methods: high-frequency asymptotics, which treats scattering and diffraction as local phenomena; or solution of an integral equation (in the frequency domain) for radiating sources on (or inside) the scattering body, which couples all parts of the body through a multiple scattering process. A third approach is the direct integration of the differential or integral form of Maxwell's equations in the time domain.

The time-domain Maxwell's equations represent a more general form than the frequency-domain vector Helmholtz equations, which are usually employed in solving scattering problems. A time-domain approach can, for instance, handle continuous wave (single frequency) as well as a single pulse (broadband frequency) transient response. Frequency-domain-based methods usually provide the RCS response for all angles of incidence at a single frequency, while time-domain-based methods provide solutions for many frequencies from a single transient calculation. Also, in a time-domain approach, one can consider time-varying material properties for treatment of active surfaces. By using Fourier transforms, the time-domain transient solutions can be processed to provide the frequency-domain response. Frequency-dependent (dispersive) and anisotropic material properties can also be included within the time-domain formulation.

CEM is a critical technology in the advancement of future aerospace development through supercomputing. As we make the transition from the present gigaflops to the next-generation teraflops computing, CEM will become integral to aerospace design not only as a standalone technology but also as part of the multidisciplinary coupling that leads to well-optimized designs.


Toward establishing a computational environment for performing multidisciplinary studies, the initial goal is to advance the state of the art in CEM with the following specific objectives:

  1. Apply algorithmic advances in Computational Fluid Dynamics (CFD) to solve Maxwell's equations in general form to study scattering (radar cross section), radiation (antenna), and a variety of electromagnetic environmental (electromagnetic compatibility, shielding, and interference) problems of interest to both the defense and commercial communities. (Mohammadian et al., 1991)

  2. Establish the viability of MIMD massively parallel architectures for tackling large-scale problems not amenable to present-day supercomputers.

  3. Develop the CEM technology to the point of being able to perform coupled CFD/CEM optimization design studies.

CEM Issues

Proper development of a CEM capability appropriate for all aspects of aerospace design must consider various issues associated with electromagnetics. Some of them are addressed in the following seven subsections.

Maxwell's Equations

In order to apply conservation principles (for example, in fluid dynamics, mass, momentum, and energy are conserved), many of the governing equations representing appropriate physical processes are written in conservation form. The general form of a differential conservation equation can be written as

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