349 RWTH Publication No: 47297        2012        IGPM349.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)