This paper examined the high frequency time harmonic localization of modal fields in two dimensional cavities along unstable periodic orbits. The elliptic formalism, combined with the random phase approach, allowed the treatment of both convex and concave boundary geometries.
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This report examines the localization of time harmonic high frequency modal fields in two dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This paper examines the enhancements for these unstable orbits when the opposing mirrors are both convex and concave. In the latter case the construction includes the treatment of interior foci.
This report investigates the feasibility of applying Adaptive Mesh Refinement (AMR) techniques to a vector finite element formulation for the wave equation in three dimensions. Possible error estimators are considered first. Next, approaches for refining tetrahedral elements are reviewed. AMR capabilities within the Nevada framework are then evaluated. We summarize our conclusions on the feasibility of AMR for time-domain vector finite elements and identify a path forward.
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This report discusses a set of verification test cases for the frequency-domain, boundary-element, electromagnetics code Eiger based on the analytical solution of plane wave scattering from a sphere. Three cases will be considered: when the sphere is made of perfect electric conductor, when the sphere is made of lossless dielectric and when the sphere is made of lossy dielectric. We outline the procedures that must be followed in order to carefully compare the numerical solution to the analytical solution. We define an error criterion and demonstrate convergence behavior for both the analytical and numerical cases. These problems test the code's ability to calculate the surface current density and secondary quantities, such as near fields and far fields.
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In this presentation, the authors will investigate the use of hybrid meshes for modeling RCS and antenna problems in three dimensions. They will consider two classes of hybrid basis functions. These include combinations of quadrilateral and triangular meshes for arbitrary 3D geometries, and combinations of axisymmetric body-of-revolution (BOR) basis functions and triangular facets. In particular, they will focus on the problem of enforcing current continuity between two surfaces which are represented by different types of surface discretizations and unknown basis function representations. They will illustrate the use of an operator-based code architecture for the implementation of these formulations, and how it facilitates the incorporation of the various types of boundary conditions in the code. Both serial and parallel code implementation issues for the formulations will be discussed. Results will be presented for both scattering and antenna problems. The emphasis will be on accuracy, and robustness of the techniques. Comparisons of accuracy between triangular meshed and quadrilateral meshed geometries will be shown. The use of hybrid meshes for modeling BORs with attached appendages will also be presented.