TY - JOUR
T1 - Hierarchical method for elliptic problems using wavelet
AU - Cai, Zhiqiang
AU - Weinan, E.
PY - 1992
Y1 - 1992
N2 - 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(log2 H/h) in two dimensions, and the condition number of the wavelet preconditioning system is bounded by O(log2 H/h) in d dimensions, instead of O(h-2) if the scaling function bases are used.
AB - 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(log2 H/h) in two dimensions, and the condition number of the wavelet preconditioning system is bounded by O(log2 H/h) in d dimensions, instead of O(h-2) if the scaling function bases are used.
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U2 - 10.1002/cnm.1630081105
DO - 10.1002/cnm.1630081105
M3 - Article
AN - SCOPUS:0026943297
SN - 0748-8025
VL - 8
SP - 819
EP - 825
JO - Communications in Applied Numerical Methods
JF - Communications in Applied Numerical Methods
IS - 11
ER -