Analysis of Volume Integral Equation Formulations for Scattering by High-Contrast Penetrable Objects

Markkanen, Johannes; Lu, Cai‐Cheng; Cao, Xiande; Ylä‐Oijala, Pasi

doi:10.1109/tap.2012.2189704

Cited by 53 publications

(38 citation statements)

References 24 publications

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“…Curved elements still pose major challenges for SST, and other methods based, e.g., on the singularity cancellation method [89] or the direct evaluation method [90] can allow much easier treatment of singular integrals in those cases. Finally, we note that methods like Duffy's transformation does not usually give satisfactory accuracy, in particular, for SIEs with strongly singular kernels and for the VIEs in the case of high material contrast [51].…”

Section: Evaluation Of Singular Integralsmentioning

confidence: 95%

“…It became extremely important to develop techniques that would improve conditioning of the linear system. In the 21st century research on various regularization and preconditioning techniques [42][43][44][45][46][47] as well as on novel integral equation formulations [48][49][50][51][52] and discretization techniques [53][54][55][56][57][58][59][60] has been very active. The research on these areas is still ongoing [61].…”

Section: Historical Overviewmentioning

confidence: 99%

“…Other possible VIE formulations are presented, e.g., in [51,76]. For a bi-anisotropic medium the VIE representations have exactly the same form as for an anisotropic medium with the difference that the volume currents contain extra terms due to the magnetoelectric coupling parameters…”

Section: Volume Integral Equation Formulationsmentioning

confidence: 99%

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SURFACE AND VOLUME INTEGRAL EQUATION METHODS FOR TIME-HARMONIC SOLUTIONS OF MAXWELL'S EQUATIONS (Invited Paper)

Ylä‐Oijala¹,

Markkanen²,

Järvenpää³

et al. 2014

PIER

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Abstract-During the last two-three decades the importance of computer simulations based on numerical full-wave solutions of Maxwell's has continuously increased in electrical engineering. Software products based on integral equation methods have an unquestionable importance in the frequency domain electromagnetic analysis and design of open-region problems. This paper deals with the surface and volume integral equation methods for finding time-harmonic solutions of Maxwell's equations. First a review of classical integral equation representations and formulations is given. Thereafter we briefly overview the mathematical background of integral operators and equations and their discretization with the method of moments. The main focus is on advanced techniques that would enable accurate, stable, and scalable solutions on a wide range of material parameters, frequencies and applications. Finally, future perspectives of the integral equation methods for solving Maxwell's equations are discussed.

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Section: Evaluation Of Singular Integralsmentioning

confidence: 95%

Section: Historical Overviewmentioning

confidence: 99%

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SURFACE AND VOLUME INTEGRAL EQUATION METHODS FOR TIME-HARMONIC SOLUTIONS OF MAXWELL'S EQUATIONS (Invited Paper)

Ylä‐Oijala¹,

Markkanen²,

Järvenpää³

et al. 2014

PIER

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“…The adaptive integral method (AIM) or precorrected-FFT algorithm (pFFT) [Bleszynski et al, 1996;Phillips and White, 1997] separates the computations of the near and far field interactions. The near field interactions are directly computed by using (26) and the far field interactions are approximated with the interpolation and the FFT.…”

Section: Acceleration With the Fftmentioning

confidence: 99%

“…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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Fast Fourier Transforms in Electromagnetics

Guo

2014

Wiley Encyclopedia of Electrical and Electronics Engineering

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This Chapter review the fast Fourier transform (FFT) technique and its application to computational electromagnetics, especially to the fast solver algorithms including the Conjugate Gradient Fast Fourier Transform (CG‐FFT) method, Precorrected Fast Fourier Transform (pFFT) method, Adaptive Integral Method (AIM), Greens Function Interpolation with FFT (GI‐FFT) method and Integral Equations with FFT (IE‐FFT) method. The basic ideas used in the FFT applications are addressed while the brief introduction to integral equation method is conducted. The general formulation and procedure in the integral equation method, surface integral equations, volume integral equations, solutions to integral equations, and their implementations of fast Fourier transform algorithm are also briefed together with fast convolution using fast Fourier transform. Fast integral equation method developed based on fast Fourier transform are reviewed where conjugate gradient fast Fourier transform method, and precorrected fast Fourier transform method (where projection operators and interpolation operators are also highlighted), adaptive integral method, Greens function interpolation with FFT approach and integral equations with FFT method are also described. While the matching schemes for gradients of Green's functions are addressed, accuracy and complexity, memory requirement and computational cost, and error controls and estimations are also discussed.

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Analysis of Volume Integral Equation Formulations for Scattering by High-Contrast Penetrable Objects

Cited by 53 publications

References 24 publications

SURFACE AND VOLUME INTEGRAL EQUATION METHODS FOR TIME-HARMONIC SOLUTIONS OF MAXWELL'S EQUATIONS (Invited Paper)

SURFACE AND VOLUME INTEGRAL EQUATION METHODS FOR TIME-HARMONIC SOLUTIONS OF MAXWELL'S EQUATIONS (Invited Paper)

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

Fast Fourier Transforms in Electromagnetics

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