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 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

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 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

Supplementary code for "Automated adjoints of coupled PDE-ODE systems"

<p>This file contains supplementary code for the paper "Automated<br> adjoints of coupled PDE-ODE systems" by P. E. Farrell, J. E. Hake,<br> S. W. Funke and M. E. Rognes.</p> <p>This research is supported by a Center of Excellence grant awarded to<br> the Center for Biomedical Computing at Simula Research Laboratory from<br> the Research Council of Norway, by EPSRC grants EP/K030930/1 and<br> EP/M011151/1, a NOTUR grant NN9316K and the generous support of Sir<br> Michael Moritz and Harriet Heyman.</p> <p>The code relies on a working installation of the FEniCS and<br> dolfin-adjoint softwares and the cbcbeat module, all available in the<br> public domain:<br> - FEniCS: www.fenicsproject.org, version 2017.1 (or later perhaps)<br> - dolfin-adjoint: www.dolfin-adjoint.org, version compatible with the above<br> - cbcbeat: www.bitbucket.org/meg/cbcbeat, version compatible with the abov</p