On the Nonnormality of Subiteration for a Fluid-Structure-Interaction Problem

Abstract

Subiteration forms the basic iterative method for solving the aggregated equations in fluid-structure-interaction problems, in which the fluid and structure equations are solved alternatingly subject to complementary partitions of the interface conditions. In the present work we establish for a prototypical model problem that the subiteration method can be characterized by recursion of a nonnormal operator. This implies that the method typically converges nonmonotonously. Despite formal stability, divergence can occur before asymptotic convergence sets in. It is shown that the transient divergence can amplify the initial error by many orders of magnitude, thus inducing a severe degradation in the robustness and efficiency of the subiteration method. Auxiliary results concern the dependence of the stability and convergence of the subiteration method on the physical parameters in the problem and on the computational time step.