On the use of perfectly matched layers in the presence of long or backward propagating guided elastic waves

Dhia, Anne‐Sophie Bonnet‐Ben; Chambeyron, Colin; Legendre, Guillaume

doi:10.1016/j.wavemoti.2013.08.001

Cited by 21 publications

(18 citation statements)

References 33 publications

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“…The discretization matrices remain local on ϒ and no information of the transversal part of the modes is necessary. For the PML one hybrid mode matched variant is known [3], which exploits the bi orthogonality of the waveguide modes. So mode matching combined with a PML is not as trivial as for the Hardy space infinite element method.…”

Section: Hardy Space Mode Matching For Scattering Problemsmentioning

confidence: 99%

“…for the perfectly matched layer method, where the damping profile is typically adjusted to one wavenumber. In [3] a hybrid perfectly matched layer/modal based method was proposed in order to reduce the error of the perfectly matched layer method arising from waveguide modes with small longitudinal wavenumbers. However, the method depends again non-linearly on ω 2 .…”

Section: Introductionmentioning

confidence: 99%

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Two scale Hardy space infinite elements for scalar waveguide problems

Halla

Nannen

2017

Adv Comput Math

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We consider the numerical solution of the Helmholtz equation in domains with one infinite cylindrical waveguide. Such problems exhibit wavenumbers on different scales in the vicinity of cut-off frequencies. This leads to performance issues for non-modal methods like the perfectly matched layer or the Hardy space infinite element method. To improve the latter, we propose a two scale Hardy space infinite element method which can be optimized for wavenumbers on two different scales. It is a tensor product Galerkin method and fits into existing analysis. Up to arbitrary small thresholds it converges exponentially with respect to the number of longitudinal unknowns in the waveguide. Numerical experiments support the theoretical error bounds.

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Section: Hardy Space Mode Matching For Scattering Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two scale Hardy space infinite elements for scalar waveguide problems

Halla

Nannen

2017

Adv Comput Math

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“…2(b), a multiplication with α leads to a rotation of iκ n in the complex plane). The modified perfectly matched layer methods presented in [28,8] combine complex scaling with a special treatment of the backward propagating mode. For scattering problems with only a few backward propagating modes this approach works well, but again it leads to non-linear eigenvalue problems when discretizing the resonance problem (2.2).…”

Section: Numerical Implementations Of the Radiation Conditionmentioning

confidence: 99%

“…They allow more flexibility in the damping than PMLs, but lose the property of being perfectly matched. For semi-infinite linear elastic cylinders in the time-harmonic setting, two methods based on bi-orthogonal relations of modal solutions were proposed: The method presented in [3] is based directly on a modal representation of the solution, whereas in [28,8] ways to modify standard PMLs are reported. They rely on a smart post processing by exchanging backward incoming with backward outgoing modes.…”

Section: Introductionmentioning

confidence: 99%

Hardy space infinite elements for time-harmonic two-dimensional elastic waveguide problems

Halla

Nannen

2015

Wave Motion

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We consider time-harmonic linear elasticity equations in domains containing two-dimensional semi-infinite strips.Since for such problems there exist modes with different signs of group and phase velocity, standard perfectly matched layer (PML) as well as standard Hardy space infinite element methods fail.We apply a recently developed infinite element method for a physically correct discretization of such waveguide problems which is based on a Laplace transform in propagation direction. In the Laplace domain the space of transformed solutions can be separated into a sum of a space of incoming and a space of outgoing functions where both function spaces are certain Hardy spaces. The Hardy space is chosen such that the construction of a simple infinite element is possible.The method does not use a modal separation and works on intervals of frequencies. On those intervals the involved operators are frequency independent and hence lead to linear eigenvalue problems when computing resonances. Numerical experiments containing convergence tests and resonance problems are included.

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“…In such configuration, the PMLs do not select the correct outgoing solution. A remedy has been proposed and analyzed in [6] where the physical solution is reconstructed a posteriori by combining several wrong fields computed with PMLs. An alternative consists in using adiabatic viscoelastic absorbing layers [8] which are not perfectly matched and need to be sufficiently large to avoid spurious reflections.…”

Section: Introductionmentioning

confidence: 99%

Iterative methods for scattering problems in isotropic or anisotropic elastic waveguides

et al. 2016

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We consider the time-harmonic problem of the diffraction of an incident propagative mode by a localized defect, in an infinite elastic waveguide. We propose several iterative algorithms to compute an approximate solution of the problem, using a classical finite element discretization in a small area around the perturbation, and a modal expansion in the unbounded straight parts of the guide. Each algorithm can be related to a socalled domain decomposition method, with an overlap between the domains. Specific transmission conditions are used, so that at each step of the algorithm only the sparse finite element matrix has to be inverted, the modal expansion being obtained by a simple projection, using a bi-orthogonality relation. The benefit of using an overlap between the finite element domain and the modal domain is emphasized. An original choice of transmission conditions is proposed which enhances the effect of the overlap and allows us to handle arbitrary anisotropic materials. As a by-product, we derive transparent boundary conditions for an arbitrary anisotropic waveguide. The transparency of these new boundary conditions is checked for twoand three-dimensional anisotropic waveguides. Finally, in the isotropic case, numerical validation for twoand three-dimensional waveguides illustrates the efficiency of the new approach, compared to other existing methods, in terms of number of iterations and CPU time.

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On the use of perfectly matched layers in the presence of long or backward propagating guided elastic waves

Cited by 21 publications

References 33 publications

Two scale Hardy space infinite elements for scalar waveguide problems

Two scale Hardy space infinite elements for scalar waveguide problems

Hardy space infinite elements for time-harmonic two-dimensional elastic waveguide problems

Iterative methods for scattering problems in isotropic or anisotropic elastic waveguides

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