with non-invasive measurements and are a...

CNR@People | Link
2013, Conference proceedings
A Modular Registration Algorithm for Medical Images
S. Bertoluzza, S. Maggi, and S. Tomatis
The aim of this communication is to present the design of a code for image registration based on a modular structure which allows to easily combine and interchange different image models, transformati...

CNR@People | DOI: 10.1007/978-3-642-39094-4_53
2013, Conference proceedings
A parallel implementation of the Mortar Method in 2D and 3D
A. Samake, S. Bertoluzza, M. Pennacchio, C. Prud'homme, and C. Zaza
We present here the generic parallel computational framework in C++called Feel++for the mortar finite element method with the arbitrary number of subdomain partitions in 2D and 3D. An iterative method...

CNR@People | DOI: 10.1051/proc/201343014
2011, Conference proceedings
Domain decomposition strategies with black box subdomain solvers
S. Bertoluzza
In a non conforming domain decomposition framework we will discuss a strategy, based on a continuous version of FETI, for solving PDEs by resorting to commercial codes, without any need of modifying t...

CNR@People | DOI: 10.1063/1.3663513
2010, Meeting abstracts
Fictitious domain and high order discretizations: Optimality of the fat boundary method
Bertoluzza S.
N/A

CNR@People
2010, Meeting abstracts
Multigrid preconditioners for adaptive wavelet collocation
Bertoluzza S.
N/A

CNR@People
2007, Conference proceedings
Preconditioners for high order mortar methods based on substructuring
S. Bertoluzza and M. Pennacchio
A class of preconditioners for the Mortar Method based on substructuring is studied. We generalize the results of Achdou, Maday and Widlund [1], obtained for the case of order one finite elements, to ...

CNR@People | DOI: 10.1007/978-3-540-34469-8_62
2005, Conference proceedings
Non-matching grids and Lagrange multipliers
S. Bertoluzza, F. Brezzi, L.D. Marini, and G. Sangalli
In this paper we introduce a variant of the three-field formulation where we use only two sets of variables. Considering, to fix the ideas, the homogeneous Dirichlet problem for -Delta u = g in Omega,...

CNR@People | DOI: 10.1007/3-540-26825-1_1
2005, Conference proceedings
The Fat Boundary Method: semidiscrete scheme and some numerical experiments
Bertoluzza S., Ismail M., Maury B.
The Fat Boundary Method (FBM) is a fictitious domain likemethod for solving partial differential equations in a domain with holes ? B -where B is a collection of smooth open subsets - that consists i...

CNR@People
2003, Conference proceedings
Non conforming domain decomposition: the Steklov-Poincaré operator point of view
Bertoluzza S.
N/A

CNR@People
2010, Technical report
The mortar method with approximate constraint: a flexible tool for coupling hetherogeneous discretizations
S. Bertoluzza, S. Falletta
In the framework of an object oriented implementation we compare the classical version of the mortarmethod with a version where the weak continuity constraint is imposed in an approximate form via apr...

CNR@People
2008, Technical report
Adaptive wavelet collocation for plane elasticity problem
S. Bertoluzza and L. Castro
N/A

CNR@People
2008, Technical report
Approximation and super-approximation properties of weakly local spaces
S. Bertoluzza and G. Iovane
N/A

CNR@People
2006, Technical report
Residual based stabilization of the three fields domain decomposition method: implementation and numerical tests
S. Bertoluzza, S. Falletta, and G. Manzini
N/A

CNR@People
2004, Technical report
An object-oriented implementation of the mortar method with approximate constraint
S. Bertoluzza and S. Falletta
N/A

CNR@People
2004, Technical report
Comparing PCG with BiCG and BiCGStab for the linear system arising in the three fields domain decomposition methods
S. Bertoluzza, M.R. Mokhtarzadeh, R. Mokhtari, and N.G. Chegini
N/A

CNR@People
2002, Technical report
Adaptive wavelet collocation for elasticity: first results.
S. Bertoluzza and L. Castro
After recalling the definition and main ideas of the adaptive collocation scheme, we apply it to some test problems arising in two dimensional elasticity, and compare the results obtained with classic...

CNR@People
2002, Technical report
The mortar wavelet method: implementation and numerical tests.
S. Bertoluzza, S. Falletta, and V. Perrier
N/A

CNR@People