The Discontinuous Galerkin Finite Element Time Domain method (DGFETD)

Gedney, Stephen D.; Kramer, T.; Luo, Chuanwen; Roden, Judith; Crawford, R.; Guernsey, B.; Beggs, John H.; Miller, Jason

doi:10.1109/isemc.2008.4652146

Cited by 36 publications

(49 citation statements)

References 14 publications

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“…The Galerkin's approach is applied in each brick element V i [1]. After making use of the divergence theorem and interface boundary conditions, one can obtain the equations [5] Vi…”

Section: Formulationmentioning

confidence: 99%

“…The discontinuous Galerkin finite-element time-domain (DG-FETD) method [1]- [5] is one of the most important time-domain methods for solving complex electromagnetic (EM) problems. This is because of the fact that the DG-FETD method is not only globally explicit, but also capable of dealing with arbitrarily-shaped and inhomogeneously-filled objects.…”

Section: Introductionmentioning

confidence: 99%

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Numerical dispersion in DG-FETD method using vector basis functions on brick elements

Hu¹,

Wang²

2013

2013 IEEE Antennas and Propagation Society International Symposium (APSURSI)

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A dispersion analysis of the discontinuous Galerkin finite-element time-domain (DG-FETD) method using brick edge elements is presented. The numerical dispersion analysis is performed on the central-flux DG-FETD formula. The dispersion analysis shows that there exist both normal and abnormal modes in the DG-FETD method using brick edge elements. The numerical results of DG-FETD modeling of TEM wave propagation in a parallel waveguide is applied to validate the dispersion analysis. I. INTRODUCTIONThe discontinuous Galerkin finite-element time-domain (DG-FETD) method [1]-[5] is one of the most important time-domain methods for solving complex electromagnetic (EM) problems. This is because of the fact that the DG-FETD method is not only globally explicit, but also capable of dealing with arbitrarily-shaped and inhomogeneously-filled objects. The numerical dispersion analysis [6]-[8] is important for understanding the effect of the spatial discretization and field expansion on the accuracy of DG-FETD method.In this paper, the analysis of numerical dispersion is performed on the central-flux DG-FETD method using zerothorder vector basis functions on brick elements. The analysis is based on the curl Maxwell's equations and leap-frog difference scheme. All of the surface and volume integrals in matrix elements are calculated analytically. The periodic boundary condition (PBC) is applied to the coefficients of basis functions since the mesh is periodic. Finally, one can obtain the numerical dispersion equation by setting the determinant of the coefficient matrix to be zero.The dispersion analysis shows that there exist both normal and abnormal modes using zeroth-order vector basis functions on brick elements. To validate the numerical dispersion equation, the DG-FETD method is applied to simulate the TEM wave propagation in a parallel-plate waveguide. The theoretical values of phase delay obtaining using the dispersion equations are compared with those from the DG-FETD method with helps of the discrete Fourier transform (DFT). Excellent agreements can be observed between the theoretical and numerical values. It is worth mentioning that the analysis approach in this paper can be extended to a dispersion analysis of the DG-FETD method using the higher-order vector basis functions on brick or tetrahedral elements.

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“…The Galerkin's approach is applied in each brick element V i [1]. After making use of the divergence theorem and interface boundary conditions, one can obtain the equations [5] Vi…”

Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical dispersion in DG-FETD method using vector basis functions on brick elements

Hu¹,

Wang²

2013

2013 IEEE Antennas and Propagation Society International Symposium (APSURSI)

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“…In this approach, the conformal perfectly matched layer (PML) [6], [10], [13] is applied to terminate the excitation coaxial line or waveguide so that the outgoing wave is absorbed by the PML with a trivial reflection. The surface magnetic current is impressed on the excitation port.…”

Section: Introductionmentioning

confidence: 99%

Higher-Order DG-FETD Modeling of Wideband Antennas With Resistive Loading

Wang

2013

Antennas Wirel. Propag. Lett.

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A discontinuous Galerkin finite-element time-domain (DG-FETD) method with higher-order tetrahedral elements is developed to model wideband antennas with resistive loading. To fully characterize the wideband fundamental parameters of the antennas with multiscaled structures, several schemes are adopted to effectively model resistive loading and accurately calculate return loss, directivity, and radiation pattern. Successful simulation of interesting antennas using the proposed DG-FETD method demonstrates its capability of modeling wideband antennas without or with resistive loading. Index Terms-DiscontinuousGalerkin finite-element time-domain (DG-FETD) method, higher-order tetrahedral elements, resistive loading, wideband antennas.

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“…In previous FETD research, discontinuous Galerkin method has been employed to implement DDM based on the EH scheme for large-scale problems where the inversion of a large mass matrix is too expensive. This method has been shown useful as the tangential continuous basis functions for E and H naturally satisfy the requirements by the numerical flux [28,[30][31][32][33][34][35]. However, the EH scheme needs more unknowns than the EB scheme.…”

Section: Introductionmentioning

confidence: 99%

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

Ren¹,

Tobon²,

Liu³

2013

PIER

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Abstract-A new discontinuous Galerkin Finite Element Time Domain (DG-FETD) method for Maxwell's equations is developed. It can suppress spurious modes using basis functions based on polynomials with the same order of interpolation for electric field intensity E and magnetic flux density B. Compared to FETD based on EH scheme, which requires different orders of interpolation polynomials for electric and magnetic field intensities, this method uses fewer unknowns and reduces the computation load. The discontinuous Galerkin method is employed to implement domain decomposition for the EB scheme based FETD. In addition, a well-posed time-domain perfectly matched layer (PML) is extended to the EB scheme to simulate the unbounded problem. Leap frog method is utilized for explicit time stepping. Numerical results demonstrate that the above proposed methods are effective and efficient for 2D time domain TMz multi-domain problems.

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The Discontinuous Galerkin Finite Element Time Domain method (DGFETD)

Cited by 36 publications

References 14 publications

Numerical dispersion in DG-FETD method using vector basis functions on brick elements

Numerical dispersion in DG-FETD method using vector basis functions on brick elements

Higher-Order DG-FETD Modeling of Wideband Antennas With Resistive Loading

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

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