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arXiv · 1803.01782

Estimates for generalized sparse grid hierarchical basis preconditioners

Peter Oswald
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Abstract

We reconsider some estimates the paper "M. Griebel, P. Oswald, On additive Schwarz preconditioners for sparse grid discretizations. Numer. Math. 66 (1994), 449-463" concerning the hierarchical basis preconditioner for sparse grid discretizations. The improvement is in three directions: We consider arbitrary space dimensions d>1, give bounds for generalized sparse grid spaces with arbitrary monotone index set, and show that the bounds are sharp up to constants depending only on d, at least for a subclass of generalized sparse grid spaces containing full grid, standard sparse grid spaces, and energy-norm optimized sparse grid spaces.

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Peter Oswald. 2018-03-05. Estimates for generalized sparse grid hierarchical basis preconditioners. https://arxiv.org/abs/1803.01782

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