A Parallel One‐Field Fictitious‐Domain Finite Element Method for Large‐Scale Fluid–Structure Interaction

ABSTRACT We present a distributed‐memory finite‐element framework for large‐scale incompressible fluid–structure interaction (FSI) based on a monolithic one‐field fictitious‐domain formulation. The velocity and pressure are defined on a fixed Eulerian background mesh and discretized using Taylor–Hood finite elements with quadratic velocity and linear pressure approximation, while the immersed solid is represented by an updated Lagrangian mesh. The resulting saddle‐point systems are solved by preconditioned MINRES with a symmetric split preconditioner, which takes a block‐Jacobi form in parallel. The method is assessed using two‐ and three‐dimensional lid‐driven‐cavity benchmarks involving deformable discs, slabs, spheres, and cylinders. Serial–parallel comparisons, temporal and background‐mesh refinement studies, and quantitative solid‐motion measures support the numerical consistency of the implementation. Strong‐scaling results are reported up to 256 MPI ranks in two dimensions and 512 MPI ranks in three dimensions. Matrix assembly scales well, whereas degradation of the block‐Jacobi preconditioner is the main factor limiting linear‐solver efficiency. Nevertheless, the parallel implementation substantially reduces wall‐clock time and enables large three‐dimensional monolithic FSI simulations that would be prohibitively expensive in serial.