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We introduce a novel multi-resolution Localized Orthogonal Decomposition (LOD) for time-harmonic acoustic scattering problems that can be modeled by the Helmholtz equation.
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S. C. Brenner and L. R. Scott · 2008
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Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation
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Applying GMRES to the Helmholtz equation with shifted Laplacian preconditioning: what is the largest shift for which wavenumber-independent convergence is guaranteed?
M. J. Gander, I. G. Graham, and E. A. Spence · 2015
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Stable multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering
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Multiscale sub-grid correction method for time-harmonic high-frequency elastodynamics with wavenumber explicit bounds
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Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations
D. L. Brown, D. Gallistl, and D. Peterseim · 2017
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The Helmholtz equation in heterogeneous media: A priori bounds, well-posedness, and resonances
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A class of iterative solvers for the Helmholtz equation: Factorizations, sweeping preconditioners, source transfer, single layer potentials, polarized traces, and optimized Schwarz methods
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Computational high frequency scattering from high-contrast heterogeneous media
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A two-level shifted laplace preconditioner for Helmholtz problems: Field-of-values analysis and wavenumber-independent convergence
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