Weak Form Nonuniform Fast Fourier Transform Method for Solving Volume Integral Equations

Fan, Zhenhong; Chen, Rushan; Chen, Hua; Ding, and Da-Zhi

doi:10.2528/pier08121308

Cited by 15 publications

(11 citation statements)

References 27 publications

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“…Solutions for the two half spaces configuration are of interest in electric field integral equation solutions and approximations thereof [4][5][6][7][8]. Such solutions are also important for modeling by local methods such as finite-difference, finite-element and finitevolume methods [9][10][11][12] as well as for inversion methods based on local forward-modeling schemes [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Green's Tensors for the Diffusive Electric Field in a Vti Half-Space

Slob¹,

Hunziker²,

Mulder³

2010

PIER

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Abstract-Explicit Green's tensors for the diffusive electric field in a configuration with two homogeneous half spaces are of interest for primary-secondary formulations of frequency domain and time domain modeling schemes. We derive the explicit expressions for the Green tensor of the electric field generated by an electric dipole in space frequency and space time. Both source and receiver can have arbitrary positions in the vertical transverse isotropic (VTI) half space below a non conductive half space. Apart from their use in modeling schemes, the expressions can be used to understand the effect of the interface between the VTI and the non conducting half space. We show that the TE-mode refracts against the interface, and its effect in the VTI half space decays exponentially as a function of depth and is inversely proportional to horizontal distance cubed for horizontal source receiver distances larger than three times the source depth. In exploration geophysics, this part of the field is known as the "airwave". The contribution from the "airwave" has a late time behavior that differs from the other contributions to the electric field. This makes time domain systems relevant for exploration geophysical applications.

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Section: Introductionmentioning

confidence: 99%

Green's Tensors for the Diffusive Electric Field in a Vti Half-Space

Slob¹,

Hunziker²,

Mulder³

2010

PIER

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“…Such heavy computation complexity and memory cost are undesirable in many applications, e.g. the reconstruction of largescale induced electric or current density in discontinuous media in computational electromagnetics [19][20][21][22][23][24] or in radar signal research domain [25,26]. Therefore, it is necessary to reduce the computation time and the memory complexity in the G-IPRM.…”

Section: Introductionmentioning

confidence: 99%

A Fast Inverse Polynomial Reconstruction Method Based on Conformal Fourier Transformation

Liu¹,

Liu²,

Zhu³

et al. 2012

PIER

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Abstract-A fast Inverse Polynomial Reconstruction Method (IPRM) is proposed to efficiently eliminate the Gibbs phenomenon in Fourier reconstruction of discontinuous functions. The framework of the fast IPRM is modified by reconstructing the function in discretized elements, then the Conformal Fourier Transform (CFT) and the Chirp Z-Transform (CZT) algorithms are applied to accelerate the evaluation of reconstruction coefficients. The memory cost of the fast IPRM is also significantly reduced, owing to the transformation matrix being discretized in the modified framework. The computation complexity and memory cost of the fast IPRM are O(M N log 2L) and O(M N ), respectively, where L is the number of the discretized elements, M is the degree of polynomials for the reconstruction of each element, and N is the number of the Fourier series. Numerical results demonstrate that the fast IPRM method not only inherits the robustness of the Generalized IPRM (G-IPRM) method, but also significantly reduces the computation time and the memory cost. Therefore, the fast IPRM method is useful for the pseudospectral time domain methods and for the volume integral equation of the discontinuous material distributions.

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“…Although these resonators or other modified versions of them such as hexagonal [2][3][4] and spiral resonators [5,6] have been used to realize canonical [7][8][9][10][11][12][13], dual [14][15][16][17][18][19][20][21], triple [22,23] and quadpassband filters [24] with complicated transmission characteristics, all of these filters suffer from the time consuming full-wave-based process of determining the physical parameters of the filter from the desired coupling factor and Q ext . The ability of soft computing techniques in modeling complicated problems in a vanishingly short time instead of using numerical or analytical approach [25][26][27][28][29][30][31][32] may provide a fast and accurate solution to this problem. Among the soft computing techniques the ability of fuzzy inference method in solving complicated electromagnetic problems such as microwave filter tuning [33,34], EMC problems [35], resonant frequency computation [36,37], determination of the transmission lines characteristic parameters [38], determination of the relative magnetic permeability [39] and also antenna modeling [40][41]…”

Section: Introductionmentioning

confidence: 99%

Active Learning Method for the Determination of Coupling Factor and External Q in Microstrip Filter Design

Rezaee¹,

Tayarani²,

Knöchel³

2011

PIER

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Abstract-In the final step of any filter design process, the desired center frequency, coupling factor and external quality factor (Q ext ) are used to determine the physical parameters of the filter. Although in the most cases the physical dimensions of a single resonator for a given center frequency are determined using exact analytical or simple approximate equations, usually such simple equations cannot be found to easily relate the required coupling factor and Q ext to the physical parameters of the filter. Analytical calculation of coupling factor and Q ext versus dimensions are usually complicated due to the geometrical complexities or in some cases such as microstrip resonators due to the lack of exact solution for the field distribution. Therefore coupling factor and Q ext of various kinds of resonators, especially microstrip resonators, are related to the physical parameters of the structure by the use of time consuming full wave simulations. In this paper a surprisingly fast and completely general approach based on a soft computing pattern-based processing technique, called active learning method (ALM) is proposed to overcome the time consuming process of coupling factor and Q ext determination. At first the ALM technique and the steps of modeling are generally described, then as an example and in order to show the ability of the method this modeling approach is implemented to model the coupling factor and Q ext surfaces of microstrip open-loop resonators versus physical parameters of the structure. Using the ALM-based extracted surfaces for coupling factor and Q ext , two four pole Chebychev bandpass filters are designed and fabricated. Good agreement between the measured and simulated results validates the accuracy of the proposed approach.

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Weak Form Nonuniform Fast Fourier Transform Method for Solving Volume Integral Equations

Cited by 15 publications

References 27 publications

Green's Tensors for the Diffusive Electric Field in a Vti Half-Space

Green's Tensors for the Diffusive Electric Field in a Vti Half-Space

A Fast Inverse Polynomial Reconstruction Method Based on Conformal Fourier Transformation

Active Learning Method for the Determination of Coupling Factor and External Q in Microstrip Filter Design

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