Hierarchical method for elliptic problems using wavelet

Zhiqiang Cai; E. Weinan

doi:10.1002/cnm.1630081105

Hierarchical method for elliptic problems using wavelet

Zhiqiang Cai, E. Weinan

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	819-825
Number of pages	7
Journal	Communications in Applied Numerical Methods
Volume	8
Issue number	11
DOIs	https://doi.org/10.1002/cnm.1630081105
State	Published - 1992
Externally published	Yes

All Science Journal Classification (ASJC) codes

Engineering(all)

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abstract = "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.",

author = "Zhiqiang Cai and E. Weinan",

year = "1992",

doi = "10.1002/cnm.1630081105",

language = "English (US)",

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T1 - Hierarchical method for elliptic problems using wavelet

AU - Cai, Zhiqiang

AU - Weinan, E.

PY - 1992

Y1 - 1992

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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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JO - Communications in Applied Numerical Methods

JF - Communications in Applied Numerical Methods

IS - 11

ER -

Hierarchical method for elliptic problems using wavelet

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