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Preprint-No.: <   349   >   Published in: October 2012   PDF-File: IGPM349_k.pdf
Title:The 2–Lagrange Multiplier Method Applied to Nonlinear Transmission Problems for the Richards Equation in Heterogeneous Soil with Cross Points
Authors:Heiko Berninger, Sébastien Loisel , Oliver Sander
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 to convex minimization problems and solved efficiently using a monotone multigrid method. We discuss and compare weak formulations of the time-discrete and fully discretized multi-domain 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 the Robin method for the Richards equation proposed in [6]. We give numerical results for a problem with realistic soil parameters.
Keywords:Richards equation, 2–Lagrange–Multiplier method,cross points, domain decomposition, monotone multigrid, optimized Schwarz method
DOI: 10.1137/120901064
Publication:SIAM Journal on Scientific Computing
36(5), A2166–A2198. (33 pages)