Finite-difference formulation accounting for field singularities

Zscheile, H.; Schmuckles, F.J.; Heinrich, W.

doi:10.1109/tmtt.2006.872796

Cited by 6 publications

(7 citation statements)

References 17 publications

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“…As an example, a cubic corner of a perfect electric conductor (PEC) is illustrated at the center of the region and we try to find the proximity potential using the finite-difference solution. [5] . …”

Section: Analysis Of the Exponent τmentioning

confidence: 99%

“…Since the boundary condition of the analysis region for the proximity potential is unknown, an iterative procedure is employed to find the appropriate boundary values as well as the proximity potential [5] . The procedure is as follows; first solve the potential using arbitrary boundary values on the surface S 1 and refine them by repeating following operations (Fig.…”

Section: Analysis Of the Exponent τmentioning

confidence: 99%

“…However, note here that the values of τ required in Eqs. (4) and (5) are also unknown. One may find and use an exact analytical solution of τ for the wedge, but τ for the tip of the corner is what we are seeking in this analysis.…”

Section: B New Iterative Proceduresmentioning

confidence: 99%

“…It is also of great interest in the field of simulation techniques for microwave circuits. A number of papers reported improvement of the accuracy and efficiency of finite-difference analyses by incorporating the singularity characteristics into their formulations [3]- [5] . The analytical solution for the exponent τ of conductor edges and wedges, which can be treated as a locally uniform two-dimensional structure in the direction of the edge line, is known.…”

Section: Introductionmentioning

confidence: 99%

“…However, we have to rely on numerical simulations for general three-dimensional corners. Recently, Zscheile et al [5] reported a numerical simulation using an iterative finitedifference analysis of proximity field potential. Their method seems universal and powerful for geometries encountered in microwave circuits.…”

Section: Introductionmentioning

confidence: 99%

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Numerical analysis of singularity exponent for sharp corners

Shibata

2009

2009 Asia Pacific Microwave Conference

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Singularity behavior of electromagnetic field near sharp edges and corners has been a crucial topic in microwave field theory and analyses. The magnitude of field components in the neighborhood of a sharp corner may increase rapidly as the point approaches the tip, which can be expressed in terms of ρ τ−1 , where ρ represents the distance from the tip of the corner and τ is a characteristic value of the exponent, which depends on materials and the local structure of the corner. Having the τ values for various corners as a preliminary knowledge, we can devise more accurate and more efficient analyses of microwave problems. This paper presents an improved numerical analysis method for τ of complex corners based on finite-difference simulation.

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Section: Analysis Of the Exponent τmentioning

confidence: 99%

Section: Analysis Of the Exponent τmentioning

confidence: 99%

Section: B New Iterative Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical analysis of singularity exponent for sharp corners

Shibata

2009

2009 Asia Pacific Microwave Conference

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Spatial sensitivity distribution assessment and Monte Carlo simulations for needle‐based bioimpedance imaging during venipuncture using the finite element method

Atmaca,

Liu,

et al. 2024

Numer Methods Biomed Eng

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Despite being among the most common medical procedures, needle insertions suffer from a high error rate. Impedance measurements using electrode‐equipped needles offer promise for improved tissue targeting and reduced errors. Impedance visualization usually requires an extensive pre‐measured impedance dataset for tissue differentiation and knowledge of the electric fields contributing to the resulting impedances. This work presents two finite element simulation approaches for both problems. The first approach describes the generation of a multitude of impedances with Monte Carlo simulations for both, homogeneous and inhomogeneous tissue to circumvent the need to rely on previously measured data. These datasets could be used for tissue discrimination. The second method describes the simulation of the spatial sensitivity distribution of an electrode layout. Two singularity analysis methods were employed to determine the bulk of the sensitivity within a finite volume, which in turn enables consistent 3D visualization. The modeled electrode layout consists of 12 electrodes radially placed around a hypodermic needle. Electrical excitation was simulated using two neighboring electrodes for current carriage and voltage pickup, which resulted in 12 distinct bipolar excitation states. Both, the impedance simulations and the respective singularity analysis methods were compared with each other. The results show that the statistical spread of impedances is highly dependent on the tissue type and its inhomogeneities. The bounded bulk of sensitivities of both methods are of similar extent and symmetry. Future models should incorporate more detailed tissue properties such as anisotropy or changing material properties due to tissue deformation to gain more accurate predictions.

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