Abstract-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-fromfrequency-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.
The 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 2DVD camera data for these asymmetric drops. The reconstruction requires a specific technique to correct for the drop image distortions due to horizontal velocities. Scattering calculations for the reconstructed asymmetric drops have been performed using a higher-order method of moments solution to the electric and magnetic field surface integral equations. Results show that the C-band scattering amplitudes of asymmetric drops are markedly different from those of oblate spheroids. The intention for future studies is to automate the entire procedure so that more realistic simulations can be performed using the 2DVD-based data, particularly for cases where collision-induced drop oscillations give rise to considerable numbers of asymmetric drops.
Two-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 distributions and equilibrium oblate shapes. This was especially pronounced for ρhv, where the MoM-SIE method showed lowered values (dip) during the passage of the line convection consistent with radar measurements, unlike the bulk method. The MoM-SIE calculations of [Zh, Zdr, Kdp] agree very well with the radar measurements, whereas linear depolarization ratio (LDR) calculations from the drop-by-drop method are found to be larger than the values from the bulk method, which is consistent with the dip in simulated and radar-measured ρhv. Our calculations show the importance of the variance of shapes resulting from asymmetric drops in the calculation of ρhv and LDR.
This paper discusses an integrated approach to electrical‐engineering education that incorporates computer‐assisted MATLAB‐based instruction and learning into the junior‐level electromagnetics course and newly created learning studio modules (LSMs). In this model, creativity class sessions are followed by two comprehensive and rather challenging multi‐week homework assignments of MATLAB problems and projects in electromagnetic fields. This is enabled by a unique and extremely comprehensive collection of MATLAB computer exercises and projects, reinforcing all important theoretical concepts, methodologies, and problem‐solving techniques in electromagnetic fields and waves, developed by one of the faculty team members. These tutorials, exercises, and codes constitute a modern tool for learning electromagnetics via computer‐mediated exploration and inquiry, exploiting the technological and pedagogical power of MATLAB software as a general learning technology. The novel approach introduces students to MATLAB programming of electromagnetic fields, as opposed to just passive demonstrations of MATLAB's tools and capabilities for computation and visualization of fields. MATLAB programming tutorials and assignments are designed to deepen student engagement and accommodate different learning styles so students can learn more effectively. In addition to improving students’ understanding and command of MATLAB use and programming within the electromagnetics context and beyond, these exercises increase their motivation to learn and appreciation of the practical relevance of the material, and equip them with the tools and skills to excel in other courses and projects. The results of this project were qualitatively analyzed through feedback surveys given to the students at the end of each MATLAB assignment. The Electromagnetics Concept Inventory was also used.
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