A parallel iterative method for variational integration
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value problems. More concretely, we explore a parallelization strategy...
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| creator | Ferraro, Sebastián J de Diego, David Martín de Almagro, Rodrigo Takuro Sato Martín |
| description | Discrete variational methods show excellent performance in numerical
simulations of different mechanical systems. In this paper, we introduce an
iterative procedure for the solution of discrete variational equations for
boundary value problems. More concretely, we explore a parallelization strategy
that leverages the capabilities of multicore CPUs and GPUs (graphics cards). We
study this parallel method for higher-order Lagrangian systems, which appear in
fully-actuated problems and beyond. The most important part of the paper is
devoted to a precise study of different convergence conditions for these
methods. We illustrate their excellent behavior in some interesting examples,
namely Zermelo's navigation problem, a fuel-optimal navigation problem,
interpolation problems or in a fuel optimization problem for a controlled
4-body problem in astrodynamics showing the potential of our method. |
| doi_str_mv | 10.48550/arxiv.2206.08968 |
| format | Article |
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simulations of different mechanical systems. In this paper, we introduce an
iterative procedure for the solution of discrete variational equations for
boundary value problems. More concretely, we explore a parallelization strategy
that leverages the capabilities of multicore CPUs and GPUs (graphics cards). We
study this parallel method for higher-order Lagrangian systems, which appear in
fully-actuated problems and beyond. The most important part of the paper is
devoted to a precise study of different convergence conditions for these
methods. We illustrate their excellent behavior in some interesting examples,
namely Zermelo's navigation problem, a fuel-optimal navigation problem,
interpolation problems or in a fuel optimization problem for a controlled
4-body problem in astrodynamics showing the potential of our method.</description><identifier>DOI: 10.48550/arxiv.2206.08968</identifier><language>eng</language><subject>Computer Science - Numerical Analysis ; Mathematics - Numerical Analysis ; Mathematics - Optimization and Control</subject><creationdate>2022-06</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2206.08968$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2206.08968$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Ferraro, Sebastián J</creatorcontrib><creatorcontrib>de Diego, David Martín</creatorcontrib><creatorcontrib>de Almagro, Rodrigo Takuro Sato Martín</creatorcontrib><title>A parallel iterative method for variational integration</title><description>Discrete variational methods show excellent performance in numerical
simulations of different mechanical systems. In this paper, we introduce an
iterative procedure for the solution of discrete variational equations for
boundary value problems. More concretely, we explore a parallelization strategy
that leverages the capabilities of multicore CPUs and GPUs (graphics cards). We
study this parallel method for higher-order Lagrangian systems, which appear in
fully-actuated problems and beyond. The most important part of the paper is
devoted to a precise study of different convergence conditions for these
methods. We illustrate their excellent behavior in some interesting examples,
namely Zermelo's navigation problem, a fuel-optimal navigation problem,
interpolation problems or in a fuel optimization problem for a controlled
4-body problem in astrodynamics showing the potential of our method.</description><subject>Computer Science - Numerical Analysis</subject><subject>Mathematics - Numerical Analysis</subject><subject>Mathematics - Optimization and Control</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8kKwjAYhHPxIOoDeDIv0Jq0WY8ibiB46b382TRQrcRS9O3V6mmYYRjmQ2hOSc4U52QJ6Rn7vCiIyInSQo2RXOE7JGga3-DY-QRd7D2--u7SOhzahHtI8RO2N_gUbp0_p8FN0ShA8_Czv05Qtd1U6312PO0O69UxAyFVFozmwVkqBRPaeFBKWwbcSSZs4ESBJdIFTQ0lBQ-h4KU0ljIDFIz1jpYTtPjNDs_re4pXSK_6S1APBOUbyYNB5A</recordid><startdate>20220617</startdate><enddate>20220617</enddate><creator>Ferraro, Sebastián J</creator><creator>de Diego, David Martín</creator><creator>de Almagro, Rodrigo Takuro Sato Martín</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220617</creationdate><title>A parallel iterative method for variational integration</title><author>Ferraro, Sebastián J ; de Diego, David Martín ; de Almagro, Rodrigo Takuro Sato Martín</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a678-fb95fdc176469bea889c4a5d746cf508ac07df91b1025ff2537bc14ba1abced13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Computer Science - Numerical Analysis</topic><topic>Mathematics - Numerical Analysis</topic><topic>Mathematics - Optimization and Control</topic><toplevel>online_resources</toplevel><creatorcontrib>Ferraro, Sebastián J</creatorcontrib><creatorcontrib>de Diego, David Martín</creatorcontrib><creatorcontrib>de Almagro, Rodrigo Takuro Sato Martín</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Ferraro, Sebastián J</au><au>de Diego, David Martín</au><au>de Almagro, Rodrigo Takuro Sato Martín</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A parallel iterative method for variational integration</atitle><date>2022-06-17</date><risdate>2022</risdate><abstract>Discrete variational methods show excellent performance in numerical
simulations of different mechanical systems. In this paper, we introduce an
iterative procedure for the solution of discrete variational equations for
boundary value problems. More concretely, we explore a parallelization strategy
that leverages the capabilities of multicore CPUs and GPUs (graphics cards). We
study this parallel method for higher-order Lagrangian systems, which appear in
fully-actuated problems and beyond. The most important part of the paper is
devoted to a precise study of different convergence conditions for these
methods. We illustrate their excellent behavior in some interesting examples,
namely Zermelo's navigation problem, a fuel-optimal navigation problem,
interpolation problems or in a fuel optimization problem for a controlled
4-body problem in astrodynamics showing the potential of our method.</abstract><doi>10.48550/arxiv.2206.08968</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Numerical Analysis Mathematics - Numerical Analysis Mathematics - Optimization and Control |
| title | A parallel iterative method for variational integration |
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