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Automated adjoints of coupled PDE-ODE systems. (English) Zbl 1420.65077
Summary: 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.
Reviewer: Reviewer (Berlin)
MSC:
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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