Uniaxial and Radial Anisotropy Models for Finite-Volume Maxwellian Absorber

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> 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 &lt;formula formulatype="inline"&gt;&lt;tex&gt;$-$&lt;/tex&gt;&lt;/formula&gt;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. </para>