Philipp Birken — Page 2

arXiv2014

Fast Solvers for Unsteady Thermal Fluid Structure Interaction

We consider time dependent thermal fluid structure interaction. The respective models are the compressible Navier-Stokes equations and the nonlinear heat equation. A partitioned coupling approach via a Dirichlet-Neumann method and a fixed point iteration is employed. As a refence solver a previously developed efficient time adaptive higher order time integration scheme is used. To improve upon this, we work on reducing the number of fixed point coupling iterations. Thus, first widely used vector extrapolation methods for convergence acceleration of the fixed point iteration are tested. In particular, Aitken relaxation, minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are considered. Second, we explore the idea of extrapolation based on data given from the time integration and derive such methods for SDIRK2. While the vector extrapolation methods have no beneficial effects, the extrapolation methods allow to reduce the number of fixed point iterations further by up to a factor of two with linear extrapolation performing better than quadratic.

math.NA↗

arXiv2014

Termination criteria for inexact fixed point methods

We analyze inexact fixed point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed point iteration. Important applications are the Picard iteration and partitioned fluid structure interaction. We prove that the iteration converges irrespective of how accurate the inner systems are solved, provided that a specific relative termination criterion is employed, whereas standard relative and absolute criteria do not have this property. For the analysis, the iteration is modelled as a perturbed fixed point iteration and existing analysis is extended to the nested case x=F(S(x)).

math.NA↗