A Low-rank Approach for Nonlinear Parameter-dependent Fluid-structure Interaction Problems

TL;DR

This paper introduces a low-rank method for approximating nonlinear fluid-structure interaction problems with parameter dependence, using a partitioned approach and Newton iterations to efficiently compute solutions.

Contribution

It proposes a novel approach that splits parameter sets and applies Newton-based approximations to handle nonlinear FSI problems more efficiently.

Findings

Effective approximation of nonlinear FSI problems demonstrated

Reduction in computational complexity for parameter-dependent problems

Method applicable to large-scale nonlinear FSI simulations

Abstract

Parameter-dependent discretizations of linear fluid-structure interaction problems can be approached with low-rank methods. When discretizing with respect to a set of parameters, the resulting equations can be translated to a matrix equation since all operators involved are linear. If nonlinear FSI problems are considered, a direct translation to a matrix equation is not possible. We present a method that splits the parameter set into disjoint subsets and, on each subset, computes an approximation of the problem related to the upper median parameter by means of the Newton iteration. This approximation is then used as initial guess for one Newton step on a subset of problems.