Domain Decomposition Method Based on Integral Equation for Solution of Scattering From Very Thin, Conducting Cavity

Hu, Jun; Zhao, Ran; Miao, Tian; Zhao, Huapeng; Jiang, Ming; Xiang, Wei; Nie, Zai Ping

doi:10.1109/tap.2014.2341701

Cited by 32 publications

(2 citation statements)

References 15 publications

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“…In [4], a non-overlapping DDM is proposed to efficiently calculate the scattering from non-penetrable objects. Afterwards, some troublesome problems from complex targets have been solved by employing integral equation domain decomposition method(IE-DDM) [5,6]. For multi-objects, DDM divides the original problem into many separable subdomains to improve the computational efficiency [7,8].…”

Section: Introductionmentioning

confidence: 99%

Efficient Sparse Algorithm for Solving Multi-Objects Scattering Based on Compressive Sensing

Chai¹,

Wang²

2019

PIER M

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To improve computational efficiency of traditional method for solving separable multiobjects scattering problems, each subdomain impedance matrix is sparsified by biorthogonal lifting wavelet transform(BLWT) without allocating auxiliary memory, and a sparse underdetermined equation is constructed by enjoying the prior knowledge from known excitation in wavelet domain, then orthogonal matching pursuit (OMP) is employed to fast and accurately solve the sparse underdetermined equation under compressive sensing (CS) framework. Numerical results of separable perfectly electric conduct (PEC) multi-objects are presented to show the efficiency of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Efficient Sparse Algorithm for Solving Multi-Objects Scattering Based on Compressive Sensing

Chai¹,

Wang²

2019

PIER M

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“…However, when SIE is used to model piecewise homogeneous or multilayered dielectric objects, careful treatment of complex junction basis functions is required to ensure the boundary conditions [9]. To overcome this difficulty, the contact-region modeling method (CRM) [10] and domain decomposition method (DDM) [11], [13], [14] have been developed. In CRM, the interface is divided into two contact surfaces to ensure the boundary condition between different regions.…”

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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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Multiscale Computational Electromagnetics

Yang,

Huang,

et al. 2024

Encyclopedia of RF and Microwave Engineering

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Maxwell's equations are valid from the atomic to intergalactic length scales. Hence, features at various spatial or temporal scales may all be significant in electromagnetic (EM) problems of interest and may affect the results of multiscale modeling and simulation in computational electromagnetics (CEM). Solving electromagnetic problems that involve multiscale structures efficiently is challenging and is of growing interest in CEM. In recent decades, various approaches have been proposed for addressing the multiscale issue of electrically large problems. These methods can be roughly categorized into three types: the “geometry‐based,” “algebra‐based,” and “physics‐based” approaches. In this chapter, we introduce these three representative approaches for modeling multiscale problems in CEM: (1) the discontinuous Galerkin integral equation method (DGIE), which is a general domain decomposition framework for dealing with structures with mesh nonconformity; (2) the nested dissection accelerated H‐LU‐based fast direct solver for sparse matrices, which is used to construct effective preconditioners; and (3) the resistive sheet boundary condition‐based hybrid finite element‐boundary integral‐multilevel fast multipole algorithm (FE–BI–MLFMA), which can simulate electromagnetic field interactions with microwave‐absorbing honeycomb structures efficiently. After we present the formulation for each approach, we present examples to demonstrate its accuracy, capability, and performance.

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Domain Decomposition Method Based on Integral Equation for Solution of Scattering From Very Thin, Conducting Cavity

Cited by 32 publications

References 15 publications

Efficient Sparse Algorithm for Solving Multi-Objects Scattering Based on Compressive Sensing

Efficient Sparse Algorithm for Solving Multi-Objects Scattering Based on Compressive Sensing

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

Multiscale Computational Electromagnetics

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