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Comparison of linear solvers for equilibrium geochemistry computations. (English) Zbl 1415.86001
Summary: 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 ($$4\times 4$$ to $$20 \times 20$$, occasionally larger) and are very ill-conditioned (condition number up to $$10^{100}$$). 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.
##### MSC:
 86-08 Computational methods for problems pertaining to geophysics 65F05 Direct numerical methods for linear systems and matrix inversion 65F35 Numerical computation of matrix norms, conditioning, scaling 80A32 Chemically reacting flows 86A05 Hydrology, hydrography, oceanography
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