A New 2d Non-Spurious Discontinuous Galerkin Finite Element Time Domain (Dg-Fetd) Method for Maxwell's Equations

Ren, Qiang; Tobon, Luis; Liu, Qing

doi:10.2528/pier13100901

Cited by 23 publications

(6 citation statements)

References 41 publications

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“…The vector potential is the solution of a secondorder differential equation [4,22]. To solve it numerically, the finite elements method or other methods are used [23,24]. The current density or the magnetic field is the result of numerical differentiation of the vector potential and thus it is loaded with a non-negligible error [25].…”

Section: Comparison Of Newly Obtained Results With Published Resultsmentioning

confidence: 99%

“…Varianta 3. The cross sections of the conductors A 2 and A 3 are [23,33] Figure 12 gives the dependence of the normed amplitude Ĵ J dc on x for several values of y in the lower half of the cross section of the conductors A 1 and A 2 . The values in the upper half of the cross sections are not given because with the large extent of the values Ĵ J dc in figure 12 they would merge with the values in the lower half of the cross sections.…”

Section: Examplementioning

confidence: 99%

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Current density in a group of long parallel conductors

Coufal

2019

Phys. Scr.

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An original method is proposed for the calculation of current density in a finite number of long parallel solid conductors of arbitrary cross section. Some pairs of the conductors under examination can be connected to a voltage source; they are active. The other conductors are passive. The currents, voltages and magnetic fields are assumed to be quasi-stationary and the displacement current is neglected. The permeability of the conductor material is constant and equals the vacuum permeability. No method has so far been published that would allow an exact calculation of current density in all the cases that satisfy the above assumptions. The application of the method is demonstrated by solving an example with two active conductors, one of which is of circular and the other of rectangular cross section, while a third passive conductor is of rectangular cross section.

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Section: Comparison Of Newly Obtained Results With Published Resultsmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Current density in a group of long parallel conductors

Coufal

2019

Phys. Scr.

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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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“…Regarding the equations to be solved, the FETD and SETD methods in electromagnetics can be implemented with the second-order wave equations, with either E or H as the unknowns [3], [6], [7], [14]- [17] or with the first-order Maxwell's equations, with two unknowns, the EB scheme [18]- [25] or EH scheme [26]- [28]. When the second approach is used, the field variables E and H are expanded in terms of edge basis functions to satisfy tangential continuity across adjacent elements.…”

mentioning

confidence: 99%

“…This will add the number of unknowns significantly in threedimensional (3-D) cases, and consequently increase memory overhead and CPU time. However, the EB scheme is free of spurious modes even with the same order of interpolation polynomials for E and B [25], [32], and this advantage will alleviate the computation load.…”

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confidence: 99%

A New 3-D Nonspurious Discontinuous Galerkin Spectral Element Time-Domain (DG-SETD) Method for Maxwell’s Equations

Ren

Tobon

Sun

et al. 2015

IEEE Trans. Antennas Propagat.

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A new discontinuous Galerkin spectral element timedomain (DG-SETD) method for Maxwell's equations based on the field variables E and B is proposed to analyze three-dimensional (3-D) transient electromagnetic phenomena. Compared to the previous SETD method based on the field variables E and H (the EH scheme), in which different orders of interpolation polynomials for electric and magnetic field intensities are required, the newly proposed method can eliminate spurious modes using basis functions with the same order interpolation for electric field intensity and magnetic flux density (the EB scheme). Consequently, it can reduce the number of unknowns and computation load. Domain decomposition for the EB scheme SETD method is completed via the DG method. In addition, the EB scheme SETD method is extended to the well-posed time-domain perfectly matched layer (PML) to truncate the computation domain when solving open-region problems. The effectiveness and advantages of the new DG-SETD method are validated by eigenvalue analysis and numerical results. Index Terms-Discontinuous Galerkin (DG) method, EB scheme, Maxwell's equations, perfectly matched layer (PML), Riemann solver, spectral element time-domain (SETD) method. I. INTRODUCTION I N computational electromagnetics, finite element timedomain (FETD) method in full-wave simulation has received much attention due to the ability to handle transient and nonlinear phenomena in complex structures [1]-[8]. It has been widely used in IC packaging, smart antennas, electromagnetic compatibility (EMC), bioelectromagnetics, etc. The spectral element time-domain (SETD) method can be viewed as a special case of the FETD method [9]-[13]. While FETD usually employs low-order tetrahedrons to mesh, the SETD method uses hexahedron elements to discretize the computation region, and the interpolation polynomials in the hexahedrons can be either of low order or high order. The SETD method is Manuscript

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A New 2d Non-Spurious Discontinuous Galerkin Finite Element Time Domain (Dg-Fetd) Method for Maxwell's Equations

Cited by 23 publications

References 41 publications

Current density in a group of long parallel conductors

Current density in a group of long parallel conductors

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

A New 3-D Nonspurious Discontinuous Galerkin Spectral Element Time-Domain (DG-SETD) Method for Maxwell’s Equations

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