Waveform relaxation method for parallel orbital propagation

[EN] A new highly parallelizable procedure to integrate perturbed Keplerian motions numerically is presented in this study. It is based on a waveform relaxation method combined with the classic fourth-order Runge–Kutta integrator. Other parallelizable algorithms are already known in the literature,...

Descripción completa

Detalles Bibliográficos
Autores: Rubio Sierra, Carlos, Delgado Marcos, Adrián, García Gutiérrez, Adrián, Escapa García, Luis Alberto
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2025
País:España
Institución:Ajuntament de Barcelona
Repositorio:BULERIA. Repositorio Institucional de la Universidad de León
OAI Identifier:oai:buleria.unileon.es:10612/24177
Acceso en línea:https://hdl.handle.net/10612/24177
Access Level:acceso abierto
Palabra clave:Ingeniería aeroespacial
Waveform relaxation
Modified Chebyshev–Picard
Parallel computing
Special perturbations
Orbit propagation
Space debris
Numerical methods
2501
1206
id ES_7f16688c8e3429627768a2bbccff571e
oai_identifier_str oai:buleria.unileon.es:10612/24177
network_acronym_str ES
network_name_str España
repository_id_str
spelling Waveform relaxation method for parallel orbital propagationRubio Sierra, CarlosDelgado Marcos, AdriánGarcía Gutiérrez, AdriánEscapa García, Luis AlbertoIngeniería aeroespacialWaveform relaxationModified Chebyshev–PicardParallel computingSpecial perturbationsOrbit propagationSpace debrisNumerical methods25011206[EN] A new highly parallelizable procedure to integrate perturbed Keplerian motions numerically is presented in this study. It is based on a waveform relaxation method combined with the classic fourth-order Runge–Kutta integrator. Other parallelizable algorithms are already known in the literature, being one of the most widespread the Picard–Chebyshev method. When formulated in Cartesian variables, however, the Picard–Chebyshev method exhibits a limited convergence interval. This limitation requires sequential integration over small segments, reducing the level of parallelization. Alternatively, the equations of motion can be transformed into modified equinoctial elements. The waveform relaxation method proposed here extends both the convergence interval and rate when using Cartesian variables, carrying them to the same level as the modified equinoctial elements. Hence, this method offers an effective parallel algorithm that can be applied directly in Cartesian variables, what simplifies the formulation of the dynamical equations, the integrator structure, and the perturbation force expressions. The convergence and performance of the new waveform relaxation method was validated by performing low-Earth orbit propagations subjected to both conservative and non-conservative perturbations. The evaluation revealed a substantial enhancement with respect to a Picard–Chebyshev method, with a reduction in the Cartesian variables parallel evaluation of the perturbations of approximately 20 times, spanning from 10 to 30 orbit periods and with no significant loss of precision.SIElsevierIngenieria AeroespacialEscuela de Ingenierias Industrial, Informática y Aeroespacial2025info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionhttps://hdl.handle.net/10612/24177reponame:BULERIA. Repositorio Institucional de la Universidad de Leóninstname:Ajuntament de BarcelonaInglésinfo:eu-repo/semantics/openAccessoai:buleria.unileon.es:10612/241772026-06-24T12:43:27Z
dc.title.none.fl_str_mv Waveform relaxation method for parallel orbital propagation
title Waveform relaxation method for parallel orbital propagation
spellingShingle Waveform relaxation method for parallel orbital propagation
Rubio Sierra, Carlos
Ingeniería aeroespacial
Waveform relaxation
Modified Chebyshev–Picard
Parallel computing
Special perturbations
Orbit propagation
Space debris
Numerical methods
2501
1206
title_short Waveform relaxation method for parallel orbital propagation
title_full Waveform relaxation method for parallel orbital propagation
title_fullStr Waveform relaxation method for parallel orbital propagation
title_full_unstemmed Waveform relaxation method for parallel orbital propagation
title_sort Waveform relaxation method for parallel orbital propagation
dc.creator.none.fl_str_mv Rubio Sierra, Carlos
Delgado Marcos, Adrián
García Gutiérrez, Adrián
Escapa García, Luis Alberto
author Rubio Sierra, Carlos
author_facet Rubio Sierra, Carlos
Delgado Marcos, Adrián
García Gutiérrez, Adrián
Escapa García, Luis Alberto
author_role author
author2 Delgado Marcos, Adrián
García Gutiérrez, Adrián
Escapa García, Luis Alberto
author2_role author
author
author
dc.contributor.none.fl_str_mv Ingenieria Aeroespacial
Escuela de Ingenierias Industrial, Informática y Aeroespacial
dc.subject.none.fl_str_mv Ingeniería aeroespacial
Waveform relaxation
Modified Chebyshev–Picard
Parallel computing
Special perturbations
Orbit propagation
Space debris
Numerical methods
2501
1206
topic Ingeniería aeroespacial
Waveform relaxation
Modified Chebyshev–Picard
Parallel computing
Special perturbations
Orbit propagation
Space debris
Numerical methods
2501
1206
description [EN] A new highly parallelizable procedure to integrate perturbed Keplerian motions numerically is presented in this study. It is based on a waveform relaxation method combined with the classic fourth-order Runge–Kutta integrator. Other parallelizable algorithms are already known in the literature, being one of the most widespread the Picard–Chebyshev method. When formulated in Cartesian variables, however, the Picard–Chebyshev method exhibits a limited convergence interval. This limitation requires sequential integration over small segments, reducing the level of parallelization. Alternatively, the equations of motion can be transformed into modified equinoctial elements. The waveform relaxation method proposed here extends both the convergence interval and rate when using Cartesian variables, carrying them to the same level as the modified equinoctial elements. Hence, this method offers an effective parallel algorithm that can be applied directly in Cartesian variables, what simplifies the formulation of the dynamical equations, the integrator structure, and the perturbation force expressions. The convergence and performance of the new waveform relaxation method was validated by performing low-Earth orbit propagations subjected to both conservative and non-conservative perturbations. The evaluation revealed a substantial enhancement with respect to a Picard–Chebyshev method, with a reduction in the Cartesian variables parallel evaluation of the perturbations of approximately 20 times, spanning from 10 to 30 orbit periods and with no significant loss of precision.
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/10612/24177
url https://hdl.handle.net/10612/24177
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:BULERIA. Repositorio Institucional de la Universidad de León
instname:Ajuntament de Barcelona
instname_str Ajuntament de Barcelona
reponame_str BULERIA. Repositorio Institucional de la Universidad de León
collection BULERIA. Repositorio Institucional de la Universidad de León
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869411798320414720
score 15.81155

Similares en LA Referencia