Double-Higher-Order Large-Domain Volume/Surface Integral Equation Method for Analysis of Composite Wire-Plate-Dielectric Antennas and Scatterers

Chobanyan, Elene; Ilić, Milan M.; Notaroš, Branislav M.

doi:10.1109/tap.2013.2281360

Cited by 17 publications

(21 citation statements)

References 46 publications

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“…According to Chobanyan et al . [], the equation describing the EM problem of an arbitrarily shaped structure consisting of dielectric materials of the equivalent complex permittivity ε e = ε − jσ/ ω in a domain V , excited by a time‐harmonic EM field of complex electric field intensity vector E i and angular frequency ω, is given by

\frac{D}{{normalε}_{normale}} - ω^{2} μ_{0} true \underset{V}{true\int} C boldD g normald V - \frac{1}{{normalε}_{0}} ([], true \underset{V}{true\int} \nabla' \cdot ((), C boldD) \cdot \nabla g normald V + true \underset{S_{d}}{true\int} boldn \cdot ((), C boldD) \nabla g normald S) = E_{i},

where D is the equivalent electric displacement vector, D = ε e E , whose normal component is continuous ( n ⋅ D 1 = n ⋅ D 2 ) across the surfaces of abrupt discontinuity in ε e , S d . The electric contrast of the dielectric with respect to free space (background medium) is defined as C = (ε e − ε 0 )/ε e , and g is the free‐space Green's function.…”

Section: Outline Of the Volume Integral Equation Theory And Numericalmentioning

confidence: 99%

“…In our discretization of equation [ Chobanyan et al ., ], the computational domain is first geometrically tessellated using Lagrange‐type generalized curved parametric hexahedra of arbitrary geometrical orders K u , K v , and K w ( K u , K v , K w ≥ 1), shown in Figure and analytically described as [ Ilić and Notaroš , ]

\begin{matrix} center \\ center r (u, v, w) = \sum_{i = 0}^{K_{u}} \sum_{j = 0}^{K_{v}} \sum_{k = 0}^{K_{w}} {boldr}_{i j k} L_{i}^{K_{u}} (u) L_{j}^{K_{v}} (v) L_{k}^{K_{w}} (w), \\ center \begin{array}{c} center & L_{i}^{K_{u}} ((), u) = true \prod_{\begin{array}{l} italicl = 0 \\ l \neq italici \end{array}}^{K_{u}} \frac{u - u_{l}}{u_{i} - u_{l}}, & - 1 \leq u, v, w \leq 1, \end{array} \end{matrix}

where r ijk = r ( u i , v j , w k ) are the position vectors of interpolation nodes and

L_{i}^{K_{u}}

represent Lagrange interpolation polynomials in the u coordinate, with u l being the uniformly spaced interpolating nodes in u defined as u l = (2 l − K u )/ K u , l = 0, 1, …, K u , and similarly for

L_{j}^{K_{v}} ((), v)

and

L_{k}^{K_{w}} ((), w)

. Curvilinear hexahedral modeling facilitates volumetric meshes that can employ very large elements, which is consistent with the double‐higher‐order large‐domain (entire‐domain) VIE paradigm.…”

Section: Outline Of the Volume Integral Equation Theory And Numericalmentioning

confidence: 99%

“…[, ], and Chobanyan et al . []. However, none of the works have provided much details about continuously inhomogeneous VIE implementations.…”

Section: Introductionmentioning

confidence: 99%

“…On one side, the technique represents a continuously inhomogeneous generalization of the double‐higher‐order (higher‐order modeling of both the geometry and the current) VIE method in Chobanyan et al . []. On the other side, it represents a VIE version of the continuously inhomogeneous FEM in Ilić et al .…”

Section: Introductionmentioning

confidence: 99%

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Lagrange‐type modeling of continuous dielectric permittivity variation in double‐higher‐order volume integral equation method

2015

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A novel double-higher-order entire-domain volume integral equation (VIE) technique for efficient analysis of electromagnetic structures with continuously inhomogeneous dielectric materials is presented. The technique takes advantage of large curved hexahedral discretization elements-enabled by double-higher-order modeling (higher-order modeling of both the geometry and the current)-in applications involving highly inhomogeneous dielectric bodies. Lagrange-type modeling of an arbitrary continuous variation of the equivalent complex permittivity of the dielectric throughout each VIE geometrical element is implemented, in place of piecewise homogeneous approximate models of the inhomogeneous structures. The technique combines the features of the previous double-higher-order piecewise homogeneous VIE method and continuously inhomogeneous finite element method (FEM). This appears to be the first implementation and demonstration of a VIE method with double-higher-order discretization elements and conformal modeling of inhomogeneous dielectric materials embedded within elements that are also higher (arbitrary) order (with arbitrary material-representation orders within each curved and large VIE element). The new technique is validated and evaluated by comparisons with a continuously inhomogeneous double-higher-order FEM technique, a piecewise homogeneous version of the double-higher-order VIE technique, and a commercial piecewise homogeneous FEM code. The examples include two real-world applications involving continuously inhomogeneous permittivity profiles: scattering from an egg-shaped melting hailstone and near-field analysis of a Luneburg lens, illuminated by a corrugated horn antenna. The results show that the new technique is more efficient and ensures considerable reductions in the number of unknowns and computational time when compared to the three alternative approaches.

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\frac{D}{{normalε}_{normale}} - ω^{2} μ_{0} true \underset{V}{true\int} C boldD g normald V - \frac{1}{{normalε}_{0}} ([], true \underset{V}{true\int} \nabla' \cdot ((), C boldD) \cdot \nabla g normald V + true \underset{S_{d}}{true\int} boldn \cdot ((), C boldD) \nabla g normald S) = E_{i},

Section: Outline Of the Volume Integral Equation Theory And Numericalmentioning

confidence: 99%

\begin{matrix} center \\ center r (u, v, w) = \sum_{i = 0}^{K_{u}} \sum_{j = 0}^{K_{v}} \sum_{k = 0}^{K_{w}} {boldr}_{i j k} L_{i}^{K_{u}} (u) L_{j}^{K_{v}} (v) L_{k}^{K_{w}} (w), \\ center \begin{array}{c} center & L_{i}^{K_{u}} ((), u) = true \prod_{\begin{array}{l} italicl = 0 \\ l \neq italici \end{array}}^{K_{u}} \frac{u - u_{l}}{u_{i} - u_{l}}, & - 1 \leq u, v, w \leq 1, \end{array} \end{matrix}

where r ijk = r ( u i , v j , w k ) are the position vectors of interpolation nodes and

L_{i}^{K_{u}}

L_{j}^{K_{v}} ((), v)

and

L_{k}^{K_{w}} ((), w)

Section: Outline Of the Volume Integral Equation Theory And Numericalmentioning

confidence: 99%

“…[, ], and Chobanyan et al . []. However, none of the works have provided much details about continuously inhomogeneous VIE implementations.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Lagrange‐type modeling of continuous dielectric permittivity variation in double‐higher‐order volume integral equation method

2015

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“…1). The results are obtained for different incidence angles in the plane θ = 90° (xy-plane -for 0° radar elevation angle [4] (6,400 unknowns). Note that the MoM-VIE technique is very suitable for simulations of inhomogeneous scatterers (e.g., melting ice particles).…”

Section: Scattering Calculations For Mixed-mode Oscillationsmentioning

confidence: 99%

Electromagnetic scattering by oscillating rain drops of asymmetric shapes

Sekeljic

Manic

Chobanyan

et al. 2014

2014 IEEE Antennas and Propagation Society International Symposium (APSURSI)

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Computational electromagnetic analysis of scatting by oscillating rain drops with asymmetric shapes is presented. Mixed-mode oscillations of drops are attributed to sustained drop collisions in events having a highly organized line convection embedded within a larger rain system. The scattering matrix and differential reflectivity of drops are dependent on the particular oscillation modes and different time instants within the oscillation cycle. The results also demonstrate the superiority of the higher order method of moments over the conventional discrete dipole approximation method in oscillating rain drop analysis.

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Investigating raindrop shapes, oscillation modes, and implications for radio wave propagation

et al. 2014

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Studies of raindrop shapes, oscillation modes, and implications for radio wave propagation are presented. Drop shape measurements in natural rain using 2-D video disdrometers (2DVDs) are discussed. As a representative exception to vast majority of the cases where the "most probable" shapes conform to the axisymmetric (2,0) oscillation mode, an event with a highly organized line convection embedded within a larger rain system is studied. Measurements using two collocated 2DVD instruments and a C-band polarimetric radar clearly show the occurrence of mixed-mode drop oscillations within the line, which in turn is attributed to sustained drop collisions. Moreover, the fraction of asymmetric drops determined from the 2DVD camera data increases with the calculated collision probability when examined as time series. Recent wind-tunnel experiments of drop collisions are also discussed. They show mixed-mode oscillations, with (2,1) and (2,2) modes dramatically increasing in oscillation amplitudes, in addition to the (2,0) mode, immediately upon collision. The damping time constant of the perturbation caused by the collision is comparable to the inverse of the collision frequency within the line convection. Scattering calculations using an advanced method of moments numerical technique are performed to accurately and efficiently determine the pertinent parameters of electrically large oscillating raindrops with asymmetric shapes needed for radio wave propagation. The simulations show that the scattering matrix and differential reflectivity of drops are dependent on the particular oscillation modes and different time instants within the oscillation cycle. The technique can be utilized in conjunction with 3-D reconstruction of drop shapes from 2DVD data.

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Double-Higher-Order Large-Domain Volume/Surface Integral Equation Method for Analysis of Composite Wire-Plate-Dielectric Antennas and Scatterers

Cited by 17 publications

References 46 publications

Lagrange‐type modeling of continuous dielectric permittivity variation in double‐higher‐order volume integral equation method

Lagrange‐type modeling of continuous dielectric permittivity variation in double‐higher‐order volume integral equation method

Electromagnetic scattering by oscillating rain drops of asymmetric shapes

Investigating raindrop shapes, oscillation modes, and implications for radio wave propagation

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