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

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Project 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. "

Original text from CORDIS.

Participants

• NATIONAL RESEARCH COUNCIL OF ITALY · BOLOGNACoordinatorItaly
• AACHEN UNIVERSITY OF TECHNOLOGY · AACHENGermany
• CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE · PARISFrance
• INSTITUT NATIONAL POLYTECHNIQUE DE GRENOBLE · GRENOBLEFrance
• POLITECNICO DI TORINO · TORINOItaly
• RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAET BONN · BONNGermany
• SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZUERICH · ZURICHSwitzerland
• TECHNISCHE UNIVERSITAET CHEMNITZ · CHEMNITZGermany
• THE BOARD OF REGENTS OF THE UNIVERSITY OF WISCONSCIN SYSTEMS · MADISONUnited States
• UNIVERSITAT DE VALENCIA · BURJASOTSpain
• UNIVERSITE PIERRE ET MARIE CURIE - PARIS VI · PARISFrance
• UNIVERSITY OF WALES - BANGOR · BANGOR (GWYNEDD)United Kingdom
• UTRECHT UNIVERSITY · UTRECHTNetherlands

Links

• View on CORDIS