A new wavelet preconditioner for finite difference operators (Q1767052)
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scientific article; zbMATH DE number 2140537
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new wavelet preconditioner for finite difference operators |
scientific article; zbMATH DE number 2140537 |
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A new wavelet preconditioner for finite difference operators (English)
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4 March 2005
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The paper deals with a multiscale preconditioner for finite difference approximations of variable coefficient problems in one space dimension. The authors use the properties of compactly supported regular wavelets that allow to cure the ill-conditioning due to differentiation as well as the ill-conditioning due to multiplication by a variable coefficient. The implementation of this construction can be made fast thanks to a hierarchical decomposition of the operators involving filters related to the fast wavelet transform. Numerical tests show the efficiency of the presented construction as well as its flexibility which is a property not shared by other multiscale preconditioners
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elliptic equation
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finite difference method
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multilevel preconditioning
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numerical examples
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