On Preconditioning and the Eigensystems of Electromagnetic Radiation Problems

Hesford, Andrew J.; Chew, Weng Cho

doi:10.1109/tap.2008.926783

Cited by 20 publications

(11 citation statements)

References 19 publications

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“…With the introduction of the relative wave impedance in (29), the residual of (29) can be interpreted as the tangential error electric field on . We shall test with , the same function space for the electric current , and subsequently, the MFIE surface penalty term can be written as (30) A sesquilinear form can be defined for each element as (31) Consequently, by extending the MFIE surface penalty terms to include all the elements, we have the following expression:…”

Section: ) Magnetic Field Integral Equationmentioning

confidence: 99%

A Discontinuous Galerkin Surface Integral Equation Method for Electromagnetic Wave Scattering From Nonpenetrable Targets

Peng

Lim

Lee

2013

IEEE Trans. Antennas Propagat.

146

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We present a discontinuous Galerkin surface integral equation method, herein referred to as IEDG, for time harmonic electromagnetic wave scattering from nonpenetrable targets. The proposed IEDG algorithm allows the implementation of the combined field integral equation (CFIE) using square-integrable, , trial and test functions without any considerations of continuity requirements across element boundaries. Due to the local characteristics of basis functions, it is possible to employ nonconformal surface discretizations of the targets. Furthermore, it enables the possibility to mix different types of elements and employ different order of basis functions within the same discretization. Therefore, the proposed IEDG method is highly flexible to apply adaptation techniques. Numerical results are included to validate the accuracy and demonstrate the versatility of the proposed IEDG method. In addition, a complex large-scale simulation is conducted to illustrate the potential benefits offered by the proposed method for modeling multiscale electrically large targets.Index Terms-Discontinuous Galerkin method, electromagnetic scattering, integral equation method, Maxwell's equations.

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Section: ) Magnetic Field Integral Equationmentioning

confidence: 99%

A Discontinuous Galerkin Surface Integral Equation Method for Electromagnetic Wave Scattering From Nonpenetrable Targets

Peng

Lim

Lee

2013

IEEE Trans. Antennas Propagat.

146

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“…As it is detailed in [9], radiation problems give rise to an impedance matrix ill-conditioned with disparate eigenvalues.…”

Section: Preconditioner Formulationmentioning

confidence: 99%

“…The convergence of the iterative solutions for this kind of problems is often very slow, essentially due to the localized nature of the excitation defined over a small portion of the mesh representing the antenna. It is also caused by the use of non-uniform meshes to accurately model the details in the neighbourhood of the feed point [9]. The convenience of applying effective preconditioners for radiation problems is thus highlighted.…”

Section: Introductionmentioning

confidence: 99%

“…Recent works have proposed the preconditioning of the ordinary equation with the transpose complex conjugate of the impedance matrix [16], a multiplicative preconditioner using Calderon identities [17] or a localized preconditioner in the vicinity of a radiation problem antenna [9]. The preconditioning scheme presented in this work acts on three main issues that are responsible for the bad convergence of radiation problems: i) it moderates the strong dominance of the self-coupling of wire or surface antennas; ii) it weights the impedance matrix and the current and voltage vectors to normalize the respective units of wire and surface elements; iii) it moderates the disparities of the impedance matrix values due to the disparate mesh size.…”

Section: Introductionmentioning

confidence: 99%

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Geometry Based Preconditioner for Radiation Problems Involving Wire and Surface Basis Functions

Araújo¹,

Bertolo

Obelleiro³

et al. 2009

PIER

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Abstract-An innovative preconditioner has been developed in this work. It significantly improves the convergence of the iterative solvers applied to electromagnetic radiation problems by a renormalization of the matrix equation. The preconditioner balances the disparities in terms of magnitude and units caused by the strong self-coupling of the antennas, the non-uniformity of the meshes and also by the coexistence of wire and surface basis functions. It can be easily integrated into different electromagnetic solvers with a negligible impact on the computational cost on account of its simple implementation.

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“…Applications range from advanced antenna design [8,9], stealth technologies [10,11], integrated circuits [12] to optics and photonics [13,14]. One advantage of SIE is that both the analysis and unknowns reside only on the boundary surfaces of the targets.…”

Section: Introductionmentioning

confidence: 99%

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

MacKie-Mason¹,

Greenwood²,

Peng³

2015

PIER

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Abstract-This work investigates an adaptive, parallel and scalable integral equation solver for very large-scale electromagnetic modeling and simulation. A complicated surface model is decomposed into a collection of components, all of which are discretized independently and concurrently using a discontinuous Galerkin boundary element method. An additive Schwarz domain decomposition method is proposed next for the efficient and robust solution of linear systems resulting from discontinuous Galerkin discretizations. The work leads to a rapidly-convergent integral equation solver that is scalable for large multi-scale objects. Furthermore, it serves as a basis for parallel and scalable computational algorithms to reduce the time complexity via advanced distributed computing systems. Numerical experiments are performed on large computer clusters to characterize the performance of the proposed method. Finally, the capability and benefits of the resulting algorithms are exploited and illustrated through different types of real-world applications on high performance computing systems.

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On Preconditioning and the Eigensystems of Electromagnetic Radiation Problems

Cited by 20 publications

References 19 publications

A Discontinuous Galerkin Surface Integral Equation Method for Electromagnetic Wave Scattering From Nonpenetrable Targets

A Discontinuous Galerkin Surface Integral Equation Method for Electromagnetic Wave Scattering From Nonpenetrable Targets

Geometry Based Preconditioner for Radiation Problems Involving Wire and Surface Basis Functions

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

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