Sparse data structure design for wavelet-based methods

CEA, IRFM, F-13108 Saint − Paul − lez  −  Durance, France. University of Strasbourg & INRIA/Calvi project, 7 rue Descartes, 67084 Strasbourg Cedex, France,
e-mail: guillaume.latu@cea.fr

Abstract

This course gives an introduction to the design of efficient datatypes for adaptive wavelet-based applications. It presents some code fragments and benchmark technics useful to learn about the design of sparse data structures and adaptive algorithms. Material and practical examples are given, and they provide good introduction for anyone involved in the development of adaptive applications. An answer will be given to the question: how to implement and efficiently use the discrete wavelet transform in computer applications? A focus will be made on time-evolution problems, and use of wavelet-based scheme for adaptively solving partial differential equations (PDE). One crucial issue is that the benefits of the adaptive method in term of algorithmic cost reduction can not be wasted by overheads associated to sparse data management.