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 efficien...
| Main Authors: | , , , |
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| Format: | Journal article |
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Society for Industrial and Applied Mathematics
2019
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| _version_ | 1797088479771885568 |
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| author | Farrell, P Hake, JE Funke, SW Rognes, ME |
| author_facet | Farrell, P Hake, JE Funke, SW Rognes, ME |
| author_sort | Farrell, P |
| collection | OXFORD |
| 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 discretization 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. |
| first_indexed | 2024-03-07T02:50:41Z |
| format | Journal article |
| id | oxford-uuid:ad9555da-da39-4d77-b5ae-213b6c774620 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:50:41Z |
| publishDate | 2019 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:ad9555da-da39-4d77-b5ae-213b6c7746202022-03-27T03:36:35ZAutomated adjoints of coupled PDE-ODE systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ad9555da-da39-4d77-b5ae-213b6c774620Symplectic Elements at OxfordSociety for Industrial and Applied Mathematics2019Farrell, PHake, JEFunke, SWRognes, MEMathematical 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 discretization 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. |
| spellingShingle | Farrell, P Hake, JE Funke, SW Rognes, ME Automated adjoints of coupled PDE-ODE systems |
| title | Automated adjoints of coupled PDE-ODE systems |
| title_full | Automated adjoints of coupled PDE-ODE systems |
| title_fullStr | Automated adjoints of coupled PDE-ODE systems |
| title_full_unstemmed | Automated adjoints of coupled PDE-ODE systems |
| title_short | Automated adjoints of coupled PDE-ODE systems |
| title_sort | automated adjoints of coupled pde ode systems |
| work_keys_str_mv | AT farrellp automatedadjointsofcoupledpdeodesystems AT hakeje automatedadjointsofcoupledpdeodesystems AT funkesw automatedadjointsofcoupledpdeodesystems AT rognesme automatedadjointsofcoupledpdeodesystems |