Conformal Perfectly Matched Layer for the Mixed Finite Element Time-Domain Method

Donderici, Burkay; Teixeira, F.L.

doi:10.1109/tap.2008.919215

Cited by 45 publications

(28 citation statements)

References 50 publications

(81 reference statements)

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“…And "o" is the analytic solution obtained by the second kind of zero order Hankel function. Refer to [18]; the resulting reflection error is shown in Figure 3(b). It can be seen from the figure that the reflection error is below −37 dB.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In the literature [17], the PML theory is used in 3-D DGTD algorithm to realize the absorption of electromagnetic wave through the conformal truncation face by Dosopoulos and Lee. Donderici and Teixeira incorporated conformal PML into the mixed FETD algorithm by utilizing PML constitutive tensors in 2008 [18]. Based on a higherorder curvilinear finite-element and the concept of transformation electromagnetics, Smull et al proposed anisotropic locally conformal PML; this new PML has favorable accuracy and efficiency [19].…”

Section: Introductionmentioning

confidence: 99%

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Implementation of an Approximate Conformal UPML in 2-D DGTD

Wei

Yang

et al. 2017

International Journal of Antennas and Propagation

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Using the numerical discrete technique with unstructured grids, conformal perfectly matched layer (PML) absorbing boundary in the discontinuous Galerkin time-domain (DGTD) can be set flexibly so as to save lots of computing resources. Based on the DGTD equations in an orthogonal curvilinear coordinate system, the processes of parameter transformation for 2-D UPML between the coordinate systems of elliptical and Cartesian are given; and the expressions of transition matrix are derived. The calculation scheme of conductivity distribution in elliptic cylinder absorbing layer is given, and the calculation coefficient of DGTD in elliptic UPML is calculated. Furthermore, the 2-D iterative formulas of DGTD and that of auxiliary equation in the elliptical cylinder UPML are derived; the conformal UPML calculation in DGTD is realized. Numerical results show that very good accuracy and computational efficiency are achieved by using the method in this paper. Compared to the rectangular computational region, both the memory and computation time of conformal UPML absorbing boundary are reduced by more than 20%.

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Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Implementation of an Approximate Conformal UPML in 2-D DGTD

Wei

Yang

et al. 2017

International Journal of Antennas and Propagation

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“…Invoking Faraday's law, one can obtain (8) where is the equivalent current on the boundary. Discretizing (8) at and using the central-difference, which yields (9a) (9b) one can reach the following equation by simply subtracting them: (10) Since the left hand side of (10) is applied as a current source, the negative of it should be substituted into (5). Afterwards, the electric field is expanded in terms of edge elements.…”

Section: Formulationmentioning

confidence: 99%

“…In contrast to the FDTD, PML formulation in FETD is much more complicated and numerical experiments have revealed late-time instabilities in the unconditionally stable (US) vector wave equation [6], [7]. Although PML applied to the conditionally stable (CS) LF-FETD do not suffer from instability issues [8], we expect the same problem in the PML for the CN-FETD due to the underlying equivalence between this and the US vector wave equation shown in Section III. Alternatively, ABCs are easy to implement and do not destroy sparsity of the FEM matrices nor produce instabilities.…”

Section: Introductionmentioning

confidence: 96%

Implementation of a First-Order ABC in Mixed Finite-Element Time-Domain Formulations Using Equivalent Currents

Akbarzadeh-Sharbaf

Giannacopoulos

2013

IEEE Microw. Wireless Compon. Lett.

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“…The latter one based on first order Maxwell's curl equations is more suitable to use a well-posed PML when an unbounded region is simulated. The FETD based on electric field intensity E and magnetic flux density B has been developed in [21,22]. This method works very well and has been combined with nonlinear circuit solvers [23,24].…”

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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Conformal Perfectly Matched Layer for the Mixed Finite Element Time-Domain Method

Cited by 45 publications

References 50 publications

Implementation of an Approximate Conformal UPML in 2-D DGTD

Implementation of an Approximate Conformal UPML in 2-D DGTD

Implementation of a First-Order ABC in Mixed Finite-Element Time-Domain Formulations Using Equivalent Currents

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

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