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Non-linear approximation and adaptivity: breaking complexity in numerical modelling and data representation

Non-linear approximation and adaptivity: breaking complexity in numerical modelling and data representation

Objective

The main research objective of this network is the joint development, analysis, implementation and optimization of a variety of mathematical concepts and computational tools that help "breaking complexity" in a variety of scientific computing tasks. Such tasks include both explicit data compression, as encountered in signal and image processing, and numerical simulation based on a mathematical model such as a partial differential or integral equation. In this last case, the object of interest is implicitly given by the model, and its compression needs to be optimally intertwined with the solution process. In both situations, we aim at developing mathematical representations, tailored data structures and fast resolution/processing algorithms, which are capable of optimally capturing (in an infonnation theoretic sense) the possible hidden simplicity of the underlying object to be stored, processed or computed. On a theoretical level, we shall gravitate around the pivoting mathematical concept of "nonlinear approximation" with the aim of fully understanding the process of adaptively representing classes of functions by N optimally chosen parameters. On a more practical level, we shall investigate practical realizations of such optimal representations, which can be implemented by fast algorithms. Classical instances include adaptive finite elements and more recently wavelets, which are still the source of theoretical and practical limitations when dealing with complicated domains and anisotropy singularities. We shall investigate these difficulties and come out with robust adaptive discretization tools that are in addition well fitted for specific problems: variational discretizations of PDE's arising in real life applications, progressive encoding in multimedia, noise reduction and inverse problems in medical imaging.

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Coordinator

NATIONAL RESEARCH COUNCIL OF ITALY

Address

Via De Marini 6
16149 Genova

Italy

Administrative Contact

Brezzi PROF. FRANCO

Participants (12)

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AACHEN UNIVERSITY OF TECHNOLOGY

Germany

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE

France

INSTITUT NATIONAL POLYTECHNIQUE DE GRENOBLE

France

POLITECNICO DI TORINO

Italy

RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAET BONN

Germany

SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZUERICH

Switzerland

TECHNISCHE UNIVERSITAET CHEMNITZ

Germany

THE BOARD OF REGENTS OF THE UNIVERSITY OF WISCONSCIN SYSTEMS

United States

UNIVERSITAT DE VALENCIA

Spain

UNIVERSITE PIERRE ET MARIE CURIE - PARIS VI

France

UNIVERSITY OF WALES - BANGOR

United Kingdom

UTRECHT UNIVERSITY

Netherlands

Project information

Grant agreement ID: HPRN-CT-2002-00286

  • Start date

    1 October 2002

  • End date

    31 March 2006

Funded under:

FP5-HUMAN POTENTIAL

  • Overall budget:

    € 1 500 000

  • EU contribution

    € 1 383 000

Coordinated by:

NATIONAL RESEARCH COUNCIL OF ITALY

Italy