Numerical Analysis of the Potential Formulation of the Volume Integral Equation for Electromagnetic Scattering

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Volume Potential-Integral-Equation Formulation for Electromagnetic Scattering by Dielectric Objects

A volume potential-integral-equation formulation for electromagnetic scattering by dielectric objects is developed and discretized with fully continuous nodal basis functions. The equations are tested with either the point-matching or Galerkin's testing procedure. Galerkin's testing shows superior accuracy over the point-matching as well as over the standard discretization of the electric field volume integral equation with Schaubert-Wilton-Glisson (SWG) functions. The potential formulation is accelerated by the precorrected-FFT method.Peer reviewe

Extension of Radiative Transfer Coherent Backscattering RT-CB code to dense discrete random media

The Radiative transfer coherent backscattering (RT-CB) code is extended to apply to dense discrete random media of optically soft spherical particles. This is achieved by utilizing the well-known static-structure-factor (SSF) correction derived from the Percus-Yevick approximation for sticky-hard-sphere (SHS) pair correlation function. The code is verified against the numerically exact electromagnetic method for small spherical media consisting of submicrometer-sized icy particles at optical wavelengths. The SSF-corrected RT-CB method significantly improves solution accuracy, and the solution agrees well with the numerically exact solution when the packing density is less than 20% and particles are optically soft, i.e., the refractive index of particles is close to that of the background medium

Thermophysical model for icy cometary dust particles

Context. Cometary dust particles are subjected to various forces after being lifted off the nucleus. These forces define the dynamics of dust, trajectories, alignment, and fragmentation, which, in turn, have a significant effect on the particle distribution in the coma. Aims. We develop a numerical thermophysical model that is applicable to icy cometary dust to study the forces attributed to the sublimation of ice. Methods. We extended the recently introduced synoptic model for ice-free dust particles to ice-containing dust. We introduced an additional source term to the energy balance equation accounting for the heat of sublimation and condensation. We use the direct simulation Monte Carlo approach with the dusty gas model to solve the mass balance equation and the energy balance equation simultaneously. Results. The numerical tests show that the proposed method can be applied for dust particles covering the size range from tens of microns to centimeters with a moderate computational cost. We predict that for an assumed ice volume fraction of 0.05, particles with a radius, r >> 1 mm, at 1.35 AU, may disintegrate into mm-sized fragments due to internal pressure build-up. Particles with r < 1 cm lose their ice content within minutes. Hence, we expect that only particles with r > 1cm may demonstrate sustained sublimation and the resulting outgassing forces

Numerical comparison of spectral properties of volume-integral-equation formulations

We study and compare spectral properties of various volume-integral-equation formulations. The equations are written for the electric flux, current, field, and potentials, and discretized with basis functions spanning the appropriate function spaces. Each formulation leads to eigenvalue distributions of different kind due to the effects of discretization procedure, namely, the choice of basis and testing functions. The discrete spectrum of the potential formulation reproduces the theoretically predicted spectrum almost exactly while the spectra of other formulations deviate from the ideal one. It is shown that the potential formulation has the spectral properties desired from the preconditioning perspective. (C) 2016 Elsevier Ltd. All rights reserved.Peer reviewe

Fast superposition T-matrix solution for clusters with arbitrarily-shaped constituent particles

A fast superposition T-matrix solution is formulated for electromagnetic scattering by a collection of arbitrarily-shaped inhomogeneous particles. The T-matrices for individual constituents are computed by expanding the Green's dyadic in the spherical vector wave functions and formulating a volume integral equation, where the equivalent electric current is the unknown and the spherical vector wave functions are treated as excitations. Furthermore, the volume integral equation and the superposition T-matrix are accelerated by the precorrected-FFT algorithm and the fast multipole algorithm, respectively. The approach allows for an efficient scattering analysis of the clusters and aggregates consisting of a large number of arbitrarily-shaped inhomogeneous particles. (C) 2016 Elsevier Ltd. All rights reserved.Peer reviewe

Discrete Helmholtz Decomposition for Electric Current Volume Integral Equation Formulation

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Dynamics of Interstellar Dust Particles in Electromagnetic Radiation Fields

We establish a theoretical framework for solving the equations of motion for an arbitrarily shaped, isotropic, and homogeneous dust particle in the presence of radiation pressure. The scattering problem involved is solved by a surface integral equation method, and a rudimentary sketch of the numerical implementation is introduced with preliminary results agreeing with predictions.Peer reviewe

Polarized scattering by Gaussian random particles under radiative torques

We study the internal alignment of a statistical ensemble of Gaussian random ellipsoids with respect to the radiation direction. We solve the rigid body dynamics due to scattering forces and torques, using a numerically exact and efficient T-matrix solver for arbitrary particle shapes and compositions. We then compare the polarization of the aligned ensemble to a randomly oriented ensemble and a perfectly aligned ensemble. We find that the ensemble becomes partially aligned under monochromatic radiation and that the internal alignment has an significant effect on the intensity and polarization of the scattered light. (C) 2017 Elsevier Ltd. All rights reserved.Peer reviewe

On the Spectrum and Preconditioning of Electromagnetic Volume Integral Equations

Spectral properties of current-based volume integral equation of electromagnetic scattering are investigated in the case of isotropic and bi-isotropic objects. Using Helmholtz decomposition the spectrum is derived separately for the solenoidal, irrotational, and harmonic subspaces. Based on this analysis, preconditioning strategies of the matrix equation are discussed.Peer reviewe