Improved combined tangential formulation for electromagnetic analysis of penetrable bodies

Solís, Diego M.; Taboada, J. M.; Rubiños-López, Óscar; Obelleiro, F.

doi:10.1364/josab.32.001780

Cited by 13 publications

(9 citation statements)

References 46 publications

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“…Recently, it has successfully been extended to the solution of metamaterial and plamonic problems in near infrared frequencies and in optics [21,22,[24][25][26]. Based on Love's equivalence principle, metallic nanostructures can be replaced by equivalent electric and magnetic currents distributed over the boundary surfaces and interfaces.…”

Section: Methods Of Moments For Surface Integral Equationsmentioning

confidence: 99%

“…Without lack of generality, let us focus on the case where a single particle is repeated, and let us first consider the problem of the isolated particle in a homogeneous medium. Applying SIE-MoM to this problem poses a matrix system as shown in Equation (26), which according to Equations (24) and (25) can be decomposed into the sum of the contribution of the Green's function through the internal and the external regions simultaneously. Since the nanoparticles are identical except from rotation and translation movements, and thanks to the translational and rotational invariance of the couplings between the basis functions of each particle, the problem can be solved via the hybridization of MoM and MLFMA as follows (see diagram in Fig.…”

Section: Acceleration Techniquesmentioning

confidence: 99%

“…In this paper, we present a deep review of the effort we have made over the last years extending the SIE-MoM [21,[24][25][26] combined with the most recent advances in spectral acceleration techniques, based on the multilevel fast multipole algorithm (MLFMA) [27][28][29] and the fast Fourier transform (FFT) [30][31][32], for the simulation of realistic large-scale plasmonic systems. This methodology was applied for the solution of problems such as the design of nanoantennas [33,34] and optical wireless interconnects [35].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

SQUEEZING MAXWELL'S EQUATIONS INTO THE NANOSCALE (Invited Paper)

Solís¹,

Taboada²,

Landesa³

et al. 2015

PIER

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Abstract-The plasmonic behavior of nanostructured materials has ignited intense research for the fundamental physics of plasmonic structures and their cutting-edge applications concerning the fields of nanoscience and biosensing. The optical response of plasmonic metals is generally well-described by classical Maxwell's Equations (ME). Thus, the understanding of plasmons and the design of plasmonic nanostructures can therefore directly benefit from lastest advances achieved in classic research areas such as computational electromagnetics. In this context, this paper is devoted to review the most recent advances in nanoplasmonic modeling, related with the latest breakthroughs in surface integral equation (SIE) formulations derived from ME. These works have extended the scope of application of Maxwell's Equations, from microwave/milimeter waves to infrared and optical frequency bands, in the emerging fields of nanoscience and medical biosensing.

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Section: Methods Of Moments For Surface Integral Equationsmentioning

confidence: 99%

Section: Acceleration Techniquesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

SQUEEZING MAXWELL'S EQUATIONS INTO THE NANOSCALE (Invited Paper)

Solís¹,

Taboada²,

Landesa³

et al. 2015

PIER

View full text Add to dashboard Cite

show abstract

“…While, in the literature, experimental studies are often supported by differential solvers, their applicability to complex problems is usually limited to small-scale and/or simplified models due to well-known drawbacks, such as need for space (host-medium) discretizations that are accompanied with artificial truncations. Major tools of computational electromagnetics, that is, surface integral equations [11,12] employing integro-differential operators, are recently applied to plasmonic problems with promising results for realistic simulations of complex structures [13][14][15][16][17][18][19][20][21][22][23]. In fact, surface integral equations need only the discretization of boundaries between different media, which usually correspond to the surface of the plasmonic object.…”

Section: Introductionmentioning

confidence: 99%

Integral-Equation Formulations of Plasmonic Problems in the Visible Spectrum and Beyond

Çekinmez¹,

Karaosmanoğlu²,

Ergül³

2017

Dynamical Systems - Analytical and Computational Techniques

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Computational modeling of nano-plasmonic structures is essential to understand their electrodynamic responses before experimental efforts in measurement setups. Similar to the other ranges of the electromagnetic spectrum, there are alternative methods for the numerical analysis of nano-plasmonic problems, while the optics literature is dominated by differential equations that require discretizations of the host media with artificial truncations. These approaches often need serious assumptions, such as periodicity, infinity, or self-similarity, in order to reduce the computational load. On the other hand, surface integral equations based on integro-differential operators can bring important advantages for accurate and efficient modeling of nano-plasmonic problems with arbitrary geometries. Electrical properties of materials, which may be obtained either experimentally or via physical modeling, can easily be inserted into integral-equation formulations, leading to accurate predictions of electromagnetic responses of complex structures. This chapter presents the implementation of such accurate, efficient, and reliable solvers based on appropriate combinations of surface integral equations, discretizations, numerical integrations, fast algorithms, and iterative techniques. As a case study, nanowire transmission lines are investigated in wide-frequency ranges, demonstrating the capabilities of the developed implementations.

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“…This plays an important role in DDM, since the well-conditioned sub-domain matrices can be used as an preconditioner for the entire system. However, this favorable iterative convergence is achieved at the expense of compromised accuracy inherited from CFIE [17]. Moreover, due to the global radiation coupling among different sub-domains, full matrices are generated in the conventional SIE-DDM system.…”

mentioning

confidence: 99%

A Local Coupling Multitrace Domain Decomposition Method for Electromagnetic Scattering From Multilayered Dielectric Objects

Zhao

Chen

et al. 2020

IEEE Trans. Antennas Propagat.

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In this paper, a local coupling multi-trace domain decomposition method (LCMT-DDM) based on surface integral equation (SIE) formulations is proposed to analyze electromagnetic scattering from multilayered dielectric objects. Different from the traditional SIE-DDM, where the interactions between sub-domains are accounted for using global radiation coupling, LCMT-DDM uses a local coupling scheme. The original multilayered object is decomposed into several independent domains, i.e. the exterior region (free space) and many homogeneous interior regions (dielectrics). The boundaries of sub-domains are all touching-faces, where only the Robin transmission conditions (RTCs) are enforced to ensure the field continuity. Hence, each sub-domain only couples with its neighboring regions, which makes the DDM system a highly sparse matrix especially when the number of sub-domains is large. In each sub-domain, the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) for dielectrics are used as the governing equations. By imposing RTCs, well-conditioned equations are formed in each sub-domain without invoking the combined field integral equation (CFIE), which usually causes accuracy issues in dielectric modeling. Since the sub-domain matrices are diagonally dominant, the flexible generalized minimal residual (FGMRES) technique is used to accelerate the iterative solution of the whole DDM system. Moreover, an effective preconditioner that can be recursively constructed is proposed.

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Improved combined tangential formulation for electromagnetic analysis of penetrable bodies

Cited by 13 publications

References 46 publications

SQUEEZING MAXWELL'S EQUATIONS INTO THE NANOSCALE (Invited Paper)

SQUEEZING MAXWELL'S EQUATIONS INTO THE NANOSCALE (Invited Paper)

Integral-Equation Formulations of Plasmonic Problems in the Visible Spectrum and Beyond

A Local Coupling Multitrace Domain Decomposition Method for Electromagnetic Scattering From Multilayered Dielectric Objects

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