Publications

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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.

CARLOS-3D is a three-dimensional scattering code which was developed under the sponsorship of the Electromagnetic Code Consortium, and is currently used by over 80 aerospace companies and government agencies. The code has been extensively validated and runs on both serial workstations and parallel super computers such as the Intel Paragon. CARLOS-3D is a three-dimensional surface integral equation scattering code based on a Galerkin method of moments formulation employing Rao- Wilton-Glisson roof-top basis for triangular faceted surfaces. Fully arbitrary 3D geometries composed of multiple conducting and homogeneous bulk dielectric materials can be modeled. This presentation describes some of the extensions to the CARLOS-3D code, and how the operator structure of the code facilitated these improvements. Body of revolution (BOR) and two-dimensional geometries were incorporated by simply including new input routines, and the appropriate Galerkin matrix operator routines. Some additional modifications were required in the combined field integral equation matrix generation routine due to the symmetric nature of the BOR and 2D operators. Quadrilateral patched surfaces with linear roof-top basis functions were also implemented in the same manner. Quadrilateral facets and triangular facets can be used in combination to more efficiently model geometries with both large smooth surfaces and surfaces with fine detail such as gaps and cracks. Since the parallel implementation in CARLOS-3D is at high level, these changes were independent of the computer platform being used. This approach minimizes code maintenance, while providing capabilities with little additional effort. Results are presented showing the performance and accuracy of the code for some large scattering problems. Comparisons between triangular faceted and quadrilateral faceted geometry representations will be shown for some complex scatterers.