|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|
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 . 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|
|Publication:||SIAM Journal on Scientific Computing |
36(5), A2166–A2198. (33 pages)