Fast And Efficient Algorithms Handle Nearly 10 Million Unknowns

"The main thrust of our work is to reduce the computational time and complexity when analyzing or synthesizing large and complicated electromagnetic systems," said Weng Chew, a U. of I. professor of electrical and computer engineering and director of the computational electromagnetics center. "We have developed a number of computational algorithms that greatly accelerate the solution of integral equations that arise in the analysis of scattering and radiation problems."

Two years ago, Chew's team could handle 2 million unknowns. By further refining the code and eliminating bottlenecks, and working with research scientist Jiming Song, the team recently solved problems with up to 9.6 million unknowns. The numerical simulation was performed using software called the Fast Illinois Solver Code. The program ran during one day on the 32-processor Silicon Graphics CRAY Origin2000(tm) computer at the U. of I.'s National Center for Supercomputing Applications. Using conventional techniques, it would have taken more than 10 years to solve the problem.

"The radar cross-section of an aircraft is a measure of how visible the aircraft is to radar, and can be used for target detection and identification purposes," Chew said. "In designing stealth technology, we want to reduce this visibility as much as possible, so we need very precise calculations."

To accurately compute the radar cross-section for a large aircraft, Chew and his colleagues first simulate the physical geometry of the aircraft's surface, then they break the resulting geometry into millions of tiny pieces, requiring meticulous and intensive electromagnetic calculations.

Fast and efficient, these algorithms can significantly reduce the turn-around time in almost any computational electromagnetic design and analysis environment. Potential applications include antenna modeling, circuit simulation, geophysical prospecting, remote sensing, wireless communication, wave propagation and bioelectromagnetics.

Chew's team -- which includes electrical and computer engineering professor Jose Schutt-Aine and postdoctoral research associate Sanjay Velamparambil -- also has assembled a cluster of 16 personal computers that can solve equivalent dense-matrix problems with up to 600,000 unknowns.

"Because the cluster costs less than $20,000, this technology could impact many branches of electrical engineering," Chew said. "Large-scale computing -- which once belonged to the realm of very expensive supercomputers -- will soon be available to researchers with much smaller budgets."