Shape-Newton Method for Isogeometric Discretizations of Free-Boundary Problems

  • K. G. van der Zee
  • G. J. van Zwieten
  • C. V. Verhoosel
  • E. H. van Brummelen
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 29)

Abstract

We derive Newton-type solution algorithms for a Bernoulli-type free-boundary problem at the continuous level. The Newton schemes are obtained by applying Hadamard shape derivatives to a suitable weak formulation of the free-boundary problem. At each Newton iteration, an updated free boundary position is obtained by solving a boundary-value problem at the current approximate domain. Since the boundary-value problem has a curvature-dependent boundary condition, an ideal discretization is provided by isogeometric analysis. Several numerical examples demonstrate the apparent quadratic convergence of the Newton schemes on isogeometric-analysis discretizations with C1-continuous discrete free boundaries.

Keywords

Newton-type methods Bernoulli free-boundary problem Shape derivative Isogeometric analysis Smooth discrete boundaries Shape-linearized free-boundary problem 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • K. G. van der Zee
    • 1
  • G. J. van Zwieten
    • 1
  • C. V. Verhoosel
    • 1
  • E. H. van Brummelen
    • 1
  1. 1.Multiscale Engineering Fluid DynamicsEindhoven University of TechnologyEindhovenThe Netherlands

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