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Hierarchical method for elliptic problems using wavelet

✍ Scribed by Cai, Zhiqiang ;Weinan, E.

Publisher
Wiley (John Wiley & Sons)
Year
1992
Tongue
English
Weight
369 KB
Volume
8
Category
Article
ISSN
0748-8025

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✦ Synopsis

In this paper we explore the hierarchical structures of wavelets, and use them for solving the linear systems which arise in the discretization of the wavelet-Galerkin method for elliptic problems. It is proved that the condition number of the stiffness matrix with respect to the wavelet bases grows like O(logz H/h) in two dimensions, and the condition number of the wavelet preconditioning system is bounded by O(log* H / h ) in d dimensions, instead of O(h-') if the scaling function bases are used.

where (. , -) denotes inner product in L z ( Q ) , and a@, v ) = 1 ((a(x)Vu).Vv + ao(x)uu) d x for any u, u E N ' ( Q ) D

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