Matrix Solvers Enable Real-World Radar Signature Predictions

Matrix Solvers Enable Real-World Radar Signature Predictions


To develop matrix-direct solution technologies that enable first-principle accurate radar cross section (RCS) characterization of real-world DoD platforms and more using high-performance computer simulation at unprecedented high levels of fidelity and frequencies. These novel technologies will also significantly advance ARA’s award-winning computational electromagnetics (CEM) projects.


To characterize RCS at frequencies of interest and enable CEM simulations beyond 10 million unknowns, ARA has developed a direct-solve Domain Decomposition Method (DDM). The method constructs Macro Basis Functions (MBFs) on subdomains, clusters of mesh elements.

This next-gen method reduced a 10 million unknown RCS problem to only 400,000 MBF unknowns. This 400,000-unknowns matrix was then compressed using the prior state-of-the-art Adaptive Cross Approximation (ACA) method and factored on a supercomputer in less than four hours, instead of days, with only 0.04 percent of the original matrix entries present in the fully-compressed matrix representation.


One application is to measure fighter and bomber backscatter to determine the aircraft’s observability. Outside the DoD, applications include self-driving car target identification and classification for all weather conditions. Recently, a leading global automobile supplier contracted ARA to characterize the RCS response of commercial cars to improve the safety of autonomous vehicles.

Until now, a direct-solve, physics-based computational electromagnetic (CEM) simulation of a car at millimeter-wave frequencies had been impossible, as it requires solving hundreds of millions of unknowns, but now, for the first time, full-size cars can be analyzed and characterized, providing very accurate data at a fraction of the cost and time.

ARA is also integrating its ACA, compressive DDM, and multi-level fast multipole method (MLFMM) with ARA’s General Electromagnetic Model for the Analysis of Complex Systems (GEMACS) CEM software.

The modernized and accelerated GEMACS software is expected to outperform commercial CEM software for large-scale, real-world RCS and antenna problems, allowing ARA to solve problems for a broad category of customers while making our world a safer place.

Computational Electromagnetics

Computational Electromagnetics & Fluid Dynamics

When faced with the challenge to solve complex computing issues in the most efficient manner possible, U.S. government agencies turn to ARA’s... more

RF Technologies

RF Technologies

ARA offers broad expertise in radio frequency (RF) technologies, including hardware design and fabrication and software programming. more