Affine conjugate adaptive Newton methods for nonlinear elastomechanics

Authors:
Martin Weiser;Peter Deuflhard;Bodo Erdmann
Affiliations:
Zuse Institute Berlin, Berlin, Germany;Zuse Institute Berlin, Berlin, Germany;Zuse Institute Berlin, Berlin, Germany
Venue:
Optimization Methods & Software
Year:
2007

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Abstract

The paper extends affine conjugate Newton methods from convex to nonconvex minimization, with particular emphasis on PDE problems originating from compressible hyperelasticity. On the basis of well-known schemes from finite dimensional nonlinear optimization, three different algorithmic variants are worked out in a function space setting, which permits an adaptive multilevel finite element implementation. These algorithms are tested on two well-known 3D test problems and a real-life example from surgical operation planning.