Ana B. Manic

Efficient and Accurate Computational Electromagnetics Approach to Precipitation Particle Scattering Analysis Based on Higher-Order Method of Moments Integral Equation Modeling

AbstractA new full-wave computational electromagnetics (CEM) approach to precipitation particle scattering analysis based primarily on a higher-order method of moments (MoM) for solving surface integral equations (SIEs) is proposed, as an alternative and addition to the conventionally used tools in this area. This is a well-established CEM approach that has not been applied, evaluated, discussed, or compared with other approaches in the scattering analysis of precipitation particles so far. Several characteristic examples of scattering from precipitation particles of various shapes demonstrate the capabilities and potential of the presented numerical methodology, and discuss its advantages over both discrete dipole approximation (DDA) and -matrix methods in cases considered. In particular, it is shown that the higher-order MoM-SIE approach is much faster, more accurate, and more robust than the DDA method, and much more general and versatile than the -matrix method. In addition, the paper illustrates prob...

Investigating raindrop shapes, oscillation modes, and implications for radio wave propagation

Studies of raindrop shapes, oscillation modes, and implications for radio wave propagation are presented. Drop shape measurements in natural rain using 2-D video disdrometers (2DVDs) are discussed. As a representative exception to vast majority of the cases where the “most probable” shapes conform to the axisymmetric (2,0) oscillation mode, an event with a highly organized line convection embedded within a larger rain system is studied. Measurements using two collocated 2DVD instruments and a C-band polarimetric radar clearly show the occurrence of mixed-mode drop oscillations within the line, which in turn is attributed to sustained drop collisions. Moreover, the fraction of asymmetric drops determined from the 2DVD camera data increases with the calculated collision probability when examined as time series. Recent wind-tunnel experiments of drop collisions are also discussed. They show mixed-mode oscillations, with (2,1) and (2,2) modes dramatically increasing in oscillation amplitudes, in addition to the (2,0) mode, immediately upon collision. The damping time constant of the perturbation caused by the collision is comparable to the inverse of the collision frequency within the line convection. Scattering calculations using an advanced method of moments numerical technique are performed to accurately and efficiently determine the pertinent parameters of electrically large oscillating raindrops with asymmetric shapes needed for radio wave propagation. The simulations show that the scattering matrix and differential reflectivity of drops are dependent on the particular oscillation modes and different time instants within the oscillation cycle. The technique can be utilized in conjunction with 3-D reconstruction of drop shapes from 2DVD data.

Measurement and characterization of winter precipitation at MASCRAD Snow Field Site

We present our ongoing studies of winter precipitation using multi-angle snowflake camera (MASC), 2D-video disdrometer, computational electromagnetic scattering methods, and state-of-the-art polarimetric radars. The newly built and established MASCRAD (MASC + Radar) Snow Field Site is one of the currently best instrumented and most sophisticated field sites for winter precipitation measurements and analysis in the nation. We present and discuss MASCRAD measurements for the snow event on Nov 15, 2014 in La Salle, Colorado.

Diakoptic Approach Combining Finite-Element Method and Method of Moments in Analysis of Inhomogeneous Anisotropic Dielectric and Magnetic Scatterers

Abstract A new diakoptic method combining the finite-element method and the method of moments is proposed for analysis of inhomogeneous anisotropic dielectric and magnetic scatterers. The method splits the original electromagnetic system into a number of closed-region finite-element method subsystems containing material complexities and an open-region method of moments subsystem, which are analyzed independently. The solution to the original problem is obtained from linear relations between coefficients in expansions of equivalent electric and magnetic surface currents on diakoptic boundary surfaces. Diakoptic electric sources and the magnetic field in finite-element method subsystems are connected using dual sets of higher-order hierarchical basis functions.

Efficient Higher Order Full-Wave Numerical Analysis of 3-D Cloaking Structures

Highly efficient and versatile computational electromagnetic analysis of 3-D transformation-based metamaterial cloaking structures based on a hybridization of a higher order finite element method for discretization of the cloaking region and a higher order method of moments for numerical termination of the computational domain is proposed and demonstrated. The technique allows for an effective modeling of the continuously inhomogeneous anisotropic cloaking region, for cloaks based on both linear and nonlinear coordinate transformations, using a very small number of large curved finite elements with continuous spatial variations of permittivity and permeability tensors and high-order p-refined field approximations throughout their volumes, with a very small total number of unknowns. In analysis, there is no need for a discretization of the permittivity and permeability profiles of the cloak, namely for piecewise homogeneous (layered) approximate models, with material tensors replaced by appropriate piecewise constant approximations. Numerical results show a very significant reduction (three to five orders of magnitude for the simplest possible 6-element model and five to seven orders of magnitude for an h-refined 24-element model) in the scattering cross section of a perfectly conducting sphere with a metamaterial cloak, in a broad range of wavelengths. Given the introduced explicit approximations in modeling of the spherical geometry and continuous material tensor profiles (both by fourth-order Lagrange interpolating functions), and inherent numerical approximations involved in the finite element and moment method techniques and codes, the cloaking effects are shown to be predicted rather accurately by the full-wave numerical analysis method.

Visual hull method based shape reconstruction of snowflakes from MASC photographs

We present utilization of the visual hull geometrical method for reconstruction of 3D shapes of snowflakes and ice particles based on high-resolution photographs of an object from multiple angles and the corresponding 2D silhouettes, for the purpose of further scattering analysis. The images are obtained by a multi-angle snowflake camera (MASC). Preliminary results appear to be much more accurate than any other available snowflake shape reconstruction examples, and are indicative of a great potential of the proposed approach.

Efficient EM scattering analysis based on MoM, HSS direct solver, and RRQR decomposition

A novel technique is presented for efficient electromagnetic (EM) scattering analysis based on a double (geometrical and current-approximation) higher order method of moments (MoM) in the surface integral equation (SIE) formulation in conjunction with a fast parallel direct solver for dense linear systems using hierarchically semiseparable structures (HSS). MoM-SIE matrix blocks are replaced by their low-rank approximations obtained by the rank-revealing QR (RRQR) decomposition for memory compression. Numerical example shows a dramatic memory compression using the novel method while preserving the accuracy of the solution.

Electromagnetic scattering by oscillating rain drops of asymmetric shapes

Computational electromagnetic analysis of scatting by oscillating rain drops with asymmetric shapes is presented. Mixed-mode oscillations of drops are attributed to sustained drop collisions in events having a highly organized line convection embedded within a larger rain system. The scattering matrix and differential reflectivity of drops are dependent on the particular oscillation modes and different time instants within the oscillation cycle. The results also demonstrate the superiority of the higher order method of moments over the conventional discrete dipole approximation method in oscillating rain drop analysis.

Duffy Method for Evaluation of Weakly Singular SIE Potential Integrals Over Curved Quadrilaterals With Higher Order Basis Functions

A Duffy method for singularity cancellation is proposed for evaluation of weakly singular potential integrals defined on generalized curved parametric quadrilateral patches with polynomial basis functions. Such integrals arise in evaluation of Galerkin matrix elements in method-of-moments analysis of antennas and scatterers in cases of coincident source and test elements. Examples demonstrate that the proposed Duffy method is more accurate, more rapidly converging with the increase of orders of Gauss-Legendre integration formulas, and faster to execute than four other methods for singularity treatment considered in the study.

Atmospheric particle scattering computation using higher order MoM-SIE method

Full-wave computational electromagnetics (CEM) approach based on the method of moments (MoM) for solving surface integral equations (SIEs) is proposed for atmospheric particle scattering analysis. The methodology is implemented as a higher order CEM technique. The paper demonstrates that the higher order MoM-SIE approach is much more efficient, accurate, general, and robust than the conventionally and almost exclusively used tools in atmospheric scattering analysis, namely, the T-matrix method and the discrete dipole approximation (DDA) method.