Preprint No.
A-12-01
Guillaume Jouvet, Carsten Gräser
An adaptive Newton multigrid method
for a model of marine ice sheets
Abstract:
In this paper, we consider a model for the time evolution of marine ice sheets.
This model combines the Shallow Ice Approximation (SIA)
for the ice deformation, the Shallow Shelf Approximation (SSA) for the
basal sliding and the mass conservation principle.
At each time step, we solve a generalized p-Laplace minimization-type
problem with obstacle (SIA), a vectorial p-Laplace minimization-type
problem (SSA) and a transport equation (mass conservation).
The two minimization problems are solved using a truncated nonsmooth Newton
multigrid method while the transport equation is solved using
a vertex-centred finite volume method.
Our approach is combined to a mesh adaptive refinement procedure
to face the large gradients of the solution that are expected close to
the grounding line which separates the ice sheet and the ice shelf.
As applications, we present some simulations of the marine ice sheet
model inter-comparison project MISMIP in two and three space dimensions.
In particular, we test the ability of our model to reproduce a reversible
grounding line after being perturbed in model parameters.
Keywords:
ice sheet model, ice flow, variational inequality, nonlinear multigrid method
Mathematics Subject Classification (MSC2010):
65K15, 65M55, 35J92, 74M10, 76A05
Language: ENG
Available: Pr-A-12-01.pdf
Contact: Carsten Gräser, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, D-14195 Berlin, Germany (graeser@math.fu-berlin.de)
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