This software innovation is designed to develop a mathematical formulation to estimate the electromagnetic scattering characteristics of complex, inhomogeneous objects using the finite-element-method (FEM) and method-of-moments (MoM) concepts, as well as to develop a FORTRAN code called FEMOM3DS (Finite Element Method and Method of Moments for 3-Dimensional Scattering), which will implement the steps that are described in the mathematical formulation. Very complex objects can be easily modeled, and the operator of the code is not required to know the details of electromagnetic theory to study electromagnetic scattering.

Consider a complex inhomogeneous object geometry, the electromagnetic scattering characteristics of which are to be estimated when illuminated by a plane electromagnetic wave. To facilitate the mathematical formulation using the hybrid FEM/MoM, the object is assumed to be enclosed by a surface indicated as a fictitious outer boundary. Inside the boundary, the electromagnetic fields are obtained using the FEM, whereas the electromagnetic fields outside the fictitious boundary are obtained using the assumed equivalent electric and magnetic currents flowing on the fictitious boundary. Continuity of the electromagnetic fields across the fictitious boundary results in partly sparse/dense matrix that is solved for the unknown fields inside the fictitious boundary including the boundary surface.

The steps laid out in the mathematical formulation are carried out in FEMOM3DS. Along with the main FEMOM3DS, the innovation uses a commercial computer-aided-design (CAD) package for geometrical modeling, and a post-processing package such as Techplot for displaying graphically the results obtained using FEMOM3DS. In the present FEMOM3DS code the COSMOS/M commercial software is used as a CAD tool to model the geometry of a given problem. The COSMOS/M is also used to discretize the FEM region using the tetrahedral elements. Various inhomogeneous regions are taken care of by having many parts in the FEM region. Using the COSMOS/M, common boundaries where boundary conditions are to be implemented are also identified. The data file created by the COSMOS/M for node and element information is then generated and processed through the preprocessor part of FEMOM3DS code to create edge information and node information. The preprocessed data are then run through the main part of FEMOM3DS to obtain electromagnetic scattering. The output files from the FEMOM3DS can be used for displaying the results in a graphical format.

The FEMOM3DS is written in FORTRAN 77. The code was successfully compiled on a CONVEX machine. However, the code can be compiled on any 32-bit machine like PCs or SUN, SGI UNIX Station. To get correct results, dimensions must be given in centimeters, frequency of operation must be given in GHz and incident and observation angles must be specified in degrees.

This work was done by Manohar Deshpande and C. J. Reddy of Langley Research Center. For more information, download the Technical Support Package (free white paper) at under the Information Sciences category. LAR-17090-1

NASA Tech Briefs Magazine

This article first appeared in the January, 2011 issue of NASA Tech Briefs Magazine.

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