Comparison of linear solvers for equilibrium geochemistry computations

Hela Machat (1, 2, 3) , Jérôme Carrayrou (1)

1 LHyGeS - Laboratoire d'Hydrologie et de Géochimie de Strasbourg
2 UJ - Université de Jendouba
3 UM - Université de Monastir - University of Monastir

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 (4x4 to 20x20, 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.

Mots clés: Geochemical modelling; Instantaneous equilibrium chemistry; Linear system inversion; Small matrix; Linear solver; Ill-conditioned matrix; Newton-Raphson algorithm

Domaines: Chemo-informatique; Géochimie

Hela Machat, Jérôme Carrayrou. Comparison of linear solvers for equilibrium geochemistry computations. Computational Geosciences, 2017, 21 (1), pp.131-150. ⟨10.1007/s10596-016-9600-5⟩. ⟨hal-03321650⟩