Volume 8, Issue 4
Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method

Shingyu Leung & Hongkai Zhao

Commun. Comput. Phys., 8 (2010), pp. 758-796.

Published online: 2010-08

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  • Abstract

We develop an efficient numerical method to compute single slit or double slit diffraction patterns from high frequency wave in inhomogeneous media. We approximate the high frequency asymptotic solution to the Helmholtz equation using the Eulerian Gaussian beam summation proposed in [20, 21]. The emitted rays from a slit are embedded in the phase space using an open segment. The evolution of this open curve is accurately computed using the recently developed Grid Based Particle Method [24] which results in a very efficient computational algorithm. Following the grid based particle method we proposed in [23, 24], we represent the open curve or the open surface by meshless Lagrangian particles sampled according to an underlying fixed Eulerian mesh. The end-points of the open curve are tracked explicitly and consistently with interior particles. To construct the overall wavefield, each of these sampling particles also carry necessary quantities that are obtained by solving advection-reaction equations. Numerical experiments show that the resulting method can model diffraction patterns in inhomogeneous media accurately, even in the occurrence of caustics.

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@Article{CiCP-8-758, author = {}, title = {Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method}, journal = {Communications in Computational Physics}, year = {2010}, volume = {8}, number = {4}, pages = {758--796}, abstract = {

We develop an efficient numerical method to compute single slit or double slit diffraction patterns from high frequency wave in inhomogeneous media. We approximate the high frequency asymptotic solution to the Helmholtz equation using the Eulerian Gaussian beam summation proposed in [20, 21]. The emitted rays from a slit are embedded in the phase space using an open segment. The evolution of this open curve is accurately computed using the recently developed Grid Based Particle Method [24] which results in a very efficient computational algorithm. Following the grid based particle method we proposed in [23, 24], we represent the open curve or the open surface by meshless Lagrangian particles sampled according to an underlying fixed Eulerian mesh. The end-points of the open curve are tracked explicitly and consistently with interior particles. To construct the overall wavefield, each of these sampling particles also carry necessary quantities that are obtained by solving advection-reaction equations. Numerical experiments show that the resulting method can model diffraction patterns in inhomogeneous media accurately, even in the occurrence of caustics.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.190809.090210a}, url = {http://global-sci.org/intro/article_detail/cicp/7594.html} }
TY - JOUR T1 - Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method JO - Communications in Computational Physics VL - 4 SP - 758 EP - 796 PY - 2010 DA - 2010/08 SN - 8 DO - http://dor.org/10.4208/cicp.190809.090210a UR - https://global-sci.org/intro/article_detail/cicp/7594.html KW - AB -

We develop an efficient numerical method to compute single slit or double slit diffraction patterns from high frequency wave in inhomogeneous media. We approximate the high frequency asymptotic solution to the Helmholtz equation using the Eulerian Gaussian beam summation proposed in [20, 21]. The emitted rays from a slit are embedded in the phase space using an open segment. The evolution of this open curve is accurately computed using the recently developed Grid Based Particle Method [24] which results in a very efficient computational algorithm. Following the grid based particle method we proposed in [23, 24], we represent the open curve or the open surface by meshless Lagrangian particles sampled according to an underlying fixed Eulerian mesh. The end-points of the open curve are tracked explicitly and consistently with interior particles. To construct the overall wavefield, each of these sampling particles also carry necessary quantities that are obtained by solving advection-reaction equations. Numerical experiments show that the resulting method can model diffraction patterns in inhomogeneous media accurately, even in the occurrence of caustics.

Shingyu Leung & Hongkai Zhao. (2020). Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method. Communications in Computational Physics. 8 (4). 758-796. doi:10.4208/cicp.190809.090210a
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