Sanja B. Manic

Efficient Time-Domain Analysis of Waveguide Discontinuities Using Higher Order FEM in Frequency Domain

A computational technique is presented for efficient and accurate time-domain analysis of multiport waveguide structures with arbitrary metallic and dielectric discontinuities using a higher order finite element method (FEM) in the frequency domain. It is demonstrated that with a highly efficient and appropriately designed frequency-domain FEM solver, it is possible to obtain extremely fast and accurate time-domain solutions of microwave passive structures performing computations in the frequency domain along with the discrete Fourier transform (DFT) and its inverse (IDFT). The technique is a higher order large-domain Galerkin-type FEM for 3- D analysis of waveguide structures with discontinuities implementing curl-conforming hierarchical polynomial vector basis functions in conjunction with Lagrange-type curved hexahedral finite elements and a simple single-mode boundary condition, coupled with standard DFT and IDFT algorithms. The examples demonstrate excellent numerical properties of the technique, which appears to be the first time-from- frequency-domain FEM solver, primarily due to (i) very small total numbers of unknowns in higher order solutions, (ii) great modeling flexibility using large (homogeneous and continuously inhomogeneous) finite elements, and (iii) extremely fast multifrequency FEM analysis (the global FEM matrix is filled only once and then reused for every subsequent frequency point) needed for the inverse Fourier transform.

Combining finite element method and Fourier transform to analyze waveguide transients

A numerical technique combining the finite element method (FEM) and Fourier transform is applied to calculate transients on 3-D microwave waveguide structures. The structures are modeled using a higher order FEM that can efficiently render frequency-domain responses at a large number of frequency samples, which are processed by the inverse discrete Fourier transform (IDFT) to obtain time-domain solutions. The FEM-IDFT approach is illustrated and its numerical properties are discussed in detail in the transient analysis of an E-plane ridge waveguide discontinuity.

Anisotropic Locally Conformal Perfectly Matched Layer for Higher Order Curvilinear Finite-Element Modeling

A perfectly matched layer (PML) method is proposed for electrically large curvilinear meshes based on a higher order finite-element modeling paradigm and the concept of transformation electromagnetics. The method maps the non-Maxwellian formulation of the locally conformal PML to a purely Maxwellian implementation using continuously varying anisotropic and inhomogeneous material parameters. An approach to the implementation of a conformal PML for higher order meshes is also presented, based on a method of normal projection for PML mesh generation around an already existing convex volume mesh of a dielectric scatterer, with automatically generated constitutive material parameters. Once the initial mesh is generated, a PML optimization method based on gradient descent is implemented to most accurately match the PML material parameters to the geometrical interface. The numerical results show that the implementation of a conformal PML in the higher order finite-element modeling paradigm dramatically reduces the reflection error when compared to traditional PMLs with piecewise constant material parameters. The ability of the new PML to accurately and efficiently model scatterers with a large variation in geometrical shape and those with complex material compositions is demonstrated in examples of a dielectric almond and a continuously inhomogeneous and anisotropic transformation-optics cloaking structure, respectively.

Double higher-order FEM modeling using an anisotropic conformal perfectly matched layer

We present a computationally efficient technique for termination of a computational domain in open-domain scattering simulations based on a double higher-order (higher order in geometry and field approximation) finite element method (DHO-FEM). The computational domain is surrounded by an anisotropic, locally-conformal perfectly matched layer (PML) utilizing higher order, continuously inhomogeneous, anisotropic material parameters.

p-Refinement for Large-Domain Waveguide Structures Analyzed by FEM-MM Technique

Coupling of a mode matching (MM) method with a higher order large-domain finite element method (FEM) is presented in analysis of three-dimensional waveguide structures with discontinuities. The new FEM-MM technique enables very effective higher order hexahedral meshes constructed from a very small number of large curved conformal finite elements (large domains) and p-refined high-order field expansions. This results in solutions with minimal total numbers of unknowns.

Scattering Calculations for Asymmetric Raindrops during a Line Convection Event: Comparison with Radar Measurements

AbstractTwo-dimensional video disdrometer (2DVD) data from a line convection rain event are analyzed using the method of moments surface integral equation (MoM-SIE) via drop-by-drop polarimetric scattering calculations at C band that are compared with radar measurements. Drop geometry of asymmetric drop shapes is reconstructed from 2DVD measurements, and the MoM-SIE model is created by meshing the surface of the drop. The differential reflectivity Zdr calculations for an example asymmetric drop are validated against an industry standard code solution at C band, and the azimuthal dependence of results is documented. Using the MoM-SIE analysis on 2DVD drop-by-drop data (also referred to as simply MoM-SIE), the radar variables [Zh, Zdr, Kdp, ρhv] are computed as a function of time (with 1-min resolution) and compared to C-band radar measurements. The importance of shape variability of asymmetric drops is demonstrated by comparing with the traditional (or “bulk”) method, which uses 1-min averaged drop size di...

MoM-SIE scattering models of snow and ice hydrometeors based on 3D shape reconstructions from MASC images

We present scattering models of snow and ice hydrometeors and computation of full polarimetrie radar variables for winter precipitation using a higher order method of moments (MoM) in the surface integral equation (SIE) formulation. The studies of winter precipitation are based primarily on measurements by a multi-angle snowflake camera (MASC), reconstruction of 3D hydrometeor shapes by means of the visual hull method, MoM-SIE scattering computations, and measured polarimetric observables by CSU-CHILL Radar.

Scattering Calculations at C-Band for Asymmetric Raindrops Reconstructed from 2D Video Disdrometer Measurements

AbstractThe distribution of raindrop shapes is well known to be important in deriving retrieval algorithms for drop size distribution parameters (such as the mass-weighted mean diameter) and rain rate, as well as for attenuation correction using the differential propagation phase constraint. While past work has shown that in the vast majority of rain events the most “probable” shapes conform to those arising primarily from the axisymmetric (2,0) oscillation mode, a more recent event analysis has shown that drop collisions can give rise to mixed-mode oscillations and that for high collision rate scenarios, a significant percentage of drops can become “asymmetric” at any given instant.As a follow-up to such studies, this study involved performing scattering calculations for 3D-reconstructed shapes of asymmetric drops using the shape measurements from a 2D video disdrometer (2DVD) during the above-mentioned rain event. A recently developed technique is applied to facilitate the 3D reconstruction from the 2DV...

Measurement and analysis of rain precipitation at MASCRAD Instrumentation Site in Colorado

We present our ongoing studies of rain precipitation synergistically using a 2D-video disdrometer, particle spectrometer, precipitation occurrence sensor system, Pluvio precipitation gauge, state-of-the-art polarimetric CSU-CHILL radar, and a higher order electromagnetic scattering method. We present and discuss measurements and analyses for several rain events in 2015 at MASCRAD Instrumentation Site in Colorado.

Multiscale electromagnetic modeling using double-higher-order quadrilateral meshes and parallel MoM-SIE direct solutions

We present the development of a scalable parallel algorithm and solver for computational electromagnetics based on a double higher order method of moments in the surface integral equation formulation in conjunction with a direct hierarchically semiseparable structures solver. Multiscale modeling using the new method, for electrically very large structures that also include electrically very small details, is discussed, with several advancement strategies.