A Discontinuous Galerkin Surface Integral Equation Method for Scattering From Multiscale Homogeneous Objects

Kong, Beibei; Sheng, Xin‐Qing

doi:10.1109/tap.2018.2803133

Cited by 46 publications

(13 citation statements)

References 31 publications

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“…The combined tangential field (CTF) equation is one of the stable surface integral formulations for the homogeneous scattering problem, which can be formulated as [14] inc…”

Section: Formulationmentioning

confidence: 99%

“…The above matrix (15) was found to convergence slowly. To obtain a linear system with a better iteration performance, a preconditioner is used to the matrix equation of (15), which yields 11 xb −− = P M P (17) The DG method with block diagonal preconditioner (BDP) provides an efficient way to solve large multiscale homogeneous scattering problems [14]. However, we found that when the dielectric constant of some scatterers becomes large, the iteration convergence speed of the DG method seriously decreased.…”

Section: Preconditioning Approachesmentioning

confidence: 99%

“…Fewer additional unknowns on the boundary of the sub-domains are needed, and the field relations on the interfaces between sub-domains in DG are intrinsically imbedded in the integral equation. The solution of DG with the surface integral equation (SIE) for non-penetrable objects has been well studied [10][11], and that for penetrable objects is presented in [12][13][14]. However, the slow convergence for DG with block diagonal preconditioner (BDP) is still observed in calculating homogeneous bodies with a high dielectric constant.…”

Section: Introductionmentioning

confidence: 99%

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A Discontinuous Galerkin Surface Integral Solution for Scattering From Homogeneous Objects With High Dielectric Constant

Kong

Huang

Sheng

2020

IEEE Trans. Antennas Propagat.

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The discontinuous Galerkin (DG) method for homogeneous bodies has been studied and shown to be an efficient tool for multi-scale homogeneous bodies. However, the slow convergence of DG with the block diagonal preconditioner (BDP) is still observed in solving high contrast homogeneous bodies. An efficient preconditioning approach is designed for the DG method in this communication by using the sparsing approach on the near-field matrix of the whole region. The iteration convergence speed of the DG method is improved while the computing resources for constructing the preconditioner are effectively reduced. Numerical experiments demonstrate the capability of the presented DG method for multi-scale homogeneous bodies, especially for those with a high dielectric constant.Index Terms-Discontinuous Galerkin method, homogeneous objects, high dielectric constant, multi-scale.

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“…The combined tangential field (CTF) equation is one of the stable surface integral formulations for the homogeneous scattering problem, which can be formulated as [14] inc…”

Section: Formulationmentioning

confidence: 99%

Section: Preconditioning Approachesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Discontinuous Galerkin Surface Integral Solution for Scattering From Homogeneous Objects With High Dielectric Constant

Kong

Huang

Sheng

2020

IEEE Trans. Antennas Propagat.

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“…In the DG method, the computational domain is first divided into smaller subdomains. By independently meshing each subdomain and developing a preconditioner based on the domain decomposition, the mesh generation process can be significantly simplified, and the condition of the matrix is improved . DG‐SIE methods have been developed for PEC targets and for homogeneous dielectric objects .…”

Section: Introductionmentioning

confidence: 99%

“…By independently meshing each subdomain and developing a preconditioner based on the domain decomposition, the mesh generation process can be significantly simplified, and the condition of the matrix is improved. [17][18][19] DG-SIE methods have been developed for PEC targets [16][17][18]20 and for homogeneous dielectric objects. 19 However, objects with IBC have not been treated with this technique.…”

mentioning

confidence: 99%

A discontinuous Galerkin surface integral equation method for scattering from IBC targets

Kong

Ylä‐Oijala

Sihvola

2019

Int J Numerical Modelling

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A discontinuous Galerkin (DG) surface integral equation method is proposed for electromagnetic scattering from targets with the impedance boundary condition (IBC). We present electric field integral equation (EFIE), magnetic field integral equation (MFIE), and self‐dual integral equation formulations for the problem and study their numerical performance. On the basis of the results of these experiments, DG is developed for EFIE and MFIE (DG‐EFIE and DG‐MFIE). The convergence of the iterative solutions and the solution accuracy of DG‐EFIE and DG‐MFIE are further investigated for a wide range of surface impedances. The numerical performance of these formulations is found to be nearly complementary with respect to the surface impedance. The capability of the proposed DG solution strategy for calculating scattering from large multiscale IBC targets is demonstrated.

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hp non-conforming a priori error analysis of an Interior Penalty Discontinuous Galerkin BEM for the Helmholtz equation

Messai

Pernet

2020

Computers & Mathematics with Applications

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This work is concerned with the construction and the hp non-conforming a priori error analysis of a Discontinuous Galerkin DG numerical scheme applied to the hypersingular integral equation related to the Helmholtz problem in 3D. The main results of this article are an error bound in a norm suited to the problem and in the L 2 -norm. Those bounds are quasi-optimal for the h-convergence and the p-convergence. Various formulation choices and penalty functions are theoretically discussed. In particular we show that a penalty function of the shape h 2 p leads to a quasi-optimal convergence of the scheme. Some numerical experiments confirm the expected rates of convergence and the effect of the penalty function.

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A Discontinuous Galerkin Surface Integral Equation Method for Scattering From Multiscale Homogeneous Objects

Cited by 46 publications

References 31 publications

A Discontinuous Galerkin Surface Integral Solution for Scattering From Homogeneous Objects With High Dielectric Constant

A Discontinuous Galerkin Surface Integral Solution for Scattering From Homogeneous Objects With High Dielectric Constant

A discontinuous Galerkin surface integral equation method for scattering from IBC targets

hp non-conforming a priori error analysis of an Interior Penalty Discontinuous Galerkin BEM for the Helmholtz equation

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