Automated adjoints of coupled PDE-ODE systems

Author: 

Farrell, P
Hake, J
Funke, S
Rognes, M

Publication Date: 

6 June 2019

Journal: 

SIAM Journal on Scientific Computing

Last Updated: 

2020-07-19T00:59:36.863+01:00

Issue: 

3

Volume: 

41

DOI: 

10.1137/17M1144532

page: 

C219-C244

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 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.

Symplectic id: 

984853

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article