Fast Hyigens sweeping methods for Schrodinger equations in the semi-classical regime

We propose fast Huygens sweeping methods for Schrodinger equations in the semi-classical regime by incorporating short-time Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) propagators into Huygens' principle. Even though the WKBJ solution is valid only for a short time period due to the occurrence of...

ver descrição completa

Detalhes bibliográficos
Autores: Leung, Shingyu, Quian, Jianliang, Serna, Susana|||0000-0002-0908-4680
Formato: artículo
Fecha de publicación:2014
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150669
Acesso em linha:https://ddd.uab.cat/record/150669
Access Level:acceso abierto
Palavra-chave:Convolution
Eikonal equation
Fast Fourier transform
Fast Huygens sweeping method
Schrodinger equation
WKBJ
id ES_498c20bcbbe67181acb64d76cd4d0b07
oai_identifier_str oai:ddd.uab.cat:150669
network_acronym_str ES
network_name_str España
repository_id_str
spelling Fast Hyigens sweeping methods for Schrodinger equations in the semi-classical regimeLeung, ShingyuQuian, JianliangSerna, Susana|||0000-0002-0908-4680ConvolutionEikonal equationFast Fourier transformFast Huygens sweeping methodSchrodinger equationWKBJWe propose fast Huygens sweeping methods for Schrodinger equations in the semi-classical regime by incorporating short-time Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) propagators into Huygens' principle. Even though the WKBJ solution is valid only for a short time period due to the occurrence of caustics, Huygens' principle allows us to construct the global-in-time semi-classical solution. To improve the computational efficiency, we develop analytic approximation formulas for the short-time WKBJ propagator by using the Taylor expansion in time. These analytic formulas allow us to develop two classes of fast Huygens sweeping methods, among which one is posed in the momentum space, and the other is posed in the position space, and both of these methods are of computational complexity O(N log N ) for each time step, where N is the total number of sampling points in the d-dimensional position space. To further speed up these methods, we also incorporate the soft-thresholding sparsification strategy into our new algorithms so that the computational cost can be further reduced. The methodology can also be extended to nonlinear Schrodinger equations. One, two, and three dimensional examples demonstrate the performance of the new algorithms. 22014-01-0120142014-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/150669reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1506692026-06-06T12:50:31Z
dc.title.none.fl_str_mv Fast Hyigens sweeping methods for Schrodinger equations in the semi-classical regime
title Fast Hyigens sweeping methods for Schrodinger equations in the semi-classical regime
spellingShingle Fast Hyigens sweeping methods for Schrodinger equations in the semi-classical regime
Leung, Shingyu
Convolution
Eikonal equation
Fast Fourier transform
Fast Huygens sweeping method
Schrodinger equation
WKBJ
title_short Fast Hyigens sweeping methods for Schrodinger equations in the semi-classical regime
title_full Fast Hyigens sweeping methods for Schrodinger equations in the semi-classical regime
title_fullStr Fast Hyigens sweeping methods for Schrodinger equations in the semi-classical regime
title_full_unstemmed Fast Hyigens sweeping methods for Schrodinger equations in the semi-classical regime
title_sort Fast Hyigens sweeping methods for Schrodinger equations in the semi-classical regime
dc.creator.none.fl_str_mv Leung, Shingyu
Quian, Jianliang
Serna, Susana|||0000-0002-0908-4680
author Leung, Shingyu
author_facet Leung, Shingyu
Quian, Jianliang
Serna, Susana|||0000-0002-0908-4680
author_role author
author2 Quian, Jianliang
Serna, Susana|||0000-0002-0908-4680
author2_role author
author
dc.subject.none.fl_str_mv Convolution
Eikonal equation
Fast Fourier transform
Fast Huygens sweeping method
Schrodinger equation
WKBJ
topic Convolution
Eikonal equation
Fast Fourier transform
Fast Huygens sweeping method
Schrodinger equation
WKBJ
description We propose fast Huygens sweeping methods for Schrodinger equations in the semi-classical regime by incorporating short-time Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) propagators into Huygens' principle. Even though the WKBJ solution is valid only for a short time period due to the occurrence of caustics, Huygens' principle allows us to construct the global-in-time semi-classical solution. To improve the computational efficiency, we develop analytic approximation formulas for the short-time WKBJ propagator by using the Taylor expansion in time. These analytic formulas allow us to develop two classes of fast Huygens sweeping methods, among which one is posed in the momentum space, and the other is posed in the position space, and both of these methods are of computational complexity O(N log N ) for each time step, where N is the total number of sampling points in the d-dimensional position space. To further speed up these methods, we also incorporate the soft-thresholding sparsification strategy into our new algorithms so that the computational cost can be further reduced. The methodology can also be extended to nonlinear Schrodinger equations. One, two, and three dimensional examples demonstrate the performance of the new algorithms.
publishDate 2014
dc.date.none.fl_str_mv 2
2014-01-01
2014
2014-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/150669
url https://ddd.uab.cat/record/150669
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869407431053803520
score 15.301603

Registos relacionados