Iterative solvers for coupled fluid-solid scattering
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation
Journal of Computational Physics
Controllability method for the Helmholtz equation with higher-order discretizations
Journal of Computational Physics
The Trefftz method for the Helmholtz equation with degeneracy
Applied Numerical Mathematics
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Iterative solvers for coupled fluid--solid scattering
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
A fast method for the solution of the Helmholtz equation
Journal of Computational Physics
ICA3PP'10 Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing - Volume Part II
Compact schemes for acoustics in the frequency domain
Mathematical and Computer Modelling: An International Journal
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The Helmholtz problem is hard to solve in heterogeneous media, in particular, when the wave number is real and large. The problem is neither coercive nor Hermitian symmetric. This article concerns the V-cycle multigrid (MG) method for high-frequency solutions of the Helmholtz problem. Since we need to choose at least 10--12 grid points per wavelength for stability, the coarse grid problem is still large. To solve the coarse grid problem efficiently, a nonoverlapping domain decomposition method is adopted without introducing another coarser subspace correction. Various numerical experiments have shown that the convergence rate of the resulting MG method is independent on the grid size and the wave number, provided that the coarse grid problem is fine enough for the solution to capture characteristics of the physical problem.