An Explicit Time-Domain Finite-Element Boundary Integral Method for Analysis of Electromagnetic Scattering

Dong, Ming; Chen, Liang; Jiang, Lijun; Li, Ping; Bağcı, Hakan

doi:10.1109/tap.2022.3142319

Cited by 7 publications

(7 citation statements)

References 28 publications

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“…To this end, in this work, a "hybrid" scheme is developed to efficiently solve the matrix system (54). The first row of ( 54) is inverted for Λ and the resulting expression is inserted into the second row to yield:…”

Section: E Hybrid Solvermentioning

confidence: 99%

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A Coupled Hybridizable Discontinuous Galerkin and Boundary Integral Method for Analyzing Electromagnetic Scattering

Zhao

Dong

Chen

et al. 2024

IEEE Trans. Antennas Propagat.

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A coupled hybridizable discontinuous Galerkin (HDG) and boundary integral (BI) method is proposed to efficiently analyze electromagnetic scattering from inhomogeneous/composite objects. The coupling between the HDG and the BI equations is realized using the numerical flux operating on the equivalent current and the global unknown of the HDG. This approach yields sparse coupling matrices upon discretization. Inclusion of the BI equation ensures that the only error in enforcing the radiation conditions is the discretization. However, the discretization of this equation yields a dense matrix, which prohibits the use of a direct matrix solver on the overall coupled system as often done with traditional HDG schemes. To overcome this bottleneck, a "hybrid" method is developed. This method uses an iterative scheme to solve the overall coupled system but within the matrix-vector multiplication subroutine of the iterations, the inverse of the HDG matrix is efficiently accounted for using a sparse direct matrix solver. The same subroutine also uses the multilevel fast multipole algorithm to accelerate the multiplication of the guess vector with the dense BI matrix. The numerical results demonstrate the accuracy, the efficiency, and the applicability of the proposed HDG-BI solver.

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Section: E Hybrid Solvermentioning

confidence: 99%

“…On the other hand, boundary integral (BI)-based approaches to truncating computation domains do not suffer from these bottlenecks [46]- [54]. In this work, HDG is used together with a BI formulation to efficiently and accurately simulate electromagnetic scattering from electrically large inhomogeneous/composite objects.…”

Section: Introductionmentioning

confidence: 99%

A Coupled Hybridizable Discontinuous Galerkin and Boundary Integral Method for Analyzing Electromagnetic Scattering

Zhao

Dong

Chen

et al. 2024

IEEE Trans. Antennas Propagat.

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“…In this section, we describe a scheme [Li et al, 2014b, Dong et al, 2020, 2022] that combines DGTD with TDBI to truncate computation domains without suffering from the shortcomings of the other methods briefly described above. TDBI represents the fields on the truncation surface in the form of a retarded time boundary integral defined over a Huygens surface enclosing the scatterer.…”

Section: Ducting (Pmc) Surfacesmentioning

confidence: 99%

“…The several advantages the DG methods comes with (as explained in Section 1.1.6) make them very suitable for multiphysics simulations. Indeed, in the last decade, they have been applied to many multiphysics problems in various fields, such as coupled simulations of electromagnetic/thermal interactions, electromagnetic/plasma interactions, and finally electromagnetic/semiconductor carrier interactions [Homsi et al, 2017, Don, 2019, Dong et al, 2022. In general, multiphysics simulations involve solving different partial differential equations simultaneously, and those partial differential equations are usually characterized by different scales in space and time.…”

Section: Multiphysics Simulation Of Optoelectronic Devicesmentioning

confidence: 99%

Discontinuous Galerkin Time‐Domain Method in Electromagnetics: From Nanostructure Simulations to Multiphysics Implementations

Dong

Chen

et al. 2022

Advances in Time‐Domain Computational Electromagnetic Methods

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In the last few decades, the discontinuous Galerkin time-domain (DGTD) method has become widely popular in various fields of engineering due the fact that it benefits from computational advantages that come with finite volume and finite element formulations. Similarly, in the field of computational electromagnetics, the superiority of the DGTD method has been quickly recognized after first few works on its formulation and 1 implementation to solve Maxwell equations. With further developments in more recent years, the DGTD method has become one of the preeminent solutions to tackle a wide variety of challenging large scale electromagnetic problems including those that require multiphysics modeling.This chapter starts with a brief introduction to the DGTD method. This introduction provides the fundamentals of numerical flux, discretization techniques that rely on vector and nodal basis functions, and incorporation of absorbing boundary conditions. This is followed by descriptions of a time-domain boundary integral(TDBI) scheme, which replaces absorbing boundary conditions within the DGTD method, and a multi-step time integration technique, which uses different time step sizes for the DGTD and TDBI parts. Numerical results show that both techniques significantly improve the efficiency, accuracy, and stability of the traditional DGTD method. Then, the chapter continues with the applications of the DGTD method to several real-life practical problems. More specifically, it describes various novel techniques developed to enable the application of the DGTD method to electromagnetic analysis of nanostructures and graphene-based devices, and multiphysics simulation of optoelectronic antennas and source generators. For each application, several numerical examples are provided to demonstrate the accuracy, efficiency, and robustness of the developed techniques.

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“…Additionally, different phenomena from the optical fields are brought together for the designing purposes of these components in the form of optical interference [4], Guidedmode resonances (GMR) (also known as the Fano-resonances) [5], Kerr effect [6], and many more. Similarly, diverse time domain mathematical approaches, i.e., Finite Difference Time Domain (FDTD) [7], Coupling method [8], Finite Integral Time Domain (FITD) [9], Plane Wave Expansion (PWE) [10], along with frequency domain methods such as the Finite Elements Method (FEM) [11], Method of Moments [12], Transfer Matric Method (TMM) [13] and Fast Multi-pole Method (FMM) [14], are being used to design these components. Mainly dielectrics and semiconductors have been utilized for the design of optical components, which in turn can be modified into different forms to achieve various functionalities, such as optical waveguides [15], directional couplers [16] and Photonic Crystals (PhCs) [17].…”

Section: Introductionmentioning

confidence: 99%

Investigation of Optical-Switching Mechanism Using Guided Mode Resonances

et al. 2022

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Recently, photonic crystals have paved the way to control photonic signals. Therefore, this research numerically investigated the design of the optical switch using the guided-mode resonances in photonic crystals operating in a communication window around 1.55 μm. The design of the device is based on a dielectric slab waveguide to make it compatible with optical waveguides in photonic circuits. Moreover, two signals are used and are termed as the data signal and control signal. The data signal is coupled into the optical waveguide using an out-of-the-plane vertical coupling mechanism, whereas the control signal is index-guided into the optical waveguide to amplify the data signal. The switching parameters of the optical switch are adjusted by changing the number of the photonic crystal periods and implementing a varying radius PhC-cavity within the middle of the PhC-lattice, where the optical characteristics in terms of resonant wavelength, reflection peaks, linewidth, and quality factor of the data signal can be adjusted. The numerical simulations are carried out in open-source finite difference time domain-based software. Congruently, 7% optical amplification is achieved in the data signal with a wavelength shift of 0.011 μm and a quality factor of 12.64. The amplification of the data signal can be utilized to implement an optical switching mechanism. The device is easy to implement and has great potential to be used in programmable photonics and optical integrated circuits.

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An Explicit Time-Domain Finite-Element Boundary Integral Method for Analysis of Electromagnetic Scattering

Cited by 7 publications

References 28 publications

A Coupled Hybridizable Discontinuous Galerkin and Boundary Integral Method for Analyzing Electromagnetic Scattering

A Coupled Hybridizable Discontinuous Galerkin and Boundary Integral Method for Analyzing Electromagnetic Scattering

Discontinuous Galerkin Time‐Domain Method in Electromagnetics: From Nanostructure Simulations to Multiphysics Implementations

Investigation of Optical-Switching Mechanism Using Guided Mode Resonances

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