A Novel Coupling Algorithm for Perfectly Matched Layer With Wave Equation-Based Discontinuous Galerkin Time-Domain Method

Sun, Qingtao; Zhang, Runren; Zhan, Qiwei; Liu, Qing

doi:10.1109/tap.2017.2769132

Cited by 19 publications

(10 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Figure 5, we compare the accuracy of the solvers with three techniques: PAL, PML n (with n = 1, \sigma 0 = (5.16, 2.78, 1.89, 1.43, 1.15, 1.01) for the wavenumber chosen as k = (50,100,150,200,250,300), respectively, which are optimal values as suggested in [10]), and PML \infty (\sigma 0 = 1/k as suggested in [8]) for various k. It can be seen from Figure 5(a) that when the wavenumber k is relatively small, the error curves (with N < 20) of these three methods intertwine with each other, and the error obtained by PML \infty is slightly smaller than that of the other two methods. However, as N increases, the error for PML \infty becomes much larger than that of the PAL and PML n due to the large roundoff errors induced by the Gauss quadrature of singular functions.…”

Section: Numerical Results and Comparisonsmentioning

confidence: 99%

“…We keep R 1 = 2 but let R 2 vary. In Table 1, we tabulate the numerical errors for fixed polynomial degrees (N 1 , N ) = (300, 30) but for various k = (10,50,100,200,300,500). Observe that the thickness d = R 2 -R 1 indeed affects the accuracy.…”

Section: Numerical Results and Comparisonsmentioning

confidence: 99%

“…Since these pioneering works of B\' erenger, the PML technique has become a widespread tool for various wave simulations, undergone in-depth analysis of its mathematical ground (see, e.g., [35,10,11,12] and the references cited therein), and been populated into major software such as COMSOL Multiphysics. In the past decade, this subject area has continued to inspire new developments---just to name a few: [7,8,23,19,50,18]. Remarkably, the essential idea of constructing PML [4] can be interpreted as a complex coordinate stretching (or transformation) [14,16].…”

mentioning

confidence: 99%

See 2 more Smart Citations

A Truly Exact Perfect Absorbing Layer for Time-Harmonic Acoustic Wave Scattering Problems

Yang¹,

Wang²,

Gao³

2021

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

In this paper, we design a truly exact perfect absorbing layer (PAL) for domain truncation of the two-dimensional Helmholtz equation in an unbounded domain with bounded scatterers. This technique is based on a complex compression coordinate transformation in polar coordinates and a judicious substitution of the unknown field in the artificial layer. Compared with the widely used perfectly matched layer (PML) methods, the distinctive features of PAL lie in that (i) it is truly exact in the sense that the PAL-solution is identical to the original solution in the bounded domain reduced by the truncation layer; (ii) with the substitution, the PAL-equation is free of singular coefficients and the substituted unknown field is essentially nonoscillatory in the layer; and (iii) the construction is valid for general star-shaped domain truncation. By formulating the variational formulation in Cartesian coordinates, the implementation of this technique using standard spectralelement or finite-element methods can be made easy as a usual coding practice. We provide ample numerical examples to demonstrate that this method is highly accurate and robust for very high wavenumbers and thin layers. It outperforms the classical PML and the recently advocated PML using unbounded absorbing functions. Moreover, it can fix some flaws of the PML approach.

show abstract

Section: Numerical Results and Comparisonsmentioning

confidence: 99%

Section: Numerical Results and Comparisonsmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

A Truly Exact Perfect Absorbing Layer for Time-Harmonic Acoustic Wave Scattering Problems

Yang¹,

Wang²,

Gao³

2021

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

show abstract

“…In the numerical results presented here, assigning a weight of 2 for PML elements in ParMetis [37], [38] yields a good load-balance. The efficiency of the DGTD scheme can further be increased by combining the WAA with techniques making use of nonconformal meshes [39] and/or p-refinement for the PML.…”

Section: Numerical Examplesmentioning

confidence: 99%

A Memory-Efficient Implementation of Perfectly Matched Layer With Smoothly Varying Coefficients in Discontinuous Galerkin Time-Domain Method

Chen¹,

Ozakin²,

Ahmed³

et al. 2021

IEEE Trans. Antennas Propagat.

View full text Add to dashboard Cite

Wrapping a computation domain with a perfectly matched layer (PML) is one of the most effective methods of imitating/approximating the radiation boundary condition in Maxwell and wave equation solvers. Many PML implementations often use a smoothlyincreasing attenuation coefficient to increase the absorption for a given layer thickness, and, at the same time, to reduce the numerical reflection from the interface between the computation domain and the PML. In discontinuous Galerkin time-domain (DGTD) methods, using a PML coefficient that varies within a mesh element requires a different mass matrix to be stored for every element and therefore significantly increases the memory footprint. In this work, this bottleneck is addressed by applying a weight-adjusted approximation to these mass matrices. The resulting DGTD scheme has the same advantages as the scheme that stores individual mass matrices, namely higher accuracy (due to reduced numerical reflection) and increased meshing flexibility (since the PML does not have to be defined layer by layer) but it requires significantly less memory.

show abstract

“…Since this pioneering work of Berenger, the PML technique has become a widespread tool for various wave simulations; undergone in-depth analysis of its mathematical ground (see, e.g., [62,19,20,18] and the references cited therein); and been populated into major softwares such as the COMSOL Multiphysics. In the past decade, this subject area continues to inspire new developments, just to name a few: [13,14,36,29,85,27]. The critical issue here is how to derive the PMLequation in the artificial layer.…”

Section: Existing Techniques For Domain Reductionmentioning

confidence: 99%

Perfect absorbing layers for wave scattering problems and related topics

Gao¹

View full text Add to dashboard Cite

List of Figures 2.3 Profiles of the PML solution U p with regular function (2.14) (σ 0 = 1, n = 2) and singular function (2.15) vs PAL solution U a in Ω and V a in Ω d with k = 99.99, (L, d) = (1, 0.2) along the x-axis at y = π/2. Left: real part solution; Right: imaginary part solution.. .. .. .. .. . 2.4 Left: illustration of the circular PAL from radial direction. Middle: schematic illustration of the rectangular PAL Ω d with four trapezoidal patches. Right: illustration of the elliptic PAL under elliptic coordinate. 2.5 Left: errors against various N for different layers (width d = 0.1) with boundary condition g(y) = sin(5y) − sin(30y); Right: errors against various N for different layers (width d = 0.5) with boundary condition g(y) = sin(5y) − sin(30y).

show abstract

A Novel Coupling Algorithm for Perfectly Matched Layer With Wave Equation-Based Discontinuous Galerkin Time-Domain Method

Cited by 19 publications

References 22 publications

A Truly Exact Perfect Absorbing Layer for Time-Harmonic Acoustic Wave Scattering Problems

A Truly Exact Perfect Absorbing Layer for Time-Harmonic Acoustic Wave Scattering Problems

A Memory-Efficient Implementation of Perfectly Matched Layer With Smoothly Varying Coefficients in Discontinuous Galerkin Time-Domain Method

Perfect absorbing layers for wave scattering problems and related topics

Contact Info

Product

Resources

About