Author	Urban, Karsten. author
Title	Wavelets in Numerical Simulation [electronic resource] : Problem Adapted Construction and Applications / by Karsten Urban
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002
Connect to	http://dx.doi.org/10.1007/978-3-642-56002-6
Descript	XV, 181 p. online resource

This research monograph addresses recent developments of wavelet concepts in the context of large scale numerical simulation. It offers a systematic attempt to exploit the sophistication of wavelets as a numerical tool by adapting wavelet bases to the problem at hand. This includes both the construction of wavelets on fairly general domains and the adaptation of wavelet bases to the particular structure of function spaces governing certain variational problems. Those key features of wavelets that make them a powerful tool in numerical analysis and simulation are clearly pointed out. The particular constructions are guided by the ultimate goal to ensure the key features also for general domains and problem classes. All constructions are illustrated by figures and examples are given

1 Wavelet Bases -- 1.1 Wavelet Bases in L2(?) -- 1.2 Wavelets on the Real Line -- 1.4 Tensor Product Wavelets -- 1.5 Wavelets on General Domains -- 1.6 Vector Wavelets -- 2 Wavelet Bases for H(div) and H(curl) -- 2.1 Differentiation and Integration -- 2.2 The Spaces H(div) and H (curl) -- 2.3 Wavelet Systems for H (curl) -- 2.4 Wavelet Bases for H(div) -- 2.5 Helmholtz and Hodge Decompositions -- 2.6 General Domains -- 2.7 Examples -- 3 Applications -- 3.1 Robust and Optimal Preconditioning -- 3.2 Analysis and Simulation of Turbulent Flows -- 3.3 Hardening of an Elastoplastic Rod -- References -- List of Figures -- List of Tables -- List of Symbols