Wave boundary elements: a theoretical overview presenting applications in scattering of short waves

Perrey‐Debain, Emmanuel; Trevelyan, J.; Bettess, P.

doi:10.1016/s0955-7997(03)00127-9

Cited by 53 publications

(45 citation statements)

References 21 publications

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“…The enrichment idea spawned a large body of literature including the work on the Partition of Unity Finite Element Method (PUFEM) [7,18,19,22] and also similar enrichment techniques such as the Generalised Finite Element Method [30,31] the Ultra-Weak Variational Formulation [14,20] and the Discontinuous Enrichment Method [9,16,34]. The enrichment approach is also used in other methods such as the Boundary Element Method [25,26,27]. A recent survey on various enrichment approaches could be found in [12].…”

Section: Introductionmentioning

confidence: 99%

Enriched finite elements for initial-value problem of transverse electromagnetic waves in time domain

Drolia

Mohamed

Laghrouche

et al. 2017

Computers & Structures

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract This paper proposes a partition of unity enrichment scheme for the solution of the electromagnetic wave equation in the time domain. A discretization scheme in time is implemented to render implicit solutions of systems of equations possible. The scheme allows for calculation of the field values at different time steps in an iterative fashion. The spatial grid is partitioned into a finite number of elements with intrinsic shape functions to form the bases of solution. Furthermore, each finite element degree of freedom is expanded into a sum of a slowly varying term and a combination of highly oscillatory functions. The combination consists of plane waves propagating in multiple directions, with a fixed frequency. This significantly reduces the number of degrees of freedom required to discretize the unknown field, without compromising on the accuracy or allowed tolerance in the errors, as compared to that of other enriched FEM approaches. Also, this considerably reduces the computational costs in terms of memory and processing time. Parametric studies, presented herein, confirm the robustness and efficiency of the proposed method and the advantages compared to another enrichment method.

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Section: Introductionmentioning

confidence: 99%

Enriched finite elements for initial-value problem of transverse electromagnetic waves in time domain

Drolia

Mohamed

Laghrouche

et al. 2017

Computers & Structures

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“…There are however other families of functions which could be used to discretised sound at the surface. One option which has attracted attention is the use of oscillatory basis functions 6,7 , since these might be able to capture some of the oscillatory behavior of the solution allowing larger elements for the same accuracy. In the Wave Matching approach this idea is taken a step further and the basis functions are chosen to be slices (on ܵ) through waves (i.e.…”

Section: Discretisation Of Sound For a Rigid Obstacle With Planar Recmentioning

confidence: 99%

“…This is encouraging initial evidence that supports the notion that the use of a wave-matching scheme does indeed allow the interaction matrices to be sparsified. Ongoing research will look at other test cases and examine how the number of interactions which must be retained varies with frequency, since this will inform us as to whether the scheme becomes quasi-geometric at high frequencies as hoped, or just gives a fixed efficiency scaling as other existing oscillatory basis functions have achieved 6,7 .…”

Section: Numerical Implementationmentioning

confidence: 99%

Towards a full-bandwidth numerical acoustic model

Hargreaves¹,

Lam²

2013

Proceedings of Meetings on Acoustics

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Prediction models are at the heart of modern acoustic engineering. Current commercial room acoustic simulation software almost exclusively approximates the propagation of sound geometrically as rays or beams. These assumptions yield efficient algorithms, but the maximum accuracy they can achieve is limited by how well the geometric assumption represents sound propagation in a given space. This comprises their accuracy at low frequencies in particular. Methods that directly model wave effects are more accurate but they have a computational cost that scales with problem size and frequency, effectively limiting them to small or low frequency scenarios. This paper will report the results of initial research into a new full-bandwidth model which aims to be accurate and efficient for all frequencies; the name proposed for this is the "Wave Matching Method". This builds on the Boundary Element Method with the premise that if an appropriate interpolation scheme is designed then the model will become 'geometrically dominated' at high frequencies. Other propagation modes may then be removed without significant error, yielding an algorithm which is accurate and efficient. This paper will present the general concepts of wave matching and the results from some numerical test cases.

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“…To overcome this difficulty, several advanced methods have been proposed in recent years. Here, we just mention the fast multipole method (FMM) [15,18,19], the wave boundary element method (WBEM) or the wave basis functions method [4,16,17] based on the partition of unity method (PUM) [13]. A review of some advanced computational methods for wave simulation in high frequency range has been presented by Bettess [4].…”

Section: Circular Arc-shaped Crackmentioning

confidence: 99%

A comparative study of three BEM for transient dynamic crack analysis of 2-D anisotropic solids

García-Sánchez

Zhang

2006

Comput Mech

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International audienceThree different boundary element methods (BEM) for transient dynamic crack analysis in two-dimensional (2-D), homogeneous, anisotropic and linear elastic solids are presented. Hypersingular traction boundary integral equations (BIEs) in frequency-domain, Laplace-domain and time-domain with the corresponding elastodynamic fundamental solutions are applied for this purpose. In the frequency-domain and the Laplace-domain BEM, numerical solutions are first obtained in the transformed domain for discrete frequency or Laplace-transform parameters. Time-dependent results are subsequently obtained by means of the inverse Fourier-transform and the inverse Laplace-transform algorithm of Stehfest. In the time-domain BEM, the quadrature formula of Lubich is adopted to approximate the arising convolution integrals in the time-domain BIEs. Hypersingular integrals involved in the traction BIEs are computed through a regulariza-tion process that converts the hypersingular integrals to regular integrals, which can be computed numerically, and singular integrals which can be integrated analytically. Numerical results for the dynamic stress intensity factors are presented and discussed for a finite crack in an infinite domain subjected to an impact crack-face loading

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Wave boundary elements: a theoretical overview presenting applications in scattering of short waves

Cited by 53 publications

References 21 publications

Enriched finite elements for initial-value problem of transverse electromagnetic waves in time domain

Enriched finite elements for initial-value problem of transverse electromagnetic waves in time domain

Towards a full-bandwidth numerical acoustic model

A comparative study of three BEM for transient dynamic crack analysis of 2-D anisotropic solids

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