In the last few year, new ideas related to multiscale decompositions and In the framework of the project we will put down a program of post-doctoral training, consisting in opening several post-doc positions in highly wavelet bases have appeared, fueled by a strong input of theoretical analysis and approximation theory. Several remarkable features of such qualified research centers (for a total of about 260 Man/Months). A program concepts seem to suggest that, if fully developed, the corresponding of doctoral studies consisting in intensive courses and summer schools methodology should be capable in the long run of advancing the frontiers. We feel that young researchers would greatly benefit from a training by leading experts in this higly interdisciplinary field, which will in numerical simulation.
The aim of this project is first to provide a addition help in broadening their horizons. In fact the expertise that they theoretical foundation addressing several crucial issues (which will be better specified in the proposal description). Secondly the project aims at will acquire applicable to fields as diverse as image processing, analysis of stochastic processes, denoising, fractals and multifractals, developing a class of innovative fast numerical schemes for the numerical solution of integral and partial differential equations. These new schemes which, though not directly included in the research project proposed, take advantage of the same tools and are of growing importance in the will combine on one hand high order approximation, and on the other adaptivity with respect to data, operators and solutions. They will be development of Numerical Analysis flexible enough to be adapted to a variety of complex problems in such areas as fluid dynamics, electromagnetism and elasticity.
Ultimately our goal is to develop efficient solvers for the numerical solution of complex industrial problems in fluid dynamic, chemical engineering, elasticiy and electromagnetism. We think that by pursuing a coordinated effort, the nine teams, eight from the EC and one in Switzerland which will participate to the project, having acquired complementary experiences on different aspects of the issues considered, will be able to succeed in these objectives.