@Article{CiCP-8-758,
author = {Shingyu Leung and Hongkai Zhao},
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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.190809.090210a},
url = {http://global-sci.org/intro/article_detail/cicp/7594.html}
}