Graduate Seminar "Aktuelle Themen der Numerik"

Thursday, Dec 19, 2013, 01:45 pm

Multigrid and domain decomposition methods for the Richards equation

Prof. Oliver Sander (IGPM, RWTH Aachen)

We consider the Richards equation for saturated--unsaturated porous media flow. This equation is numerically difficult, because it involves very ill-conditioned Newton matrices.  If the material is assumed to be homogeneous in a certain sense, however, the classical Kirchhoff transformation allows to turn it into an alternative form, which is equivalent to a convex minimization problem. We show how this minimization problem can be solved robustly and efficiently using Monotone Multigrid and related techniques.

If the soil is homogeneous only on each subdomain of a partition of the domain, domain decomposition techniques can be used. Applying the Kirchhoff transformation on each subdomain separately leads to a set of semilinear subproblems coupled by nonlinear transmission conditions. Each subproblem can be solved efficiently using
monotone multigrid. The coupled problem can be approached with various nonlinear nonoverlapping Schwarz methods. Comparison with the linear case shows that many desirable properties are retained in the nonlinear setting.

[joint work with Heiko Berninger and Ralf Kornhuber]

Time: 01:45 pm

Location: Room 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen