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Coupled Systems Mechanics
  Volume 1, Number 4, December 2012 , pages 325-343
DOI: https://doi.org/10.12989/csm.2012.1.4.325
 

Operator-splitting methods respecting eigenvalue problems for shallow shelf equations with basal drag
Jurgen Geiser and Reinhard Calov

 
Abstract
    We present different numerical methods for solving the shallow shelf equations with basal drag (SSAB). An alternative approach of splitting the SSAB equation into a Laplacian and diagonal shift operator is discussed with respect to the underlying eigenvalue problem. First, we solve the equations using standard methods. Then, the coupled equations are decomposed into operators for membranes stresses, basal shear stress and driving stress. Applying reasonable parameter values, we demonstrate that the operator of the membrane stresses is much stiffer than the operator of the basal shear stress. Here, we could apply a new splitting method, which alternates between the iteration on the membrane-stress operator and the basal-shear operator, with a more frequent iteration on the operator of the membrane stresses. We show that this splitting accelerates and stabilize the computational performance of the numerical method, although an appropriate choice of the standard method used to solve for all operators in one step speeds up the scheme as well.
 
Key Words
    partial differential equations; operator-splitting methods; laplacian operator, diagonal shift operator iterative methods; eigenvalue approach; ice streams; membrane stress; shallow shelf approximation
 
Address
Jurgen Geiser : Department of Physics, Ernst-Moritz-Arndt University of Greifswald, Felix-Hausdorff-Str. 6, D-17489 Greifswald, Germany
Reinhard Calov : Potsdam Institute for Climate Impact Research, PO Box 60 12 03, D-14412 Potsdam, Germany
 

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