A wavelet based sparse grid method for the electronic Schrödinger equation
A wavelet based sparse grid method for the electronic Schrödinger equation
Dokument öffnen (7.1MB)Datum der Veröffentlichung
05.2006Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
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Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11974
Inhalt
We present a direct discretization of the electronic Schrödinger equation. It is based on one-dimensional Meyer wavelets from which we build an anisotropic multiresolution analysis for general particle spaces by a tensor product construction. We restrict these spaces to the case of antisymmetric functions. To obtain finite-dimensional subspaces we first discuss semi-discretization with respect to the scale parameter by means of sparse grids which relies on mixed regularity and decay properties of the electronic wave functions. We then propose different techniques for a discretization with respect to the position parameter. Furthermore we present the results of our numerical experiments using this new generalized sparse grid methods for Schrödinger’s equation.
Schlagwörter
Schrödinger equation, numerical approximation, sparse grid method, antisymmetric sparse grids
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.4171/022-3/71Reihe, Nummer
INS Preprints ; 0603Griebel, Michael; Hamaekers, Jan: A wavelet based sparse grid method for the electronic Schrödinger equation. In: INS Preprints, 0603.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11974
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11974
@unpublished{handle:20.500.11811/11974,
author = {{Michael Griebel} and {Jan Hamaekers}},
title = {A wavelet based sparse grid method for the electronic Schrödinger equation},
publisher = {Institut für Numerische Simulation (INS)},
year = 2006,
month = may,
INS Preprints},
volume = 0603,
note = {We present a direct discretization of the electronic Schrödinger equation. It is based on one-dimensional Meyer wavelets from which we build an anisotropic multiresolution analysis for general particle spaces by a tensor product construction. We restrict these spaces to the case of antisymmetric functions. To obtain finite-dimensional subspaces we first discuss semi-discretization with respect to the scale parameter by means of sparse grids which relies on mixed regularity and decay properties of the electronic wave functions. We then propose different techniques for a discretization with respect to the position parameter. Furthermore we present the results of our numerical experiments using this new generalized sparse grid methods for Schrödinger’s equation.},
url = {https://hdl.handle.net/20.500.11811/11974}
}
author = {{Michael Griebel} and {Jan Hamaekers}},
title = {A wavelet based sparse grid method for the electronic Schrödinger equation},
publisher = {Institut für Numerische Simulation (INS)},
year = 2006,
month = may,
INS Preprints},
volume = 0603,
note = {We present a direct discretization of the electronic Schrödinger equation. It is based on one-dimensional Meyer wavelets from which we build an anisotropic multiresolution analysis for general particle spaces by a tensor product construction. We restrict these spaces to the case of antisymmetric functions. To obtain finite-dimensional subspaces we first discuss semi-discretization with respect to the scale parameter by means of sparse grids which relies on mixed regularity and decay properties of the electronic wave functions. We then propose different techniques for a discretization with respect to the position parameter. Furthermore we present the results of our numerical experiments using this new generalized sparse grid methods for Schrödinger’s equation.},
url = {https://hdl.handle.net/20.500.11811/11974}
}
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