The semismooth Newton method for the solution of reactive transport problems including mineral precipitation-dissolution reactions

Buchholzer H, Kanzow C, Knabner P, Kräutle S (2011)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2011

Journal

Computational Optimization and Applications Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 50

Pages Range: 193-221

Journal Issue: 2

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_2011/2011_BuchholzerKanzowKnKraeutle_TheSemismoothNewtonMethodForSolutionIncludeMineral

DOI: 10.1007/s10589-010-9379-6

Abstract

The semismooth Newton method was introduced in a paper by Qi and Sun (Math. Program. 58:353-367, 1993) and the subsequent work by Qi (Math. Oper. Res. 18:227-244, 1993). This method became the basis of many solvers for certain classes of nonlinear systems of equations defined by a nonsmooth mapping. Here we consider a particular system of equations that arises from the discretization of a reactive transport model in the subsurface including mineral precipitation-dissolution reactions. The model is highly complicated and uses a coupling of PDEs, ODEs, and algebraic equations, together with some complementarity conditions arising from the equilibrium conditions of the minerals. The aim is to show that this system, though quite complicated, usually satisfies the convergence criteria for the semismooth Newton method, and can therefore be solved by a locally quadratically convergent method. This gives a theoretical sound approach for the solution of this kind of applications, whereas the geoscientists community most frequently applies algorithms involving some kind of trial-and-error strategies. © 2010 Springer Science+Business Media, LLC.

Authors with CRIS profile

Peter Knabner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Serge Kräutle Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Julius-Maximilians-Universität Würzburg DE Germany (DE)

How to cite

APA:

Buchholzer, H., Kanzow, C., Knabner, P., & Kräutle, S. (2011). The semismooth Newton method for the solution of reactive transport problems including mineral precipitation-dissolution reactions. Computational Optimization and Applications, 50(2), 193-221. https://doi.org/10.1007/s10589-010-9379-6

MLA:

Buchholzer, Hannes, et al. "The semismooth Newton method for the solution of reactive transport problems including mineral precipitation-dissolution reactions." Computational Optimization and Applications 50.2 (2011): 193-221.

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