Fluid-Structure Interactions: One-Field Monolithic Fictitious Domain Method and Its Parallelization (Advances in Applied Mathematics and Mechanics, 2025)
In this paper, we delve into the parallelization of the one-field monolithic fictitious domain (MFD) method, a comprehensive algorithm designed for simulating fluid-structure interactions (FSI). This method treats the velocity fields of both the fluid and solid as a unified field through an $L^2$ projection, enabling synchronous equation solving instead of sequential approaches. Given the computational intensity of 3D domain simulations, parallelizing the algorithm and the linear systems derived from discretization becomes imperative. This parallelization significantly reduces simulation time from several months to just a few days. We focus on parallelizing the algorithm for FSI simulations on uniform meshes. Our primary aim is to develop an efficient and robust algorithm capable of handling complex FSIs, including scenarios involving collisions of multiple immersed solids in fluid. Such scenarios often require high-resolution meshes to accurately resolve phenomena near collision points and fluid-structure interfaces.