Parallel block‐preconditioned monolithic solvers for fluid‐structure interaction problems

Abstract

In this work, we consider the solution of fluid-structure interaction (FSI) problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary Lagrangian-Eulerian framework and a nonlinear harmonic mesh motion model. Monolithic approaches require the solution of large ill-conditioned linear systems of algebraic equations at every Newton step. Direct solvers tend to use too much memory even for a relatively small number of degrees of freedom and, in addition, exhibit superlinear growth in arithmetic complexity. Thus, iterative solvers are the only viable option. To ensure convergence of iterative methods within a reasonable amount of iterations, good and, at the same time, cheap preconditioners have to be developed. We study physics-based block preconditioners, which are derived from the block-LDU factorization of the FSI Jacobian, and their performance on distributed memory parallel computers in terms of two-and three-dimensional test cases permitting large deformations. KEYWORDS fluid-structure interaction, monolithic formulation, parallel solvers, physics-based block preconditioners Int J Numer Methods Eng. 2019;117:623-643.wileyonlinelibrary.com/journal/nme

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