Iterative solvers for coupled fluid--solid scattering

Authors:
Jan Mandel;Mirela O. Popa
Affiliations:
Department of Mathematics, University of Colorado at Denver, and Department of Aerospace Engineering Sciences, University of Colorado at Boulder, USA;General Dynamics Armament and Technical Products, Charlotte, NC 28217, USA
Venue:
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Year:
2005

Citing 8
Cited 1

GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
Multigrid convergence for nonsymmetric, indefinite variational problems on one smoothing step

Applied Mathematics and Computation - Second Copper Mountain conference on Multigrid methods Copper Mountain, Colorado
Stable coupling method for interface scattering problems by combined integral equations and finite elements

Journal of Computational Physics
First-Order System Least-Squares for the Helmholtz Equation

SIAM Journal on Scientific Computing
An iterative substructuring method for coupled fluid-solid acoustic problems

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A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations

SIAM Journal on Scientific Computing
Multigrid Simulation for High-Frequency Solutions of the Helmholtz Problem in Heterogeneous Media

SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems

An optimization-based approach for solving a time-harmonic multiphysical wave problem with higher-order schemes

Journal of Computational Physics

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Abstract

The multigrid method is used for coupled fluid-solid scattering discretized by linear finite elements. Numerical results show that using Krylov methods as smoothers allows coarser spaces than with standard smoothers, such as Jacobi and Gauss-Seidel. Block diagonal preconditioning for the 2x2 block diagonal matrix of the coupled system is also considered. Both multigrid and block diagonal preconditioned iterations fail to converge for frequencies when the scatterer is at resonance. It is shown how to transform the system into an equivalent one to avoid the resonance and to recover the convergence of the iterations.