# Parallel time-stepping for fluid-structure interactions

## TL;DR

This paper introduces a parallel-in-time method for fluid-structure interaction problems, combining monolithic formulation, finite element discretization, and Crank-Nicolson scheme to improve computational efficiency in 2D and 3D cases.

## Contribution

It develops a parallel-in-time solution approach for fluid-structure interactions within a monolithic framework, addressing efficiency and specific challenges.

## Key findings

- Demonstrates efficiency improvements in 2D and 3D test cases
- Analyzes challenges related to the structure of fluid-structure interaction problems
- Provides insights into limitations of the parallel-in-time method

## Abstract

We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space is based on equal order finite element for all variables and a variant of the Crank-Nicolson scheme is used as second order time integrator. To accelerate the solution of the systems, we analyze a parallel-in time method. For different numerical test cases in 2d and in 3d we present the efficiency of the resulting solution approach. We also discuss some special challenges and limitations that are connected to the special structure of fluid-structure interaction problem.