Solution of Helmholtz Equation in the Exterior Domain by Elementary Boundary Integral Methods

Amini, S.; Kirkup, Stephen Martin

doi:10.1006/jcph.1995.1093

Cited by 76 publications

(61 citation statements)

References 7 publications

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“…Note that the required accuracy can be achieved for an arbitrary set of parameters, i.e., for any value of the contrast between the cylinder and the host medium. It is free from the inaccuracies intrinsic to finite-difference timedomain (FDTD) approximations [25]- [27] near to the sharp natural-mode resonances, as well as near to the non-physical "numerical resonances" caused by the spurious eigenvalues occurring if using non-MBIEs [15], [16].…”

Section: Problem Formulation Methods Description and Main Characmentioning

confidence: 99%

“…As discussed in [17] and [18], the spurious eigenvalues are absent for the Muller boundary IE (MBIE) [19], which, in the two-dimensional (2-D) case, is a pair of coupled second-kind IEs for the field components tangential to the scatterer contour [16], [17], [19],. This is unlike the combined-field IE [18], which only pushes the spurious eigenvalues off from the real axis.…”

Section: Manipulation Of Backscattering From a Dielectricmentioning

confidence: 99%

“…However, one should keep in mind that many forms of the boundary IEs are contaminated by the presence of spurious eigenvalues [15], [16]. For instance, all the works [3]- [14] dealt with such IE although this fact was fully acknowledged only in the paper [10].…”

Section: Manipulation Of Backscattering From a Dielectricmentioning

confidence: 99%

See 2 more Smart Citations

Manipulation of Backscattering From a Dielectric Cylinder of Triangular Cross-Section Using the Interplay of GO-Like Ray Effects and Resonances

Sukharevsky

Nosich

Altintas

2015

IEEE Trans. Antennas Propagat.

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Abstract-A triangular dielectric cylinder (dielectric prism) of the size, in cross-section, comparable to or moderately larger than the wavelength is a scatterer, which blends together two different types of electromagnetic behavior: geometrical optics (GO) and resonance. As shown in this paper, the first is responsible, for instance, for enhanced reflection from an isosceles 90• prism, if illuminated from the base. The second is responsible for the peaks in the total scattering and absorption cross-sections (ACSs) at the natural-mode frequencies. The numerical analysis is performed by solving the well-conditioned Muller-type boundary integral equation (IE) discretized using an algorithm with controlled accuracy.

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Section: Problem Formulation Methods Description and Main Characmentioning

confidence: 99%

Section: Manipulation Of Backscattering From a Dielectricmentioning

confidence: 99%

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Manipulation of Backscattering From a Dielectric Cylinder of Triangular Cross-Section Using the Interplay of GO-Like Ray Effects and Resonances

Sukharevsky

Nosich

Altintas

2015

IEEE Trans. Antennas Propagat.

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“…The subspace spanned by the eigenfunctions of ∆ S1 has a dimension equal to 2 + 1. (1) are respectively the spherical Bessel and first-kind Hankel functions of order , we have the following proposition (see [2,40]). …”

Section: The Example Of the Spherementioning

confidence: 96%

Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation

Antoine¹,

Darbas²

2007

ESAIM: M2AN

116

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“…Moreover, in classical studies, the quadrature error is rarely considered important in comparison with that from the boundary discretisation (e.g., [19]). However, care must be taken that it is sufficiently small [20]. For regular integrals, this constraint is of no particular consequence as standard quadrature routines are able to compute the required integration tasks very accurately.…”

Section: Article In Pressmentioning

confidence: 99%

A practical examination of the errors arising in the direct collocation boundary element method for acoustic scattering

Treeby

2009

Engineering Analysis with Boundary Elements

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a b s t r a c tFor many engineers and acousticians, the boundary element method (BEM) provides an invaluable tool in the analysis of complex problems. It is particularly well suited for the examination of acoustical problems within large domains. Unsurprisingly, the widespread application of the BEM continues to produce an academic interest in the methodology. New algorithms and techniques are still being proposed, to extend the functionality of the BEM, and to compute the required numerical tasks with greater accuracy and efficiency. However, for a given global error constraint, the actual computational accuracy that is required from the various numerical procedures is not often discussed. Within this context, this paper presents an investigation into the discretisation and computational errors that arise in the BEM for acoustic scattering. First, accurate routines to compute regular, weakly singular, and nearly weakly singular integral kernels are examined. These are then used to illustrate the effect of the requisite boundary discretisation on the global error. The effects of geometric and impedance singularities are also considered. Subsequently, the actual integration accuracy required to maintain a given global error constraint is established. Several regular and irregular scattering examples are investigated, and empirical parameter guidelines are provided.

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Solution of Helmholtz Equation in the Exterior Domain by Elementary Boundary Integral Methods

Cited by 76 publications

References 7 publications

Manipulation of Backscattering From a Dielectric Cylinder of Triangular Cross-Section Using the Interplay of GO-Like Ray Effects and Resonances

Manipulation of Backscattering From a Dielectric Cylinder of Triangular Cross-Section Using the Interplay of GO-Like Ray Effects and Resonances

Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation

A practical examination of the errors arising in the direct collocation boundary element method for acoustic scattering

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