An Accurate Conformal Fourier Transform Method for 2d Discontinuous Functions

Zhu, Chunhui; Liu, Qing; Shen, Yuelei; Liu, Li Jun

doi:10.2528/pier11072306

Cited by 5 publications

(3 citation statements)

References 25 publications

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“…Time-domain forward simulation is a method to obtain high detection accuracy. [7][8][9][10] The frequency-domain DOI: 10.1002/adts.202100398 electromagnetic detection method can describe large-scale geoelectric structures with only a few frequency points of electromagnetic responses, and is more efficient than the time-domain electromagnetic detection method which is based on time step iteration. Therefore, it is often used for oil and gas reservoir detection based on steel casing devices.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Grid‐Based Finite‐Element Approach For 3D Steel Casing Forward Modeling

Gao

et al. 2021

Advcd Theory and Sims

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Steel casing forward modeling often requires considering the slender casing in the study area to study the influence of this casing on the underground electromagnetic field, which can be implemented by the unstructured finite-element (FE) method based on tetrahedra. However, the calculation efficiency of applying the unstructured FE method directly to the steel casing model is poor. To this end, this article develops an FE approach based on a hybrid grid by using slender prismatic elements to mesh the steel casing area, while the remaining areas are still discretely meshed with tetrahedra. By showing numerical examples of the vertical single steel casing and L-shaped steel casing models, the advantages of the method are tested by evaluating the response curves and the degrees of freedom. The results show that prismatic elements are suitable for discretizing steel casing areas. This approach can maintain the high accuracy of the numerical solution and reduce the number of elements required for discretizing the steel casing area. Hybrid grids can greatly increase the computational efficiency of the FE method for steel casing forward modeling.

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Section: Introductionmentioning

confidence: 99%

A Hybrid Grid‐Based Finite‐Element Approach For 3D Steel Casing Forward Modeling

Gao

et al. 2021

Advcd Theory and Sims

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“…Direct extension of Manuscript received xxx; revised xxx these algorithms to high dimensions still requires that the area is meshed into a Cartesian orthogonal grid [9], which is not flexible for an arbitrary boundary shape. Recently, a conformal Fourier transform (CFT) algorithm has been proposed for 2D discontinuous functions in [10], [17] to allow an arbitrary boundary shape. As an extension of the 2D CFT, this work develops the conformal Fourier transform algorithm for 3D discontinuous functions distributing in a volume with an arbitrary boundary shape.…”

Section: Introductionmentioning

confidence: 99%

An Accurate Conformal Fourier Transform Method for 3D Discontinuous Functions

Zhu

Liu

2015

IEEE Trans. Antennas Propagat.

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Fourier transform of discontinuous functions are often encountered in computational electromagnetics and other areas. In this work, a highly accurate, fast conformal Fourier transform (CFT) algorithm is proposed to evaluate the finite Fourier transform of 3D discontinuous functions. A curved tetrahedron mesh combined with curvilinear coordinate transform, instead of the Cartesian grid, is adopted to flexibly model an arbitrary shape of the discontinuity boundary. This enables us to take full advantages of high order interpolation and Gaussian quadrature methods to achieve highly accurate Fourier integration results with a low sampling density. The 3D nonuniform fast Fourier transform (NUFFT) helps to keep the complexity of the proposed algorithm to that similar to the traditional 3D FFT algorithm. Therefore, the proposed CFT algorithm can achieve order of magnitude higher accuracy than 3D FFT with lower sampling density and similar computation time. The convergence is proved and verified.

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“…In order to get the PDF from the inverse Fourier-transform [23,96,97] of characteristic function, the characteristic function should be sampled at discrete angular frequencies. The sampling interval ω s|k is…”

Section: Formulation In Frequency Domainmentioning

confidence: 99%

Performance Analysis of Radar Target Recognition Using Natural Frequency: Frequency Domain Approach

Lee¹,

Cho²,

Park³

et al. 2012

PIER

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Abstract-We consider the performance analysis of natural frequency-based radar target recognition in the frequency domain. Based on the probability density function (PDF) of some quantity consisting of the projections of the frequency response onto the column spaces of the matrices constructed using the natural frequencies of the specific targets, we propose to analytically calculate the probability of the correct classification, where the PDF is obtained from the inverse Fourier transform of the characteristic function. The scheme is validated by comparing the performance using the analytic method with that using the Monte-Carlo simulation.

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An Accurate Conformal Fourier Transform Method for 2d Discontinuous Functions

Cited by 5 publications

References 25 publications

A Hybrid Grid‐Based Finite‐Element Approach For 3D Steel Casing Forward Modeling

A Hybrid Grid‐Based Finite‐Element Approach For 3D Steel Casing Forward Modeling

An Accurate Conformal Fourier Transform Method for 3D Discontinuous Functions

Performance Analysis of Radar Target Recognition Using Natural Frequency: Frequency Domain Approach

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