An overview of the null-field method. II: Convergence and numerical stability

We develop from our generalized null field method a generalization of the Kirchhoff, or physical optics, approach to diffraction theory. Corresponding to each particular null field method there is a corresponding physical optics approximation, which becomes exact when one of the coordinates being used is constant over the surface of the scattering body. We show how to improve these approximations by a computational procedure which is more efficient than those introduced in the previous paper. The reradiations from our physical optics surface sources more nearly satisfy the extinction theorem the deeper they penetrate the interiors of scattering bodies. We find that we have to introduce a new definition of the parts of a body’s surface that are directly illuminated and shadowed, and we suggest that this may be more apposite in general than the usual definition. The computational examples presented herein indicate that useful approximations to surface source densities are obtained in the umbra and penumbra of bodies. These examples also show that our scattered fields are in several particulars superior to those obtained from the conventional Kirchhoff approach. It is important to choose that physical optics approximation most appropriate for the scattering body in question.

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Direct and inverse resonance problems for shielded composite objects treated by means of the null-field method

IEEE Transactions on Microwave Theory and Techniques ◽

10.1109/22.41038 ◽

1989 ◽

Vol 37 (11) ◽

pp. 1732-1739 ◽

Cited By ~ 4

Author(s):

W. Zheng

Keyword(s):

Field Method ◽

Null Field ◽

Composite Objects

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Null-field method to electromagnetic scattering from uniaxial anisotropic particles

Optics Communications ◽

10.1016/s0030-4018(03)01164-7 ◽

2003 ◽

Vol 218 (1-3) ◽

pp. 11-17 ◽

Cited By ~ 17

Author(s):

Adrian Doicu

Keyword(s):

Electromagnetic Scattering ◽

Field Method ◽

Anisotropic Particles ◽

Null Field

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Null Field and Interior Field Methods for Laplace’s Equation in Actually Punctured Disks

Abstract and Applied Analysis ◽

10.1155/2013/927873 ◽

2013 ◽

Vol 2013 ◽

pp. 1-15 ◽

Cited By ~ 1

Author(s):

Hung-Tsai Huang ◽

Ming-Gong Lee ◽

Zi-Cai Li ◽

John Y. Chiang

Keyword(s):

Error Analysis ◽

Numerical Solutions ◽

Field Method ◽

Boundary Integral ◽

Laplace’S Equation ◽

Algebraic Equations ◽

Field Methods ◽

Laplace's Equation ◽

Null Field ◽

Boundary Methods

For solving Laplace’s equation in circular domains with circular holes, the null field method (NFM) was developed by Chen and his research group (see Chen and Shen (2009)). In Li et al. (2012) the explicit algebraic equations of the NFM were provided, where some stability analysis was made. For the NFM, the conservative schemes were proposed in Lee et al. (2013), and the algorithm singularity was fully investigated in Lee et al., submitted to Engineering Analysis with Boundary Elements, (2013). To target the same problems, a new interior field method (IFM) is also proposed. Besides the NFM and the IFM, the collocation Trefftz method (CTM) and the boundary integral equation method (BIE) are two effective boundary methods. This paper is devoted to a further study on NFM and IFM for three goals. The first goal is to explore their intrinsic relations. Since there exists no error analysis for the NFM, the second goal is to drive error bounds of the numerical solutions. The third goal is to apply those methods to Laplace’s equation in the domains with extremely small holes, which are called actually punctured disks. By NFM, IFM, BIE, and CTM, numerical experiments are carried out, and comparisons are provided. This paper provides an in-depth overview of four methods, the error analysis of the NFM, and the intriguing computation, which are essential for the boundary methods.

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