A Monolithic FEM/Multigrid Solver for an ALE Formulation of Fluid-Structure Interaction with Applications in Biomechanics

  • Jaroslav Hron
  • Stefan Turek
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 53)


We investigate a new method of solving the problem of fluid-structure interaction of an incompressible elastic object in laminar incompressible viscous flow. Our proposed method is based on a fully implicit, monolithic formulation of the problem in the arbitrary Lagrangian-Eulerian framework. High order FEM is used to obtain the discrete approximation of the problem. In order to solve the resulting systems a quasi-Newton method is applied with the linearized systems being approximated by the divided differences approach. The linear problems of saddle-point type are solved by a standard geometric multigrid with local multilevel pressure Schur complement smoothers.


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© Springer 2006

Authors and Affiliations

  • Jaroslav Hron
    • 1
  • Stefan Turek
    • 1
  1. 1.Institute for Applied Mathematics and NumericsUniversity of DortmundDortmundGermany

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