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Comparison of linear solvers for equilibrium geochemistry computations

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Abstract

Equilibrium chemistry computations and reactive transport modelling require the intensive use of a linear solver under very specific conditions. The systems to be solved are small or very small (4 × 4 to 20 × 20, occasionally larger) and are very ill-conditioned (condition number up to 10100). These specific conditions have never been investigated in terms of the robustness, accuracy, and efficiency of the linear solver. In this work, we present the specificity of the linear system to be solved. Several direct and iterative solvers are compared using a panel of chemical systems, including or excluding the formation of mineral species. We show that direct and iterative solvers can be used for these problems and propose computational keys to improve the chemical solvers.

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Authors and Affiliations

  1. CNRS, ENGEES, LHyGeS UMR 7517, Université de Strasbourg, 67000, Strasbourg, France

    Hela Machat & Jérôme Carrayrou

  2. Ecole Supérieure des Ingénieur de l’Equipement Rural de Medjez el Bab, Université de Jendouba, Jendouba, Tunisia

    Hela Machat

  3. Université de Monastir, UR13ES63-Chimie Appliquée et Environnement, 5000, Monastir, Tunisia

    Hela Machat

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  1. Hela Machat
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  2. Jérôme Carrayrou
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Correspondence to Jérôme Carrayrou.

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Machat, H., Carrayrou, J. Comparison of linear solvers for equilibrium geochemistry computations. Comput Geosci 21, 131–150 (2017). https://doi.org/10.1007/s10596-016-9600-5

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