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Convergence acceleration of iterative sequences for equilibrium chemistry computations

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Abstract

The modeling of thermodynamic equilibria leads to complex nonlinear chemical systems which are often solved with the Newton-Raphson method. But this resolution can lead to a non convergence or an excessive number of iterations due to the very ill-conditioned nature of the problem. In this work, we combine a particular formulation of the equilibrium system called the Positive Continuous Fraction method with two iterative methods, Anderson Acceleration method and Vector extrapolation methods (namely the reduced rank extrapolation and the minimal polynomial extrapolation). The main advantage of this approach is to avoid forming the Jacobian matrix. In addition, a strategy is used to improve the robustness of the Anderson acceleration method which consists in reducing the condition number of matrix of the least squares problem in the implementation of the Anderson acceleration so that the numerical stability can be guaranteed. We compare our numerical results with those obtained with the Newton-Raphson method on the Acid Gallic test and the 1D MoMas benchmark test case and we show the high efficiency of our approach.

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Acknowledgements

We thank referees as well as Jérôme Carrayrou for their helpful comments and interesting suggestions which allowed to improve the actual version of the article. This work is supported by the project NEEDS-NewSolChem of CNRS.

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Authors and Affiliations

  1. UR 2597, LMPA, Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville, Université du Littoral Côte d’Opale, F-62100, Calais, France

    Safaa Al Nazer & Carole Rosier

  2. CNRS FR2037, Paris, France

    Safaa Al Nazer & Carole Rosier

  3. LaMA-Liban, Laboratoire de recherche en Mathématiques et Applications, Université Libanaise, P.O. Box 37, Tripoli, Libanon

    Safaa Al Nazer & Mustapha Jazar

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  1. Safaa Al Nazer
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  2. Mustapha Jazar
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Correspondence to Carole Rosier.

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Nazer, S.A., Jazar, M. & Rosier, C. Convergence acceleration of iterative sequences for equilibrium chemistry computations. Comput Geosci 25, 1509–1538 (2021). https://doi.org/10.1007/s10596-021-10054-1

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