Fast orthogonalization to the kernel of the discrete gradient operator with application to Stokes problem

We obtain a simple tensor representation of the kernel of the discrete d -dimensional gradient operator defined on tensor semi-staggered grids. We show that the dimension of the nullspace grows as O ( n d - 2 ) , where d is the dimension of the problem, and n is one-dimensional grid size. The tensor...

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Bibliographic Details
Published in:Linear algebra and its applications 2010-03, Vol.432 (6), p.1492-1500
Main Authors: Oseledets, Ivan, Muravleva, Ekaterina
Format: Article
Language:English
Subjects:
Discrete gradient operator
Fast orthogonalization
Kernel
Stokes problem
Tensor structure
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Summary:We obtain a simple tensor representation of the kernel of the discrete d -dimensional gradient operator defined on tensor semi-staggered grids. We show that the dimension of the nullspace grows as O ( n d - 2 ) , where d is the dimension of the problem, and n is one-dimensional grid size. The tensor structure allows fast orthogonalization to the kernel. The usefulness of such procedure is demonstrated on three-dimensional Stokes problem, discretized by finite differences on semi-staggered grids, and it is shown by numerical experiments that the new method outperforms usually used stabilization approach.
ISSN:0024-3795
DOI:10.1016/j.laa.2009.11.010