Partitioned solution strategies for coupled BEM-FEM acoustic fluid-structure interaction problems

TL;DR

This paper compares two FEM-BEM coupling methods for acoustic fluid-structure interaction, introducing a new localized Lagrange multiplier approach and demonstrating its advantages over traditional mortar methods in non-matching interface scenarios.

Contribution

It introduces a novel localized Lagrange multiplier method for FEM-BEM coupling in FSI problems and compares it with the mortar method, highlighting improved performance in non-conforming meshes.

Findings

Localized LLM method performs well with non-matching interfaces.

The iterative solver shows excellent scalability.

Comparison favors the new LLM over mortar in certain scenarios.

Abstract

This paper investigates two FEM-BEM coupling formulations for acoustic fluid-structure interaction (FSI) problems, using the Finite Element Method (FEM) to model the structure and the Boundary Element Method (BEM) to represent a linear acoustic fluid. The coupling methods described interconnect fluid and structure using classical or localized Lagrange multipliers, allowing the connection of non-matching interfaces. First coupling technique is the well known mortar method, that uses classical multipliers and is compared with a new formulation of the method of localized Lagrange multipliers (LLM) for FSI applications with non-matching interfaces. The proposed non-overlapping domain decomposition technique uses a classical non-symmetrical acoustic BEM formulation for the fluid, although a symmetric Galerkin BEM formulation could be used as well. A comparison between the localized methodology and the mortar method in highly non conforming interface meshes is presented. Furthermore, the methodology proposes an iterative preconditioned and projected bi-conjugate gradient solver which presents very good scalability properties in the solution of this kind of problems.