Wave-Field Interaction With Complex Structures Using Equivalence Principle Algorithm

Li, Maokun; Chew, Weng Cho

doi:10.1109/tap.2006.888453

Cited by 177 publications

(102 citation statements)

References 15 publications

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“…Clustering techniques, such as the Fast Multiple Method [7] and the Hmatrices [8], fall into the second category. The third approach (actually dating as far back as the fifties with the seminal work on diakoptics by Kron [9]) has produced the so-called domain decomposition methods (DDMs) (e.g., [10][11][12][13][14][15]) which, like as not, are applied in tandem with ad hoc entire-domain basis functions [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the application of the ACA for the extraction of macro basis functions from low-rank operators in LEGO is new, and constitutes the main contribution of this work. What's more, this approach is fairly general and capable of extension to other DDMs similarly based on equivalence separation surfaces, such as the Equivalence Principle Algorithm [10,14] and the Generalized Surface Integral Equation method [13], because the scattering operators therein can be rank-deficient as well.…”

Section: Introductionmentioning

confidence: 99%

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Extracting Surface Macro Basis Functions From Low-Rank Scattering Operators With the Aca Algorithm

Lancellotti

2016

PIER M

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Abstract-The Adaptive Cross Approximation (ACA) algorithm has been used to compress the rankdeficient sub-blocks of the matrices that arise in the numerical solution of integral equations (IEs) with the Method of Moments. In the context of the linear embedding via Green's operator (LEGO) method -a domain decomposition technique based on IEs -an electromagnetic problem is modelled by combining "bricks" in turn described by scattering operators which, in many situations, are singular. As a result, macro basis functions defined on the boundary of a brick can be generated by applying the ACA to a scattering operator. Said functions allow compressing the weak form of the LEGO functional equations which then use up less computer memory and are faster to invert.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extracting Surface Macro Basis Functions From Low-Rank Scattering Operators With the Aca Algorithm

Lancellotti

2016

PIER M

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“…Each brick is then characterized by its scattering operator and the electromagnetic interaction among the bricks is captured by transfer operators. Hence, LEGO shares the very same idea of first solving a small problem before a larger one by tearing apart the structure into pieces with methods such as the nested equivalence principle algorithm [21] and the equivalence principle algorithm [22]. The idea of isolating a body with different electromagnetic properties from the surroundings within a designated domain as a "target" for optimization was already applied in [5] in a former 2-D implementation of LEGO.…”

Section: Introductionmentioning

confidence: 99%

An efficient approach to the local optimization of finite electromagnetic band-gap structures

Duque

Lancellotti

Hon

et al. 2014

Turk J Elec Eng & Comp Sci

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Abstract:We propose a methodology based on linear embedding via Green's operators (LEGO) and the eigencurrent expansion method (EEM) to efficiently deal with and locally optimize 2-D electrically large electromagnetic band-gap (EBG) structures. In LEGO terminology, the composite EBG structure is broken up (diakopted) into constitutive elements called "bricks" that we characterize through scattering operators by invoking Love's equivalence principle, while, at the same time, the electromagnetic interaction among the bricks is captured by transfer operators. The resulting electromagnetic problem is then succinctly formulated through an integral equation involving the total inverse scattering operator S −1 of the structure. To perform local optimization, the formulation of the problem allows for variations of the electromagnetic properties and the shape of a set of objects in the EBG structure with respect to those of the others, thereby allowing us to tune a compact designated domain within a large one. Finally, the method of moments and the EEM are applied to achieve a considerable reduction in memory use for the overall problem.

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“…This will lead the reduction of computational time. Equivalence principle algorithm (EPA) which bases on surface equivalence principle and domain decomposition method (DDM) is introduced in [22][23][24][25][26][27][28]. In this algorithm, virtual surfaces are utilized to enclose the sub-regions and translate the unknowns on objects to the unknowns on equivalence surfaces [18,24,28].…”

Section: Introductionmentioning

confidence: 99%

“…In this algorithm, virtual surfaces are utilized to enclose the sub-regions and translate the unknowns on objects to the unknowns on equivalence surfaces [18,24,28]. When complex structures, fine structures, or high permittivity dielectrics are involved in this problem, the density of unknowns on equivalence surfaces is much smaller than that on original objects [22]. Thus, EPA can reduce the number of unknowns and save computational costs.…”

Section: Introductionmentioning

confidence: 99%

Radiation Analysis of Large Antenna Array by Using Periodic Equivalence Principle Algorithm

Zhang¹,

Yang²,

Yang³

et al. 2013

PIER

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Abstract-In this paper, an improved equivalence principle algorithm is proposed to solve the radiation problems of large antenna arrays with periodic structures. This method is a hybridization in which the typical scheme of periodic Green's function is combined with the original equivalence principle algorithm. The repeated elements are changed from the original antenna units into the surfaces enclosing the original ones. The proposed approach is compared with periodic method of moments which is based on the integral equation and the periodic Green's function. Numerical results validate the feasibility of the improved method.

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Wave-Field Interaction With Complex Structures Using Equivalence Principle Algorithm

Cited by 177 publications

References 15 publications

Extracting Surface Macro Basis Functions From Low-Rank Scattering Operators With the Aca Algorithm

Extracting Surface Macro Basis Functions From Low-Rank Scattering Operators With the Aca Algorithm

An efficient approach to the local optimization of finite electromagnetic band-gap structures

Radiation Analysis of Large Antenna Array by Using Periodic Equivalence Principle Algorithm

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