Wavelet based preconditioners for sparse linear systems

B. V. Rathish Kumar

doi:10.1016/j.amc.2005.01.060

2005-12-01

PRE

B. V. Rathish Kumar

Mani Mehra

DOI：10.1016/j.amc.2005.01.060

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摘要

En 中文

A class of efficient preconditioners based oil Daubechies family of wavelets for sparse, unsymmetric linear systems that arise in numerical solution of Partial Differential Equations (PDEs) in a wide variety of scientific and engineering disciplines are introduced. Complete and Incomplete Discrete Wavelet Transforms in conjunction with row and column permutations are used in the construction of these preconditioners. With these Wavelet Transform, the transformed matrix is permuted to band forms. The efficiency Of Our preconditioners with several Krylov subspace methods is illustrated by solving matrices from Harwell Boeing collection and Tim Davis collection. Also matrices resulting in the solution of Regularized Burgers Equation, free convection in porous enclosure are tested. Our results indicate that the preconditioner based oil Incomplete Discrete Haar Wavelet Transform is both cheaper to construct and gives good convergence. (c) 2005 Elsevier Inc. All rights reserved.

Keyword:

preconditioning

sparse matrices

wavelet transform

Krylov subspace solvers