Gaussian Beam Summation for Diffraction in Inhomogeneous Media Based on the Grid Based Particle Method (Communications in Computational Physics, 2010)
We develop an efficient numerical method to compute single slit or doubleslit diffraction patterns from high frequency wave in inhomogeneous media. Weapproximate the high frequency asymptotic solution to the Helmholtz equation usingthe Eulerian Gaussian beam summation proposed in [20, 21]. The emitted rays froma slit are embedded in the phase space using an open segment. The evolution of thisopen curve is accurately computed using the recently developed Grid Based ParticleMethod [24] which results in a very efficient computational algorithm. Following thegrid based particle method we proposed in [23, 24], we represent the open curve orthe open surface by meshless Lagrangian particles sampled according to an underlyingfixed Eulerian mesh. The end-points of the open curve are tracked explicitlyand consistently with interior particles. To construct the overall wavefield, each ofthese sampling particles also carry necessary quantities that are obtained by solvingadvection-reaction equations. Numerical experiments show that the resulting methodcan model diffraction patterns in inhomogeneous media accurately, even in the occurrenceof caustics.