Automated Adjoints of Coupled PDE-ODE Systems

DOI10.1137/17M1144532zbMath1420.65077arXiv1708.07648OpenAlexW2963843244WikidataQ127742812 ScholiaQ127742812MaRDI QIDQ5230591

J. E. Hake, Simon W. Funke, Marie E. Rognes, Patrick E. Farrell

Publication date: 28 August 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.07648

zbMATH Keywords

finite element methodscode generationFEniCSadjointscoupled PDE-ODEdolfin-adjoint

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)

Related Items (4)

Hybrid FEM-NN models: combining artificial neural networks with the finite element method ⋮ A 3D Haar wavelet method for a coupled degenerate system of parabolic equations with nonlinear source coupled with non-linear ODEs ⋮ Automated Adjoints of Coupled PDE-ODE Systems ⋮ Long time behavior of a parabolic \(p\)-Laplacian equation coupled to a compartmental ODE system with an induction threshold phenomenon

Uses Software

• Chaste
• revolve
• SUNDIALS
• DOLFIN
• FEniCS
• CVODES
• Feel++
• FATODE
• UFL
• FFC
• Firedrake

Cites Work

• Unnamed Item
• Automated solution of differential equations by the finite element method. The FEniCS book
• Mathematical modelling of pulmonary gas transport
• Singly diagonally implicit Runge-Kutta methods with an explicit first stage
• Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs
• FATODE: A Library for Forward, Adjoint, and Tangent Linear Integration of ODEs
• DOLFIN
• Newton Methods for Nonlinear Problems
• Firedrake
• Splitting methods
• An optimal control approach to a posteriori error estimation in finite element methods
• Feel++ : A computational framework for Galerkin Methods and Advanced Numerical Methods
• Algorithm 799: revolve
• Perspectives in Flow Control and Optimization
• Automated Adjoints of Coupled PDE-ODE Systems
• Computing the Electrical Activity in the Heart
• Unified form language
• On the Construction and Comparison of Difference Schemes
• Numerical Methods for Ordinary Differential Equations

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