A math computational method more than a century and a half old, thought of little use in the modern era of computers, could once again be a useful research tool, researchers say.
Known as the Jacobi iterative method after German mathematician Carl Gustav Jacob Jacobi who introduced it in 1845, it is a manner of solving linear equations by beginning with an initial rough guess then performing a repeating series of mathematical operations, again and again, until a practical solution is achieved.
Dismissed in the early years of the 20th century as too slow for modern applications, now researchers at Johns Hopkins University say they've souped up the process to be as much as 200 times faster.
That could accelerate computer models and simulations used in climate and weather studies, aerospace design, biomechanics and a number of engineering tasks, they say.
"For people who want to use the Jacobi method in computational mechanics, a problem that used to take 200 days to solve may now take only one day," mechanical engineering Professor Rajat Mittal says.
"Our paper provides the recipe for how to speed up this method significantly by just changing four or five lines in the computer code," says Mittal, senior author of the study reported in the Journal of Computational Physics.
In 2012, Mittal was explaining the Jacobi approach to his class on Numerical Methods, characterizing it as mathematically elegant technique that was for the most part useless for modern practical applications.
One student listening to Mittal's lecture was Xiang Yang.
"[The iterative method] just took so much time and so many computations to get to the answer you wanted," says Yang, a graduate student in mechanical engineering. "And there were better methods. That's why this Jacobi method isn't being used much today."
However, he says, his curiosity was piqued and he began toying with the Jacobi scheme, looking for a way to speed up the progression of repeating numerical estimates to make it more efficient, with encouragement from Mittal.
"Instead of saying that this method has been around for 169 years, and that everyone has already tried to improve it without much success, Professor Mittal told me that he felt my idea was very promising," Yang said, "and he encouraged me to work on it."
Yang and Mittal then started working together to come up with what they've dubbed a "scheduled relaxation Jacobi method," and reported their work in the journal article.
"I expect this to be adopted very quickly," Mittal says. "Everyone is competing for access to powerful computer systems, and the new Jacobi method will save time. In fact, the beauty of this method is that it is particularly well suited for the large-scale parallel computers that are being used in most modern simulations."
