A review of absorbing boundary conditions for two and three-dimensional electromagnetic scattering problems

Mittra, R.; Ramahi, O.O.; Khebir, A.; Gordon, Richard K.; Kouki, Ammar B.

doi:10.1109/20.34361

Cited by 56 publications

(21 citation statements)

References 8 publications

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“…An alternate derivation [5] of the boundary operators can also be carried out by imposing the requirement that u(p, <j>) in (3) satisfy the wave equation and then deriving a recursion relationship in terms of the angular derivatives. The second order ABC thus reduces to 1…”

Section: Two-dimensional Abcsmentioning

confidence: 99%

“…However, in tests carried out using the vector ABC derived in [6], reliable results have been obtained on placing the mesh truncation boundary a fraction of a wavelength distant from the scatterer. The first section presents a scalar ABC proposed in [5] and the second section is devoted to the formulation of vector ABCs derived in [5] and [6]. It can then be shown that the coefficients in the series expansion, a n , satisfy the following recursion relationship -1jkna n = n(n -l)a n _x + -Da n -i…”

Section: Three Dimensional Abcsmentioning

confidence: 99%

“…The two dimensional ones investigated here are the well-known Bayliss-Turkel [3] and Engquist-Majda [4] absorbing boundary conditions. The three dimensional ABCs presented here are those derived by Mittra [5] and Kanellopoulos and Webb [6]. All the ABCs discussed here are derived from the Wilcox expansion and can only be applied on a spherical outer boundary.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Application of edge-based finite elements and vector ABCs in 3-D scattering

Chatterjee

Jin

Volakis

1992

IEEE Antennas and Propagation Society International Symposium 1992 Digest

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Section: Two-dimensional Abcsmentioning

confidence: 99%

Section: Three Dimensional Abcsmentioning

confidence: 99%

See 1 more Smart Citation

Application of edge-based finite elements and vector ABCs in 3-D scattering

Chatterjee

Jin

Volakis

1992

IEEE Antennas and Propagation Society International Symposium 1992 Digest

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“…The most important are the hybrid finite-element/boundary integral (FE-BI) methods [2], [3], the absorbing boundary condition (ABC) methods [4]- [6], and the artificial absorber (AA) methods [7], [8].…”

Section: Introductionmentioning

confidence: 99%

Finite-element solution to electromagnetic scattering problems by means of the Robin boundary condition iteration method

Alfonzetti

Borzì

2002

IEEE Trans. Antennas Propagat.

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A new numerical method, called Robin boundary condition iteration (RBCI), is proposed for the finite-element (FE) solution of electromagnetic scattering problems in open boundary domains. The unbounded domain is truncated to a bounded one by means of a fictitious boundary that contains the scatterer and on which a suitable nonhomogeneous Robin (mixed) boundary condition is assumed for the Helmholtz equation in the bounded domain. The Robin condition is expressed by means of an integral formula (the second Green identity) in terms of the field in the interior of the bounded domain, with the integration surface being a surface strictly enclosed by the truncation boundary. The discretized differential and integral equations are then coupled together to solve the problem. The formulation is completely immune from the well-known interior resonance problems. A simple and effective iterative solving scheme is described. Examples are also provided to validate RBCI and compare it with other methods. Index Terms-Finite-element (FE) methods, integral equations, scattering.

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“…In high frequency problems ABC stands for Absorbing Boundary Condition [5], whereas in low frequency problems it stands for Asymptotic Boundary Condition [6]. Recently electrostatic and magnetostatic ABCs for two-dimensional and axisymmetric finite element models have been developed [7] and have been shown to give accurate fields in typical problems [8].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic boundary condition for three dimensional magnetostatic finite elements

Brauer¹,

Schaefer²,

Lee

et al. 1991

IEEE Trans. Magn.

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An asymptotic boundary condition (ABC) is derived for open boundaries of three dimensional magnetic vector potential magnetostatic finite element models. The new boundary condition avoids any increase in matrix bandwidth and hence is computationally very efficient. The ABC is used on boundaries of three dimensional finite element models of both a circular coil and a square coil; the computed magnetic fields or inductances of the two models agree within a few percent with Biot-Savart or classical solutions.

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A review of absorbing boundary conditions for two and three-dimensional electromagnetic scattering problems

Cited by 56 publications

References 8 publications

Application of edge-based finite elements and vector ABCs in 3-D scattering

Application of edge-based finite elements and vector ABCs in 3-D scattering

Finite-element solution to electromagnetic scattering problems by means of the Robin boundary condition iteration method

Asymptotic boundary condition for three dimensional magnetostatic finite elements

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