Solving the volume integral equations of electromagnetic scattering

Botha, Matthys M.

doi:10.1016/j.jcp.2006.02.004

Cited by 79 publications

(48 citation statements)

References 37 publications

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“…Different forms of Electric Field Integral Equations (EFIE) have been studied by many researchers [1][3-5] [7,8]. The new EFIEs are based on those studies and are carefully formed by considering the characteristics of basis functions.…”

Section: Efies and Impedance Matrixmentioning

confidence: 99%

Volume-Surface Integral Equations with hybrid curl-conforming and divergence-conforming basis functions

Cao

2010

2010 IEEE Antennas and Propagation Society International Symposium

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Section: Efies and Impedance Matrixmentioning

confidence: 99%

Volume-Surface Integral Equations with hybrid curl-conforming and divergence-conforming basis functions

Cao

2010

2010 IEEE Antennas and Propagation Society International Symposium

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“…The choice of the formulation and the unknown allows us to construct several different VIE formulations for dielectric scattering problems [Botha, 2006;Sun and Chew, 2009;Markkanen et al, 2012b]. The choice also decides the type of basis and testing functions that should be used in order to obtain a converging numerical solution.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of the Potential Formulation of the Volume Integral Equation for Electromagnetic Scattering

Markkanen

2017

Radio Science

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We present a discretization of the potential volume integral equation for electromagnetic scattering by dielectric objects. The equations are written for the vector and scalar potentials combined with the Lorenz gauge condition. The advantage of the potential formulation over the more conventional formulations, that is, the field, flux, or current formulations, is that the potentials are continuous across material interfaces enabling the use of fully continuous basis functions. The discretization with the fully continuous basis functions leads to a better conditioned system matrix compared to those of the other formulations discretized with the fully or partially discontinuous functions. Thus, it speeds up the iterative solution. The method is accelerated with the precorrected fast Fourier transform algorithm.

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“…Volume integral equations are a popular tool for numerically solving scattering problems in the engineering community, see, e.g., [4,6,11,22,28,35,41,42]. However, the discretization of the integral operator itself is sometimes done in a crude way, and a convergence analysis of the technique is often missing, in particular when material parameters are not globally smooth.…”

Section: Introductionmentioning

confidence: 99%

A volume integral equation method for periodic scattering problems for anisotropic Maxwell's equations

Nguyen

2015

Applied Numerical Mathematics

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Solving the volume integral equations of electromagnetic scattering

Cited by 79 publications

References 37 publications

Volume-Surface Integral Equations with hybrid curl-conforming and divergence-conforming basis functions

Volume-Surface Integral Equations with hybrid curl-conforming and divergence-conforming basis functions

Numerical Analysis of the Potential Formulation of the Volume Integral Equation for Electromagnetic Scattering

A volume integral equation method for periodic scattering problems for anisotropic Maxwell's equations

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