Krishnaswamy Sankaran

Spherical Perfectly Matched Absorber for Finite-Volume 3-D Domain Truncation

The theory of 2-D radial perfectly matched Maxwellian absorber is extended to 3-D domain truncation problems using a generalized approximate formulation of a spherical finite-volume absorber. The mathematical modeling of the spherical absorber is presented and update equations are derived. The performance of the absorber is characterized with numerical experiments. As practical application of the technique, a complex problem considering the coupling between two spiral antennas is simulated using the finite-volume time-domain method. The comparison of the results to measured data demonstrates the excellent performance of the spherical absorber.

Cell-centered finite-volume-based perfectly matched Layer for time-domain Maxwell system

The perfectly matched layer (PML) technique is extended for a cell-centered finite-volume time-domain (FVTD) method. A step-by-step procedure for the performance characterization of the FVTD PML is presented for both structured and unstructured finite-volume meshes. The FVTD PML is compared with the standard first-order Silver-Müller absorbing boundary condition (SM ABC) for practical applications. It is found that the FVTD PML for an unstructured grid achieves a reflection coefficient lower than -40 dB for incident angles up to 45° and outperforms the SM ABC by 15-20 dB.

Uniaxial and Radial Anisotropy Models for Finite-Volume Maxwellian Absorber

The uniaxial finite-volume Maxwellian absorber used as a perfectly matched layer is extended to incorporate radial anisotropy for modeling cylindrical geometries. Theoretical background and practical applications of both uniaxial and radial absorber models are presented. Both these models employ spatially and temporally co-located electromagnetic field quantities in an unstructured mesh. The uniaxial Maxwellian absorber model is tested for a truncated waveguide problem. The influence of absorber thickness and material loss parameter on the performance of the model is analyzed. Numerical reflection coefficients down to -60 dB are achieved for fine mesh discretization with approximately 20 points per wavelength confirming the convergence of numerical results. As an extension of the technique, a radially anisotropic absorber model is tested for cylindrical mesh truncation using a representative problem involving two different test scenarios. Results are compared with an existing technique commonly used in finite-volume time-domain simulations, demonstrating substantial reduction in numerical error due to cylindrical mesh truncation

Finite-Volume Maxwellian Absorber on Unstructured Grid

A novel finite-volume time-domain (FVTD) model for the Maxwellian absorber is presented to aid numerical simulations on unstructured grid. In the present approach all the electromagnetic (EM) field quantities are co-located in both space and time. Theoretical development of the co-located FVTD formulation and a practical application of the Maxwellian absorber as an unsplit perfectly matched layer (PML) for waveguide problems are presented. For variations of the angle of incidence from near normal to 50 degree, the reflection coefficient of the FVTD-Maxwellian absorber is lower than -40 dB

Radial Absorbers for Conformal Time-Domain Methods: A Solution to Corner Problems in Mesh Truncation

A radial perfectly matched absorber is investigated for accurate computational domain truncation in con-formal time-domain methods. Using the finite-volume time-domain implementation, this radial absorber is compared with the standard unsplit perfectly matched layer (PML) and numerical reflections are computed for different test conditions. The broadband numerical results demonstrate a substantial reduction in reflection errors compared to standard PML techniques where corner reflections are dominant. For the model problem with approximately 15 points per wavelength, numerical reflection coefficients in the range of -50 to -60 dB are achieved. The presented model can be naturally adapted to other conformal time-domain methods.

Radar remote sensing for oil spill classification (optimization for enhanced classification)

Oil spills are a major factor in the ocean pollution. The complications involved in detecting oil spills are due to varying wind and sea surface conditions. The main aim of this paper is to find the best combination of transmit and receive polarizations for optimal detection of oil spills which can extend the tolerance and validity ranges of single and dual polarization spaceborne missions. The optimization has to be handled in a careful way for the oil spill detection because the backscattering is very low from the oil spilled region due to high Fresnel reflection. This paper deals with an improved optimization technique for the detection and classification scheme using the spaceborne imaging radar (SIR) data sets of the oil spilled regions. Both the theory and the experimental results obtained are discussed.

Beyond DIV, CURL and GRAD: modelling electromagnetic problems using algebraic topology

Abstract Have you ever questioned why do we almost always use vector calculus and differential equations in electromagnetics? Are these the only tools at our disposal for studying and modelling electromagnetic problems? Well, the answer is no and this paper is about an alternative approach to model electromagnetic problems using algebraic topology. This approach has a few advantages compared to the familiar differential formulation-based methods in modelling electromagnetic and multiphysics problems. In differential formulation we need one of the several numerical methods like finite difference, finite element, method of moments and spectral methods to obtain approximate solution to the electromagnetic problem. In contrast, algebraic topology-based method leads directly to discrete formulation using global quantities. Furthermore, in the case of electromagnetics, all underlying global quantities are scalars. Hence, there is no need for vector calculus. In addition, we also avoid interpolating local vector field quantities as required in several numerical methods. Though algebraic topology offers powerful and elegant tools for solving various engineering problems, many applied physicists and engineers are not familiar with this subject. This is partly due to the fact that most publications on this topic burden us with complicated mathematical analysis filled with convoluted jargons. If one can introduce the key ideas of algebraic topology using familiar concepts, computational and applied physics, and engineering community can appreciate and benefit from its advantages over methods based on differential formulation. With this goal, we present the main ideas of algebraic topology applied to electromagnetics problems.

An Investigation of the Accuracy of Finite-Volume Radial Domain Truncation Technique

The accuracy and performance of the radial domain truncation technique is presented in the framework of finite-volume time-domain method. In the present approach all the electromagnetic field quantities are co-located in both space and time and the performance is evaluated using unstructured grid. The influence of the radius of curvature of the absorber is investigated using a waveguide and a horn-antenna as practical examples. Numerical reflection errors are computed using a reference solutions and the convergence of the results is studied for increasing radius of curvature of the absorber. Low-level effects on the antenna radiation patterns further illustrates the convergence of the technique.

Split and Unsplit Finite-Volume Absorbers: Formulation and Performance Comparison

Time-domain models of split and unsplit finite-volume absorbers (FiVA) used as perfectly matched layer (PML) are analyzed in this paper. These models are employed on unstructured meshes in the framework of the finite-volume time-domain (FVTD) method. A systematic comparison with emphasis on the differences in their mathematical construct and dynamic performance is presented. Numerical analysis on the absorber thickness and loss-parameter is carried out to study the limitations of these absorber models. Numerical reflection coefficients in the range of -80 dB are achieved demonstrating the capability of these models

Hybrid PML-ABC truncation techniques for finite-volume time-domain simulations

Computational domain truncations using pure and hybrid techniques in the framework of the finite-volume time-domain (FVTD) method are presented. Accurate truncation of the split-field perfectly matched layer (PML) using the first-order Silver-Mueller absorbing boundary condition (SM-ABC) provides a substitute for standard perfect electric conductor (PEC) based truncation without extra computational effort. Strategies to adapt SM-ABC for truncating PML and the broadband performance analysis of the FVTD- PML models are explored with supporting numerical results. Numerical reflection coefficients in the range of -75 dB were achieved at normal incidence for a broadband source excitation. A similar analysis at 45 degree incidence angle results in numerical reflection coefficient below -45 dB.