Mathieu functions and their applications to scattering by a coated strip

Holland, Robert C.; Cable, V.

doi:10.1109/15.121661

Cited by 27 publications

(16 citation statements)

References 5 publications

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“…In this section we examine the even functions, which are given by the series [13]- [15], Here m and n are both even or both odd. Substituting from (2) into (1), we obtain the following second order recurrence relation for the expansion coefficients B e n (h, m) [13]- [15], [17]:…”

Section: Calculation Of the Expansion Coefficients For The Even Functmentioning

confidence: 99%

Power series expansions for Mathieu functions with small arguments

Kokkorakis

Roumeliotis

2000

Math. Comp.

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Section: Calculation Of the Expansion Coefficients For The Even Functmentioning

confidence: 99%

Power series expansions for Mathieu functions with small arguments

Kokkorakis

Roumeliotis

2000

Math. Comp.

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“…For a DR with very large dielectric permittivity, the dielectricair interface can be approximated by a hypothetical perfect magnetic conductor (PMC), which requires that the tangential components of the magnetic field vanish on that surface. In elliptical coordinate the scalar Helmholtz equation can be written in the form [11]:…”

Section: Wave and Helmholtz Equation In Elliptic Coordinatesmentioning

confidence: 99%

Resonance Frequencies and Far Field Patterns of Elliptical Dielectric Resonator Antenna: Analytical Approach

Tadjalli¹,

Sebak²,

Denidni³

2006

PIER

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Abstract-In this paper the classical boundary value approach employing the separation of variable technique is used to analyze the properties of elliptic dielectric resonator antennas. In this approach, the fields inside the resonator are expanded in terms of Mathieu and modified Mathieu functions. Numerical results are given for resonant frequencies of different modes as well for fields distribution inside the resonator. Series Green's functions are used to calculate the fields inside the cavity and also far field patterns for a given feed. Using the Green's function method provides more accurate results compared to a pure cavity model technique. The analysis and design are verified through numerical simulations. A parametric study has been performed to show effects of the elliptical dielectric resonator antennas (EDRAs) parameters on far field patterns.

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“…The Mathieu functions have found their applications in various areas (see, e.g., [16,11,7]). Some spectral approximation results in Sobolev spaces were first derived in [17].…”

Section: Approximation By Mathieu Functionsmentioning

confidence: 99%

An improved estimate of PSWF approximation and approximation by Mathieu functions

Wang

Zhang

2011

Journal of Mathematical Analysis and Applications

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In this paper, an error estimate of spectral approximations by prolate spheroidal wave functions (PSWFs) with explicit dependence on the bandwidth parameter and optimal order of convergence is derived, which improves the existing result in [Chen et al., Spectral methods based on prolate spheroidal wave functions for hyperbolic PDEs, SIAM J. Numer. Anal. 43 (5) (2005) 1912-1933]. The underlying argument is applied to analyze spectral approximations of periodic functions by Mathieu functions, which leads to new estimates featured with explicit dependence on the intrinsic parameter.

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Mathieu functions and their applications to scattering by a coated strip

Cited by 27 publications

References 5 publications

Power series expansions for Mathieu functions with small arguments

Power series expansions for Mathieu functions with small arguments

Resonance Frequencies and Far Field Patterns of Elliptical Dielectric Resonator Antenna: Analytical Approach

An improved estimate of PSWF approximation and approximation by Mathieu functions

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