Estimates for generalized sparse grid hierarchical basis preconditioners
Estimates for generalized sparse grid hierarchical basis preconditioners
View/Date of Publication
03.2018Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
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Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11806
Abstract
We reconsider some estimates from the 1994 paper [6] 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 Λ, and show that the bounds are sharp up to constants depending only on d, at least for a subclass of Λ containing full grid, standard sparse grid spaces, and energy-norm optimized sparse grid spaces.
Subjects
Generalized sparse grid spaces, hierarchical basis, tensor-product Faber-Schauder systems, preconditioners for elliptic problems
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.48550/arXiv.1803.01782Part of Series
INS Preprints ; 1803Peter Oswald: Estimates for generalized sparse grid hierarchical basis preconditioners. In: INS Preprints, 1803.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11806
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11806
@unpublished{handle:20.500.11811/11806,
author = {{ }},
title = {Estimates for generalized sparse grid hierarchical basis preconditioners},
publisher = {Institut für Numerische Simulation (INS)},
year = 2018,
month = mar,
INS Preprints},
volume = 1803,
note = {We reconsider some estimates from the 1994 paper [6] 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 Λ, and show that the bounds are sharp up to constants depending only on d, at least for a subclass of Λ containing full grid, standard sparse grid spaces, and energy-norm optimized sparse grid spaces.},
url = {https://hdl.handle.net/20.500.11811/11806}
}
author = {{ }},
title = {Estimates for generalized sparse grid hierarchical basis preconditioners},
publisher = {Institut für Numerische Simulation (INS)},
year = 2018,
month = mar,
INS Preprints},
volume = 1803,
note = {We reconsider some estimates from the 1994 paper [6] 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 Λ, and show that the bounds are sharp up to constants depending only on d, at least for a subclass of Λ containing full grid, standard sparse grid spaces, and energy-norm optimized sparse grid spaces.},
url = {https://hdl.handle.net/20.500.11811/11806}
}
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