Automated adjoints of coupled PDE-ODE systems
Mathematical models that couple partial differential equations (PDEs) and spatially distributed ordinary differential equations (ODEs) arise in biology, medicine, chemistry and many other fields. In this paper we discuss an extension to the FEniCS finite element software for expressing and efficient...
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| creator | Farrell, Patrick E Hake, Johan E Funke, Simon W Rognes, Marie E |
| description | Mathematical models that couple partial differential equations (PDEs) and
spatially distributed ordinary differential equations (ODEs) arise in biology,
medicine, chemistry and many other fields. In this paper we discuss an
extension to the FEniCS finite element software for expressing and efficiently
solving such coupled systems. Given an ODE described using an augmentation of
the Unified Form Language (UFL) and a discretisation described by an arbitrary
Butcher tableau, efficient code is automatically generated for the parallel
solution of the ODE. The high-level description of the solution algorithm also
facilitates the automatic derivation of the adjoint and tangent linearization
of coupled PDE-ODE solvers. We demonstrate the capabilities of the approach on
examples from cardiac electrophysiology and mitochondrial swelling. |
| doi_str_mv | 10.48550/arxiv.1708.07648 |
| format | Article |
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spatially distributed ordinary differential equations (ODEs) arise in biology,
medicine, chemistry and many other fields. In this paper we discuss an
extension to the FEniCS finite element software for expressing and efficiently
solving such coupled systems. Given an ODE described using an augmentation of
the Unified Form Language (UFL) and a discretisation described by an arbitrary
Butcher tableau, efficient code is automatically generated for the parallel
solution of the ODE. The high-level description of the solution algorithm also
facilitates the automatic derivation of the adjoint and tangent linearization
of coupled PDE-ODE solvers. We demonstrate the capabilities of the approach on
examples from cardiac electrophysiology and mitochondrial swelling.</description><identifier>DOI: 10.48550/arxiv.1708.07648</identifier><language>eng</language><subject>Mathematics - Numerical Analysis</subject><creationdate>2017-08</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/1708.07648$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1708.07648$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Farrell, Patrick E</creatorcontrib><creatorcontrib>Hake, Johan E</creatorcontrib><creatorcontrib>Funke, Simon W</creatorcontrib><creatorcontrib>Rognes, Marie E</creatorcontrib><title>Automated adjoints of coupled PDE-ODE systems</title><description>Mathematical models that couple partial differential equations (PDEs) and
spatially distributed ordinary differential equations (ODEs) arise in biology,
medicine, chemistry and many other fields. In this paper we discuss an
extension to the FEniCS finite element software for expressing and efficiently
solving such coupled systems. Given an ODE described using an augmentation of
the Unified Form Language (UFL) and a discretisation described by an arbitrary
Butcher tableau, efficient code is automatically generated for the parallel
solution of the ODE. The high-level description of the solution algorithm also
facilitates the automatic derivation of the adjoint and tangent linearization
of coupled PDE-ODE solvers. We demonstrate the capabilities of the approach on
examples from cardiac electrophysiology and mitochondrial swelling.</description><subject>Mathematics - Numerical Analysis</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzrsKwjAYhuEsDqJegJO9gdSkOf0ZResBBB3cy2-SQsVaaaro3XucPniHj4eQMWepBKXYFNtHdU-5YZAyoyX0CZ3duqbGLvgE_ampLl1MmjJxze16frf9Iqe7RZ7EZ-xCHYekV-I5htF_B-SwzA_zNd3uVpv5bEtRG6AKfGYtD2UIwIGpkDnBoZROamHgXY3TQjGJR2-t5xYRAA1zzhidwTGIAZn8br_e4tpWNbbP4uMuvm7xAvgkPEc</recordid><startdate>20170825</startdate><enddate>20170825</enddate><creator>Farrell, Patrick E</creator><creator>Hake, Johan E</creator><creator>Funke, Simon W</creator><creator>Rognes, Marie E</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20170825</creationdate><title>Automated adjoints of coupled PDE-ODE systems</title><author>Farrell, Patrick E ; Hake, Johan E ; Funke, Simon W ; Rognes, Marie E</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a678-58d2991efee81805e2c318f4c46378fee7c63504abd99d19aa88a70cc77628be3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Mathematics - Numerical Analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Farrell, Patrick E</creatorcontrib><creatorcontrib>Hake, Johan E</creatorcontrib><creatorcontrib>Funke, Simon W</creatorcontrib><creatorcontrib>Rognes, Marie E</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Farrell, Patrick E</au><au>Hake, Johan E</au><au>Funke, Simon W</au><au>Rognes, Marie E</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Automated adjoints of coupled PDE-ODE systems</atitle><date>2017-08-25</date><risdate>2017</risdate><abstract>Mathematical models that couple partial differential equations (PDEs) and
spatially distributed ordinary differential equations (ODEs) arise in biology,
medicine, chemistry and many other fields. In this paper we discuss an
extension to the FEniCS finite element software for expressing and efficiently
solving such coupled systems. Given an ODE described using an augmentation of
the Unified Form Language (UFL) and a discretisation described by an arbitrary
Butcher tableau, efficient code is automatically generated for the parallel
solution of the ODE. The high-level description of the solution algorithm also
facilitates the automatic derivation of the adjoint and tangent linearization
of coupled PDE-ODE solvers. We demonstrate the capabilities of the approach on
examples from cardiac electrophysiology and mitochondrial swelling.</abstract><doi>10.48550/arxiv.1708.07648</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Numerical Analysis |
| title | Automated adjoints of coupled PDE-ODE systems |
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