Papers by Silvia Bertoluzza
Coupling of human visual system model and wavelet transform for image compression
Storage and Retrieval for Image and Video Databases, 1994
In this work we study a combination between wavelet transform and a model of the human visual sys... more In this work we study a combination between wavelet transform and a model of the human visual system both from the mathematical and the computational point of view. We will combine the two procedures in such a way that the computational complexity of the whole procedure is reduced for the maximum possible amount. The gaol is to improve the quality
Human vision model and wavelets for high-quality image compression
Fifth International Conference on Image Processing and its Applications, 1995
ABSTRACT
Lecture Notes in Computational Science and Engineering, 2005
The Fat Boundary Method (FBM) is a fictitious domain like method for solving partial differential... more The Fat Boundary Method (FBM) is a fictitious domain like method for solving partial differential equations in a domain with holes Ω \ Bwhere B is a collection of smooth open subsets -that consists in splitting the initial problem into two parts to be coupled via Schwartz type iterations: the solution, with a fictitious domain approach, of a problem set in the whole domain Ω, for which fast solvers can be used, and the solution of a collection of independent problems defined on narrow strips around the connected components of B, that can be performed fully in parallel. In this work, we give some results on a semi-discrete FBM in the framework of a finite element discretization, and we present some numerical experiments.
In this paper we present some results regarding wavelet interpolation. After discussing the chara... more In this paper we present some results regarding wavelet interpolation. After discussing the characterization of interpolating scaling functions, we give two examples of construction of an interpolation operator in the framework of a multiresolu tion analysis, the first obtained by constructing an interpolating scaling function in a given multiresolution analysis and the second based on the autocorrelation function of a compactly supported Daubechies wavelet. For both examples we give an estimate of the order of the interpolation error.
SIAM Journal on Numerical Analysis, 2000
A new functional framework for consistently stabilizing discrete approximations to convection-di ... more A new functional framework for consistently stabilizing discrete approximations to convection-di usion problems was recently proposed by the authors. The key ideas are the evaluation of the residual in an inner product of the type H ?1=2 (unlike classical SUPG methods, which use elemental weighted L 2 -inner products), and the realization of this inner product via explicitely computable multilevel decompositions of function spaces (such as those given by wavelets or hierarchical nite elements). In the present paper, we rst provide further motivations for our approach. Next, we carry on a detailed analysis of the method, which covers all regimes (convection-dominated and di usion-dominated). A consistent part of the analysis justi es the use of easily computable truncated forms of the stabilizing inner product. Numerical results, in close agreement with the theory, are given at the end of the paper.
Wavelet Methods for the Numerical Solution of Boundary Value Problems on the Interval
Wavelet Analysis and Its Applications, 1994
... In this way one Wavelets: Theory, Algorithms, and Applications 425 Charles K. Chui, Laura Mon... more ... In this way one Wavelets: Theory, Algorithms, and Applications 425 Charles K. Chui, Laura Montefusco, and Luigia Puccio (eds.), pp. 425-448. Copyright© 1994 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-174575-9 Page 444. ...
Transport Theory and Statistical Physics, 2000
We introduce two space-frequency adaptive strategies for the numerical approximation of the solut... more We introduce two space-frequency adaptive strategies for the numerical approximation of the solutions of quantum hydrodynamic models for semiconductors, based respectively on wavelets and wavelet packets. The two strategies are compared on a test case, and wavelet packets perform better in approximating with fewer degrees of freedom the high frequency dispersive oscillations of the solution.
Numerische Mathematik, 2007
In this paper we introduce a variant of the three-field formulation where we use only two sets of... more 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 −∆ u = g in Ω, our variables are i) the approximations u s h of u in each sub-domain Ω s (each on its own grid), and ii) an approximation ψ h of u on the skeleton (the union of the interfaces of the sub-domains) on an independent grid (that could often be uniform). The novelty is in the way to derive, from ψ h , the values of each trace of u s h on the boundary of each Ω s . We do it by solving an auxiliary problem on each ∂Ω s that resembles the mortar method but is more flexible. Under suitable assumptions, quasi-optimal error estimates are proved, uniformly with respect to the number and size of the subdomains. A preliminary version of the method and of its theoretical analysis has been presented in .
Numerische Mathematik, 2011
The Fat Boundary Method is a method of the Fictitious Domain class, which was proposed to solve e... more The Fat Boundary Method is a method of the Fictitious Domain class, which was proposed to solve elliptic problems in complex geometries with nonconforming meshes. It has been designed to recover optimal convergence at any order, despite of the non-conformity of the mesh, and without any change in the discrete Laplace operator on the simple shape domain. We propose here a detailed proof of this high-order convergence, and propose some numerical tests to illustrate the actual behaviour of the method.
Journal of Fourier Analysis and Applications, 2003
We present a new approach to the construction of orthonormal wavelets on the interval which allow... more 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 to construct wavelets for ]0, 1[ also at large scales in such a way that, in the range of validity of the existing constructions, the two approaches give the same result.
Wavelet Stabilization and Preconditioning for Domain Decomposition
The aim of this paper is to propose a stabilization technique in order to circumventthe two inf--... more The aim of this paper is to propose a stabilization technique in order to circumventthe two inf--sup conditions needed for stability of the discretization of the ThreeFields Formulation for domain decomposition methods [BM93, BM94]. Realization ofthis technique in terms of wavelets is presented. Furthermore, the resulting discreteproblem is shown to admit an asymptotically optimal preconditioner also based onwavelets.Key words: Three
ESAIM: Mathematical Modelling and Numerical Analysis, 2001
Abstract. This paper deals with the use of wavelets in the framework of the Mortar method. We fir... more Abstract. This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and ...
Buckling analysis of laminated plates by wavelets
Computers & Structures, 2011
This paper addresses, for the first time, the buckling analysis of isotropic and laminated plates... more 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 numerical approach is based on collocation with wavelets. It is shown that the present method produces highly accurate critical loads and modes.
A dynamically adaptive wavelet method for solving partial differential equations
Computer Methods in Applied Mechanics and Engineering, 1994
ABSTRACT
Computer Methods in Applied Mechanics and Engineering, 2005
In this paper we propose and study a subgrid model for linear convection-diffusion-reaction equat... more 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 residual from coarser scales using a computed solution on a finest scale as reference. We show in experiments that a solution with subgrid model on a scale h in most cases corresponds to a solution without subgrid model on a scale less than h/4. We also present error estimates for the modeling error in terms of modeling residuals.
A study of bending deformations of sandwich plates using a layerwise theory of laminated or sandw... more 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 accurate results. Numerical results for symmetric laminated composite and sandwich plates are presented and discussed.
A high order collocation method for the static and vibration analysis of composite plates using a first-order theory
Composite Structures, 2009
A study of static deformations and free vibrations of shear flexible isotropic and laminated comp... more A study of static deformations and free vibrations of shear flexible isotropic and laminated composite plates with a first-order shear deformation theory is presented. The analysis is based on collocation with a Deslaurier Dubuc interpolating basis to produce highly accurate results. Numerical results for isotropic and symmetric laminated composite plates are presented and discussed for various thickness-to-length ratios. The high
Applied Numerical Mathematics, 2000
The numerical solution of partial di erential equations involves the computation of integrals of ... more The numerical solution of partial di erential equations involves the computation of integrals of products of given functions and (derivatives of) trial and test functions. We study this problem using adaptively chosen wavelet bases. Firstly, we reduce this problem to the computation of 1{dimensional integrals. Then, we consider appropriate adaptive approximations and study the induced error. Finally, we present an algorithm for computing these integrals and give numerical results.
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Papers by Silvia Bertoluzza