An Iterative Substructuring Method for Coupled Fluid-Solid Acoustic Problems
COLORADO UNIV AT DENVER
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A fast parallel iterative method is proposed for the solution of linear systems arizing from Finite Element discretization of the time harmonic acoustics of coupled uid-solid systems in uid pressure and solid displacement formulation. The method generalizes the FETI-H method for the Helmholtz equation to elastic scattering. The uid and the solid domains are decomposed into non-overlapping subdomains. Continuity of the solution 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 the GCR method preconditioned by a subspace correction. In each iteration, the method requires the solution of one independent acoustic problem per subdomain, and the solution of a coarse 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 number of iterations was mostly about same as the number of iterations of the FETI-H method for the related Helmholtz problem with Neumann boundary condition instead of elastic scatterer. Convergence is explained from the spectrum of the iteration operator.
- Numerical Mathematics