Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger Equation

[EN] We present a new family of fourth-order splitting methods with positive co-efficients especially tailored for the time integration of linear parabolic problems and, in particular, for the time dependent Schrodinger equation, both in real and imaginary time. They are based on the use of a double...

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Autores: Blanes Zamora, Sergio|||0000-0001-5819-8898, Casas, Fernando, González, Cesáreo, Thalhammer, Mechthild
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/212320
Acceso en línea:https://riunet.upv.es/handle/10251/212320
Access Level:acceso abierto
Palabra clave:Schrodinger equation
Imaginary time propagation
Parabolic equations
Operator splitting methods
Modified potentials
MATEMATICA APLICADA
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spelling Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger EquationBlanes Zamora, Sergio|||0000-0001-5819-8898Casas, FernandoGonzález, CesáreoThalhammer, MechthildSchrodinger equationImaginary time propagationParabolic equationsOperator splitting methodsModified potentialsMATEMATICA APLICADA[EN] We present a new family of fourth-order splitting methods with positive co-efficients especially tailored for the time integration of linear parabolic problems and, in particular, for the time dependent Schrodinger equation, both in real and imaginary time. They are based on the use of a double commutator and a modified processor, and are more efficient than other widely used schemes found in the literature. Moreover, for certain potentials, they achieve order six. Several examples in one, two and three dimensions clearly illustrate the computational advantages of the new schemes.Part of this work was developed during a research stay at the Wolfgang Pauli Institute Vienna; the authors are grateful to the director Norbert Mauser and the staff members for their support and hospitality. This work has been supported by Ministerio de Ciencia e Innovacion (Spain) through projects PID2019-104927GB-C21 and PID2019-104927GB-C22, MCIN/AEI/10.13039/501100011033, ERDF ("A way of making Europe") . SB and FC also acknowledge the support of the Conselleria d'Innovacio, Universitats, Ciencia i Societat Digital from the Generalitat Valenciana (Spain) through project CIAICO/2021/180. The authors would like to thank to Ander Murua for extensive feedback and discussions on processed methods with starter.Global Science PressDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialInstituto Universitario de Matemática MultidisciplinarGENERALITAT VALENCIANAAgencia Estatal de InvestigaciónEuropean Regional Development FundRepositorio Institucional de la Universitat Politècnica de València Riunet20232023-04-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/212320reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-104927GB-C21 METODOS DE INTEGRACION GEOMETRICA PARA PROBLEMAS CUANTICOS, MECANICA CELESTE Y SIMULACIONES MONTECARLO IAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-104927GB-C22 METODOS DE INTEGRACION GEOMETRICA PARA PROBLEMAS CUANTICOS, MECANICA CELESTE Y SIMULACIONES MONTECARLO IIGeneralitat Valenciana https://doi.org/10.13039/501100003359 CIAICO%2F2021%2F180 MÉTODOS DE INTEGRACIÓN GEOMÉTRICA PARA PROBLEMAS CUÁNTICOS, MECÁNICA CELESTE Y MODELOS EPIDEMIOLÓGICOSopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2123202026-06-13T07:49:27Z
dc.title.none.fl_str_mv Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger Equation
title Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger Equation
spellingShingle Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger Equation
Blanes Zamora, Sergio|||0000-0001-5819-8898
Schrodinger equation
Imaginary time propagation
Parabolic equations
Operator splitting methods
Modified potentials
MATEMATICA APLICADA
title_short Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger Equation
title_full Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger Equation
title_fullStr Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger Equation
title_full_unstemmed Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger Equation
title_sort Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger Equation
dc.creator.none.fl_str_mv Blanes Zamora, Sergio|||0000-0001-5819-8898
Casas, Fernando
González, Cesáreo
Thalhammer, Mechthild
author Blanes Zamora, Sergio|||0000-0001-5819-8898
author_facet Blanes Zamora, Sergio|||0000-0001-5819-8898
Casas, Fernando
González, Cesáreo
Thalhammer, Mechthild
author_role author
author2 Casas, Fernando
González, Cesáreo
Thalhammer, Mechthild
author2_role author
author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Instituto Universitario de Matemática Multidisciplinar
GENERALITAT VALENCIANA
Agencia Estatal de Investigación
European Regional Development Fund
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Schrodinger equation
Imaginary time propagation
Parabolic equations
Operator splitting methods
Modified potentials
MATEMATICA APLICADA
topic Schrodinger equation
Imaginary time propagation
Parabolic equations
Operator splitting methods
Modified potentials
MATEMATICA APLICADA
description [EN] We present a new family of fourth-order splitting methods with positive co-efficients especially tailored for the time integration of linear parabolic problems and, in particular, for the time dependent Schrodinger equation, both in real and imaginary time. They are based on the use of a double commutator and a modified processor, and are more efficient than other widely used schemes found in the literature. Moreover, for certain potentials, they achieve order six. Several examples in one, two and three dimensions clearly illustrate the computational advantages of the new schemes.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-04-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/212320
url https://riunet.upv.es/handle/10251/212320
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-104927GB-C21 METODOS DE INTEGRACION GEOMETRICA PARA PROBLEMAS CUANTICOS, MECANICA CELESTE Y SIMULACIONES MONTECARLO I
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-104927GB-C22 METODOS DE INTEGRACION GEOMETRICA PARA PROBLEMAS CUANTICOS, MECANICA CELESTE Y SIMULACIONES MONTECARLO II
Generalitat Valenciana https://doi.org/10.13039/501100003359 CIAICO%2F2021%2F180 MÉTODOS DE INTEGRACIÓN GEOMÉTRICA PARA PROBLEMAS CUÁNTICOS, MECÁNICA CELESTE Y MODELOS EPIDEMIOLÓGICOS
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Global Science Press
publisher.none.fl_str_mv Global Science Press
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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