A high-order algorithm for multiple electromagnetic scattering in three dimensions

Abstract

We describe a fully discrete high-order algorithm for simulating multiple scattering of electromagnetic waves in three dimensions by an ensemble of perfectly conducting scattering objects. A key component of our surface integral algorithm is high-order tangential approximation of the surface current on each obstacle in the ensemble. The high-order nature of the algorithm leads to relatively small numbers of unknowns, which allows us to use either a direct method or an iterative boundary decomposition method for simulations of multiple scattering. We demonstrate the algorithm using both of these techniques for near and well separated obstacles. Using a small computing cluster (with 20 processors), we simulate multiple scattering by up to 125 objects for frequencies in the resonance region, and by paired obstacles of diameter 20 to 30 times the incident wavelength. Many physically important problems, such as scattering by atmospheric aerosols or ice crystals, involve multiple scattering by ensembles of particles, each particle having its own distinct shape, but with all particles fitting a stochastic description with a small number of fixed parameters in local spherical coordinates. We demonstrate our algorithm for multiple scattering by ensembles of such unique particles, Support of the Australian Research Council is gratefully acknowledged. 470Numer Algor (2009) 50:469-510 whose stochastic description corresponds to computer models of ice crystals and dust particles.

A spectrally accurate method for the direct and inverse scattering problems by multiple 3D dielectric obstacles

“…To decrease the number of unknowns, they introduce a normal transformation acting from the tangent plane to the boundary Γ onto the tangent plane to the unit sphere, so that one only has to seek a solution in terms of tangential vector spherical harmonics [16]. The latter approach was extended to the solution of the scattering problem by multiple perfect conductors [17]. Here we use a different approach based on the Piola transform of a diffeomorphism from S 2 to Γ that maps the energy space H…”

“…Acknowledgments I thank Olha Ivanyshyn Yaman for providing the Matlab code of the acoustic operators [12] and visualisation tools developed [30] that has been extended to the electromagnetic case [16,17] in this work. Thorsten Hohage is gratefully acknowledged for providing the inversion toolbox he developed with Matlab programming language [27,28] and for helpful discussions.…”

A reduced basis method for electromagnetic scattering by multiple particles in three dimensions

“…We may avoid solving the coupled global system by some iterative procedure [23] based on the observation in (3.5)-(3.6), but this approach also requires solving J uncoupled N × N system of equations at each iteration. The large number of degrees of freedom of the boundary element discretization for the three dimensional scattering problem likewise makes this expensive.…”

An efficient algorithm for simulating scattering by a large number of two dimensional particles

“…This Neumann iterative technique was used for acoustic and electromagnetic scattering in two and three dimensions [2,5,6]. Acoustic scattering by only two obstacles has been demonstrated [2,5], but other work demonstrated that, even for two obstacles, the Neumann iterations diverge when the obstacles are close together [6].…”

“…Although the boundary decomposition removes the memory bottleneck, we observed that in many C149 cases the Neumann iterations in (16) do not converge, even after several days of computations (with L > 1000). This is not unexpected; divergence has been demonstrated for scattering by even two nearby obstacles [6]. Indeed the theory imposes separation conditions on the particles that are not feasible for configurations consisting of hundreds of particles [3].…”