On the solution of differential-algebraic equations through gradient flow embedding

Ehecatl Antonio del Rio-Chanona, Craig Bakker, Fabio Fiorelli, Michail Paraskevopoulos, Felipe Scott, Raúl Conejeros, Vassilios S. Vassiliadis

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper Gradient Flow methods are used to solve systems of differential-algebraic equations via a novel reformulation strategy, focusing on the solution of index-1 differential-algebraic equation systems. A reformulation is first effected on semi-explicit index-1 differential-algebraic equation systems, which casts them as pure ordinary differential equation systems subject to an embedded pointwise least-squares problem. This is then formulated as a gradient flow optimization problem. Rigorous proofs for this novel scheme are provided for asymptotic and epsilon convergence. The computational results validate the predictions of the effectiveness of the proposed approach, with efficient and accurate solutions obtained for the case studies considered. Beyond the theoretical and practical value for the solution of DAE systems as pure ODE ones, the methodology is expected to have an impact in similar cases where an ODE system is subjected to algebraic constraints, such as the Hamiltonian necessary conditions of optimality in optimal control problems.
Original languageAmerican English
Pages (from-to)165-175
Number of pages11
JournalComputers and Chemical Engineering
Volume103
DOIs
StatePublished - 1 Jan 2017

Keywords

  • DAE
  • Differential-algebraic equations
  • Gradient flow
  • Ordinary differential equations
  • Semi-explicit index-1

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