dorsal/arxiv
View SchemaCombining multigrid and wavelet ideas to construct more efficient multiscale algorithms for the solution of Poisson's equation
| Authors | S. Goedecker |
|---|---|
| Categories | |
| ArXiv ID | physics/0209040 |
| URL | https://arxiv.org/abs/physics/0209040 |
Abstract
It is shown how various ideas that are well established for the solution of Poisson's equation using plane wave and multigrid methods can be combined with wavelet concepts. The combination of wavelet concepts and multigrid techniques turns out to be particularly fruitful. We propose a modified multigrid V cycle scheme that is not only much simpler, but also more efficient than the standard V cycle. Whereas in the traditional V cycle the residue is passed to the coarser grid levels, this new scheme does not require the calculation of a residue. Instead it works with copies of the charge density on the different grid levels that were obtained from the underlying charge density on the finest grid by wavelet transformations. This scheme is not limited to the pure wavelet setting, where it is faster than the preconditioned conjugate gradient method, but equally well applicable for finite difference discretizations.
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"date_created": "2026-03-02T18:00:39.534000Z",
"date_modified": "2026-03-02T18:00:39.534000Z",
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"abstract": "It is shown how various ideas that are well established for the solution of\nPoisson\u0027s equation using plane wave and multigrid methods can be combined with\nwavelet concepts. The combination of wavelet concepts and multigrid techniques\nturns out to be particularly fruitful. We propose a modified multigrid V cycle\nscheme that is not only much simpler, but also more efficient than the standard\nV cycle. Whereas in the traditional V cycle the residue is passed to the\ncoarser grid levels, this new scheme does not require the calculation of a\nresidue. Instead it works with copies of the charge density on the different\ngrid levels that were obtained from the underlying charge density on the finest\ngrid by wavelet transformations. This scheme is not limited to the pure wavelet\nsetting, where it is faster than the preconditioned conjugate gradient method,\nbut equally well applicable for finite difference discretizations.",
"arxiv_id": "physics/0209040",
"authors": [
"S. Goedecker"
],
"categories": [
"physics.comp-ph"
],
"title": "Combining multigrid and wavelet ideas to construct more efficient multiscale algorithms for the solution of Poisson\u0027s equation",
"url": "https://arxiv.org/abs/physics/0209040"
},
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