Analysis of low frequency scattering from penetrable scatterers

Chen, S.Y.; Chew, Weng Cho; Song, Jiming; Zhao, Junsheng

doi:10.1109/36.917883

Cited by 66 publications

(53 citation statements)

References 17 publications

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“…This property has been first derived in [30]. A related property can be found for the identity operator: if both t (r) and b (r) are solenoidal currents, then…”

Section: Lf Behavior Of Integral Operatorsmentioning

confidence: 96%

Low-Frequency Scaling of the Standard and Mixed Magnetic Field and Müller Integral Equations

Bogaert

Cools

Andriulli

et al. 2014

IEEE Trans. Antennas Propagat.

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Abstract-The standard and mixed discretizations for the Magnetic Field Integral Equation (MFIE) and the Müller Integral Equation (MUIE) are investigated in the context of lowfrequency (LF) scattering problems involving simply connected scatterers. It is proved that, at low frequencies, the frequency scaling of the nonsolenoidal part of the solution current can be incorrect for the standard discretization. In addition, it is proved that the frequency scaling obtained with the mixed discretization is correct. The reason for this problem in the standard discretization scheme is the absence of exact solenoidal currents in the rotated RWG finite element space. The adoption of the mixed discretization scheme eliminates this problem and leads to a well-conditioned system of linear equations that remains accurate at low frequencies. Numerical results confirm these theoretical predictions and also show that, when the frequency is lowered, a finer and finer mesh is required to keep the accuracy constant with the standard discretization.

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“…This property has been first derived in [30]. A related property can be found for the identity operator: if both t (r) and b (r) are solenoidal currents, then…”

Section: Lf Behavior Of Integral Operatorsmentioning

confidence: 96%

Low-Frequency Scaling of the Standard and Mixed Magnetic Field and Müller Integral Equations

Bogaert

Cools

Andriulli

et al. 2014

IEEE Trans. Antennas Propagat.

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show abstract

“…Indeed, the local basis loops reside on the surface and do not pass through any local test loops, since those are located slightly inside of the (1), just like all the blocks involving stars. The excitation, when tested with a loop, yields a result of O (ω) [8]. Summarizing these results, the following scaling is obtained for the matrix equation (4)…”

Section: Low Frequency Stability Of the Solution Currentmentioning

confidence: 99%

“…As was mentioned in [1], the block M ll scales as O ω 2 at low frequencies. For a proof we refer to [8]. For global loops, however, the proof given in [8] is not generally valid.…”

Section: Low Frequency Stability Of the Solution Currentmentioning

confidence: 99%

“…For a proof we refer to [8]. For global loops, however, the proof given in [8] is not generally valid. However, it can be proven that the following rule applies to both local and global loops: when the basis loop does not pass through the test loop (as in the rightmost graph in Figure 1), the matrix element scales as O ω 2 .…”

Section: Low Frequency Stability Of the Solution Currentmentioning

confidence: 99%

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Low frequency scaling of the mixed MFIE for scatterers with a non-simply connected surface

Bogaert

Cools

Andriulli³

et al. 2011

2011 International Conference on Electromagnetics in Advanced Applications

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-The Magnetic Field Integral Equation (MFIE) is a widely used integral equation for the solution of electromagnetic scattering problems involving perfectly conducting objects. It is usually discretized by means of RWG functions as both basis and test functions. This discretization of the MFIE is well-known for its good condition number. However, it is equally well-known for the inferior accuracy of its solution when compared to the Electric Field Integral Equation (EFIE). What is less-known is that this accuracy problem becomes even more serious when the frequency is lowered. Recently it has been proved that the so-called mixed discretization of the MFIE, also called 'mixed MFIE', eliminates this low-frequency accuracy problem on simply connected scatterers. The mixed MFIE utilizes the so-called Buffa-Christiansen or Chen-Wilton functions for testing. In this contribution, the low frequency behavior of the mixed MFIE is investigated for scatterers with a non-simply connected surface. An analysis shows the presence of an approximate nullspace in the mixed MFIE at low frequencies. This nullspace becomes exact when the frequency is zero. This behavior matches known results for the continuous MFIE. Numerical results are presented that confirm this analysis. Despite the approximate nullspace at low frequencies, numerical results indicate that the mixed MFIE still delivers accurate results for toroidal scatterers.

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“…SWG basis functions [13] are one of the well known basis functions used to model volume displacement currents. For quasistatic problems, because of the EM decoupling, recently developed loop tree bases or loop-star bases [14][15][16][17][18] based on SWG bases should be employed to make the MoM matrix equation stable. Moreover, for the magneto-quasistatic problems, only volume loop bases are needed for modeling the divergence free currents [15,18].…”

Section: Introductionmentioning

confidence: 99%

Combing Multilevel Green's Function Interpolation Method With Volume Loop Bases for Inductance Extraction Problems

Wang¹,

Zhao²

2008

PIER

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Abstract-In this paper, a fast integral equation method is developed for extracting the inductances in RF ICs, RF MEMs, IC packages, and deep submicron ICs etc. This method combines a recently developed Multilevel Green's Function Interpolation Method (MLGFIM) [1,2] with the volume integral equation discretized using Volume Loop (VL) basis functions. In it, instead of using the filaments model to simulate the currents flowing in the inductors, we use the conventional SWG basis functions for this kind of basis functions is flexible for problems with complex geometries. The shortest path finding algorithm is also used to find the source loop basis functions. The inductance extractions from the straight line, the spiral inductors, the bump, and the parallel buses in this paper demonstrate the validity and efficiency of this hybrid method.

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Analysis of low frequency scattering from penetrable scatterers

Cited by 66 publications

References 17 publications

Low-Frequency Scaling of the Standard and Mixed Magnetic Field and Müller Integral Equations

Low-Frequency Scaling of the Standard and Mixed Magnetic Field and Müller Integral Equations

Low frequency scaling of the mixed MFIE for scatterers with a non-simply connected surface

Combing Multilevel Green's Function Interpolation Method With Volume Loop Bases for Inductance Extraction Problems

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