Computation of the RCS of a Complex BOR Using FEM with Coupled Azimuth Potentials and PML

Abstract

An efficient finite element method ( E M ) to compute scattering from a complex body of revolution (BOR) is discussed. The BOR is composed of perfect conductor and impedance surfaces and arbitrary inhomogeneous materials. The FEM equations are developed using the coupled azimuth potential (CAP) formulation. The FEM mesh is truncated with a perfectly matched layer (PML) in cylindrical coordinates. The use of PML in cylindrical coordinates avoids the wasted compulation which results from a spherical mesh boundary with an elongated scatterer. The FEM equations are solved by ordering the unknowns with a reverse Cuthill-McKee algorithm and applying a banded-matrix solution algorithm. Numerical results are presented and compared to exact results and measurements and to results from a previous FEM algorithm which uses edge-based vector basis functions to expand the transverse field components and node-based scalar basis functions lo expand the angular component. Problems associated with the CAP formulation are discussed and demonstrated through numerical examples.

A Review of Metamaterials and its Applications

“…To solve the problems of inhomogeneous anisotropic materials and complex structures the finite-element method (FEM) is used [41][42]. It eliminates the problem of spurious solutions by expanding the angular and transverse field components with the node-based scalar and edge-based vector basis functions respectively [43].…”

Finite-Element Analysis of Three-Dimensional Axisymmetrical Invisibility Cloaks and Other Metamaterial Devices

“…and a discussion of appropriate functions for ǫ p ρρ , ǫ p φφ , and ǫ p zz can be found in [13][14][15]. The PML to air interface is reflectionless in the cylindrical coordinates, and waves which propagate through the PML is attenuated.…”

“…The finite-element method (FEM) is characterized by the very flexible material handling capabilities and is often preferred for problems involving complex structures and inhomogeneous anisotropic materials [13,14]. By taking advantage of the rotational symmetry, the 3D problem can be reduced to a 2D computational domain.…”

“…Triangular elements are applied to conveniently and accurately model arbitrary shapes of body of revolution. The FEM mesh is truncated with a cylindrical perfectly matched layer (PML) [13][14][15], which is much more efficient for arbitrarily-shaped scatterers than is a spherical boundary. The accurately numerical results are presented to show the validity and efficiency of the method.…”

Locally corrected Nyström method for EM scattering by bodies of revolution

“…Two of the widely used BOR-MoM FORTRAN codes for EM radiation and scattering analysis are JRMBOR [20] and CICERO/CARLOS-BOR [14]. Other methods include PDE based techniques for inhomogeneous BOR problems, [9,[16][17][18], where scalar potentials are introduced to reduce the number of unknowns for large scatterers, hybrid method [15], pseudospectral method [25], and FFT method [7].…”