Quasi-Newton waveform iteration for partitioned surface-coupled multiphysics applications

Research output: Contribution to journalArticle


We present novel coupling schemes for partitioned multiphysics simulation that combine four important aspects for strongly coupled problems: implicit coupling per time step, fast and robust acceleration of the corresponding iterative coupling, support for multirate time stepping, and higher-order convergence in time. To achieve this, we combine waveform relaxation—a known method to achieve higher-order in applications with split time stepping based on continuous representations of coupling variables in time— with interface quasi-Newton coupling, which has been developed throughout the last decade and is generally accepted as a very robust iterative coupling method even for gluing together black-box simulation codes. We show convergence results (in terms of convergence of the iterative solver and in terms of approximation order in time) for two academic testcases—a heat transfer scenario and a fluid-structure interaction simulation. We show that we achieve the expected approximation order and that our iterative method is competitive in terms of iteration counts with those designed for simpler first-order-in-time coupling.


  • Benjamin Rüth
  • Benjamin Uekermann
  • Miriam Mehl
  • Philipp Birken
  • Azahar Monge
  • Hans Joachim Bungartz
External organisations
  • Technical University of Munich
  • Eindhoven University of Technology
  • University of Stuttgart
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics


  • conjugate heat transfer, fluid-structure interaction, higher-order, multiphysics, multirate, multiscale, quasi-Newton, waveform iteration
Original languageEnglish
JournalInternational Journal for Numerical Methods in Engineering
Publication statusE-pub ahead of print - 2020 Jun 2
Publication categoryResearch