An Iterative Substructuring Method for Coupled Fluid–Solid Acoustic Problems

A fast parallel iterative method is proposed for the solution of linear equations arising from finite element discretization of the time harmonic coupled fluid–solid systems in fluid pressure and solid displacement formulation. The fluid and the solid domains are decomposed into nonoverlapping subdomains. Continuity of the solution is enforced by Lagrange multipliers. The system is augmented by duplicating the degrees of freedom on the wet interface. The original degrees of freedom are then eliminated and the resulting system is solved by iterations preconditioned by a coarse space correction. In each iteration, the method requires the solution of one independent local acoustic problem per subdomain and the solution of a global problem with several degrees of freedom per subdomain. Computational results show that the method is scalable with the problem size, frequency, and the number of subdomains. The method generalizes the FETI-H method for the Helmholtz equation to coupled fluid–elastic scattering. The number of iterations is about same as for the FETI-H method for the related Helmholtz problem with Neumann boundary condition instead of an elastic scatterer if enough coarse space functions are used. Convergence behavior is explained from the spectrum of the iteration operator and from numerical near decoupling of the equations in the fluid and in the solid regions.