Affine conjugate adaptive Newton methods for nonlinear elastomechanics

Please always quote using this URN: urn:nbn:de:0297-zib-7768
  • The paper extends affine conjugate Newton methods from convex to nonconvex minimization, with particular emphasis on PDE problems originating from compressible hyperelasticity. Based on 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.

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Author:Martin WeiserORCiD, Peter Deuflhard, Bodo Erdmann
Document Type:ZIB-Report
Tag:affine conjugate Newton methods; cranio-maxillofacial surgery; multilev; nonconvex minimization; nonlinear elastomechnics; soft tissue simulation
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M15 Newton-type methods
65-XX NUMERICAL ANALYSIS / 65Kxx Mathematical programming, optimization and variational techniques / 65K10 Optimization and variational techniques [See also 49Mxx, 93B40]
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Bxx Elastic materials / 74B20 Nonlinear elasticity
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Gxx Equilibrium (steady-state) problems / 74G65 Energy minimization
Date of first Publication:2004/04/23
Series (Serial Number):ZIB-Report (04-01)
Published in:Appeared in: Opt. Meth. Softw. 22(3): 413-431 (2007)