Computation of electromagnetic scattering with a non‐conforming discontinuous spectral element method

Kopriva, David A.; Woodruff, S.; Hussaini, M. Y.

doi:10.1002/nme.394

Cited by 146 publications

(106 citation statements)

References 19 publications

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“…In this article, we adopt the spectral-element method (SEM), which combines the accuracy of pseudospectral methods with the flexibility of the FEM, thereby providing key advantages in terms of computational performance (e.g., Tromp et al, 2008). If need be, the SEM can be implemented as a discontinuous Galerkin method (Kopriva et al, 2002;Kopriva, 2006;Acosta Minolia and Kopriva, 2011). The SEM has been used to study 2D and 3D local, regional, and global seismic-wave propagation problems (e.g., Cohen et al, 1993;Priolo et al, 1994;Faccioli et al, 1997;Komatitsch, 1997;Komatitsch and Vilotte, 1998;Komatitsch and Tromp, 2002a,b;Chaljub and Valette, 2004;Komatitsch et al, 2004Komatitsch et al, , 2005Liu et al, 2004;Stich and Morelli, 2007;Lee et al, 2008;Stich et al, 2009;Stupazzini et al, 2009;Tape et al, 2010;Zhu et al, 2012a,b).…”

Section: Introductionmentioning

confidence: 99%

Spectral-Element Simulations of Seismic Waves Generated by the 2009 L'Aquila Earthquake

Magnoni¹,

Casarotti²,

Michelini³

et al. 2013

Bulletin of the Seismological Society of America

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We adopt a spectral-element method (SEM) to perform numerical simulations of the complex wavefield generated by the 6 April 2009 M w 6.3 L'Aquila earthquake in central Italy. The mainshock is represented by a finite-fault solution obtained by inverting strong-motion and Global Positioning System data, testing both 1D and 3D wavespeed models for central Italy. Surface topography, attenuation, and the Moho discontinuity are also accommodated. Including these complexities is essential to accurately simulate seismic-wave propagation. Three-component synthetic waveforms are compared to corresponding velocimeter and strong-motion recordings. The results show a favorable match between data and synthetics up to ∼0:5 Hz in a 200 km × 200 km × 60 km model volume, capturing features mainly related to topography or low-wavespeed basins. We construct synthetic peak ground velocity maps that, for the 3D model, are in good agreement with observations, thus providing valuable information for seismic-hazard assessment. Exploiting the SEM in combination with an adjoint method, we calculate finite-frequency kernels for specific seismic arrivals. These kernels capture the volumetric sensitivity associated with the selected waveform and highlight prominent effects of topography on seismic-wave propagation in central Italy.

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Section: Introductionmentioning

confidence: 99%

Spectral-Element Simulations of Seismic Waves Generated by the 2009 L'Aquila Earthquake

Magnoni¹,

Casarotti²,

Michelini³

et al. 2013

Bulletin of the Seismological Society of America

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“…As in a usual FV method, the Riemann solver [46] stabilizes the solution. However in this case higher accuracy may be achieved by increasing the order of the approximation, N, as well as by reducing the size of the elements, h. The DGSEM is used in a wide range of applications such as compressible flows [5,35], electromagnetics and optics [1,13,14,29], heat transfer [32], aeroacoustics [9,36,42,43], meteorology [22,23,38], and geophysics [16,17].…”

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confidence: 99%

Quasi-A Priori Truncation Error Estimation in the DGSEM

et al. 2014

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In this paper we show how to accurately perform a quasi-a priori estimation of the truncation error of steady-state solutions computed by a discontinuous Galerkin spectral element method. We estimate the spatial truncation error using the r-estimation procedure. While most works in the literature rely on fully time-converged solutions on grids with different spacing to perform the estimation, we use non time-converged solutions on one grid with different polynomial orders. The quasi-a priori approach estimates the error while the residual of the time-iterative method is not negligible. Furthermore, the method permits one to decouple the surface and the volume contributions of the truncation error, and provides information about the anisotropy of the solution as well as its rate of convergence in polynomial order. First, we focus on the analysis of one dimensional scalar conservation laws to examine the accuracy of the estimate. Then, we extend the analysis to two dimensional problems. We demonstrate that this quasi-a priori approach yields a spectrally accurate estimate of the truncation error.

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“…Las ecuaciones de Maxwell en un medio homogéneo isotrópico, sin considerar cargas y densidad de corriente en la superficie de la interfaz, se pueden reescribir en la siguiente forma conservativa, [12] y [8]:…”

Section: Ecuación Del Modelounclassified

Método de elementos espectrales de Galerkin discontinuo para calcular reflexión y transmisión de ondas electromagnéticas

Mazo

Minoli

Toro-Zapata

2018

RMTA

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Este trabajo tiene por objetivo presentar el desarrollo y la validación de un algoritmo de alto orden de precisión, basado en el método de elementos espectrales nodal de Galerkin discontinuo, por su siglas en inglés (DGSEM), para calcular la reflexión y la transmisión de ondas electromagnéticasviajando en dos medios isotrópicos y homogéneos, los cuales se encuentran separados por una interfaz plana vertical con características diferentes de permitividad " y permeabilidad . Para discretizar espacialmente se derivó el método DGSEM sobre las ecuaciones de Maxwell. Posteriormente, se derivó un resolvente de Riemann para calcular el flujo numérico entre los elementos que componen la malla del dominio computacional, para calcular la reflexión y la transmisión de onda en la interfaz, y para introducir las respectivas condiciones de frontera. Finalmente, para discretizar en el tiempo, se utilizó el método de Runge-Kutta explícito de tercer orden de Williamson. Los resultados del algoritmo, en comparación con la solución analítica, demuestran convergencia espectral en el espacio y de tercer orden en el tiempo.

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Computation of electromagnetic scattering with a non‐conforming discontinuous spectral element method

Cited by 146 publications

References 19 publications

Spectral-Element Simulations of Seismic Waves Generated by the 2009 L'Aquila Earthquake

Spectral-Element Simulations of Seismic Waves Generated by the 2009 L'Aquila Earthquake

Quasi-A Priori Truncation Error Estimation in the DGSEM

Método de elementos espectrales de Galerkin discontinuo para calcular reflexión y transmisión de ondas electromagnéticas

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