The 2-Lagrange multiplier method applied to nonlinear transmission problems for the Richards equation in heterogeneous soil with cross points

Heiko Berninger, Sebastien Loisel, Oliver Sander

Research output: Contribution to journalArticle

6 Citations (Scopus)
41 Downloads (Pure)

Abstract

We formulate the 2-Lagrange multiplier method for the Richards equation in heterogeneous soil. This allows a rigorous formulation of a discrete version of the Richards equation on subdomain decompositions involving cross points. Using Kirchhoff transformation, the individual subdomain problems can be transformed into convex minimization problems and solved efficiently using a monotone multigrid method. We discuss and compare weak formulations of the time-discrete and fully discretized multidomain problem. It is shown that in the case of two subdomains, when solving the resulting discrete system with a Richardson iteration, the new method is equivalent to a parallel version of the nonlinear Robin method for the Richards equation proposed in [H. Berninger and O. Sander, Comput. Vis. Sci., 13 (2010), pp. 187-205]. We give numerical results for a problem with realistic soil parameters.

Original languageEnglish
Pages (from-to)A2166-A2198
Number of pages33
JournalSIAM Journal on Scientific Computing
Volume36
Issue number5
DOIs
Publication statusPublished - 2014

Keywords

  • 2-Lagrange multiplier method
  • Cross points
  • Domain decomposition
  • Heterogeneous soil
  • Kirchhoff transformation
  • Monotone multigrid
  • Optimized Schwarz method
  • Richards equation
  • Transmission problem

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Fingerprint Dive into the research topics of 'The 2-Lagrange multiplier method applied to nonlinear transmission problems for the Richards equation in heterogeneous soil with cross points'. Together they form a unique fingerprint.

  • Profiles

    No photo of Sebastien Loisel

    Cite this