Solving electromagnetic scattering problems at resonance frequencies
作者:
W. D. Murphy,
V. Rokhlin,
M. S. Vassiliou,
期刊:
Journal of Applied Physics
(AIP Available online 1990)
卷期:
Volume 67,
issue 10
页码: 6061-6065
ISSN:0021-8979
年代: 1990
DOI:10.1063/1.345217
出版商: AIP
数据来源: AIP
摘要:
The ‘‘resonance problem’’ is that at certain values of the wave numberk(the resonantk’s), the second‐kind integral equation for solving scattering problems can become extremely ill‐conditioned. This adversely affects both the accuracy and speed of numerical solutions. We consider transverse‐magnetic scattering from a conductor (Dirichlet problem). The integral equation (derived using double‐layer potentials) is discretized using approximately fourth‐order convergent quadrature formulas. At resonantk’s for circular and elliptical scatterers, we find very large condition numbers for the discrete matrices [up toO(107) ], generally leading to poor solutions. We apply two approaches to alleviate the resonance problem. The first is to use a different integral equation, based on both single‐ and double‐layer potentials. This leads to low condition numbers and good solutions at resonantk. The second method is to use the original second‐kind integral equation, introduce a small imaginary part ink, and extrapolate back to the real axis. Solutions obtained by the two methods are in excellent agreement. The extrapolation technique will be particularly useful in the case of the exterior Neumann problem, when the application of the first technique will be numerically more difficult. By solving the resonance problem, we ensure that fast and accurate solutions are obtainable at any arbitrary wave number.
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