Wavelets on General Domains
Karsten Urban · Oxford University Press eBooks · 2008
Abstract The construction of wavelets on general domains is performed in three steps. This chapter starts by introducing the construction of scaling functions and wavelets on bounded univariate intervals. Next, building tensor products allows constructing wavelets on rectangular domains. Finally, the Wavelet Element Method (WEM) is introduced. Using non-overlapping domain decomposition and mapping to the unit cube the WEM matches scaling functions and wavelets across the interfaces of the subdomains in order to obtain a globally continuous basis. The realization of the construction in terms of software is shown as well how to use this software.