Workshop on Biomechanics and Chemotaxis, Fri, 14 Dec, 2007
Speaker: Christian Wieners
Abstract
We introduce a general parallel solution method for coupled nonlinear
and time-dependent problems for porous media models. Our model
includes the deformation of the solid skeleton coupled with
the pressure (determining the seepage velocity of the pore fluid by
Darcy's law).
For the application of this model to a bio-mechanical configuration we have to
consider large deformations (modeled by a specially adapted hyperelastic
material law allowing only for limited compressions determined by the
porosity), strong anisotropy for modeling fibered materials, and large
variations in the permeability. A stable discretization is provided by
Taylor-Hood elements in space and the backward Euler method in time.
The parallel solution process is realized by a clear and lean interface of a
parallel front-end (responsible for the parallel data management of the mesh
and parallel preconditioned iterative solver) and the finite element software
PANDAS (responsible for the model and the discretization). The solution of
the arrising linear systems requires efficient parallel preconditioning. Here,
we use an overlapping domain decomposition preconditioner with approximate ILU
solving on the subdomains and an algebraic coarse problem correction which is
constructed on a structured overlay mesh.
We demonstrate the application of our solution methods by parallel
3-d simulations of the mechanical behavior of the intervertebral disc.
C. Wieners (Karlsruhe)
B. Markert, N. Karajan, W. Ehlers (Stuttgart)
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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