On the interface matrix for fluid-structure interaction problems with fictitious domain approach

TL;DR

This paper investigates the computation of the interface matrix in a fictitious domain approach for fluid-structure interaction, emphasizing the importance of accurate integration for optimal convergence.

Contribution

It analyzes the interface matrix computation involving two meshes and highlights the necessity of precise integration for the method's effectiveness.

Findings

Accurate interface matrix computation is crucial for optimal convergence.

Numerical tests demonstrate the impact of integration accuracy on performance.

The study provides insights into finite element discretization in fluid-structure interaction.

Abstract

We study a recent formulation for fluid-structure interaction problems based on the use of a distributed Lagrange multiplier in the spirit of the fictitious domain approach. In this paper, we focus our attention on a crucial computational aspect regarding the interface matrix for the finite element discretization: it involves integration of functions supported on two different meshes. Several numerical tests show that accurate computation of the interface matrix has to be performed in order to ensure the optimal convergence of the method.