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Record Billions of Equations Solved in 10 Minutes by Stanford, US Army Grid

Professor Charbel Farhat

Professor Charbel Farhat (Photo: Stanford University)

Stanford University researchers have joined hands with the U.S. Army Research Laboratory (ARL) to set a computational record of solving billions of mathematical equations in just a few minutes, a rare feat in computational engineering.

Stanford Professor Charbel Farhat and the Army High Performance Computing Research Center (AHPCRC) used a new, high-end, massively parallel computer to test the power of algorithms enabling processors to work at enormous speeds. They used 22,000 processors to achieve the feat.

Farhat, director of AHPCRC at Stanford said, “We’ve solved over 10 billion equations in a little over three minutes.”

The experiment was taken up after the ARL acquired Excalibur, a Cray XC40 computer with 101,184 processors, set it up at ARL’s Maryland-based Defense Computing Resource Center (ARL DSRC), to support dozens – potentially hundreds – of research projects.

Farhat and his team worked on it to harness Excalibur’s massive computational power to solve large-scale equations and the team succeeded far beyond Farhat’s last endeavor, said a statement.

“The last time we’d had access to a large machine like this one, we probably ran our algorithms on about 3,000 processors,” said Farhat, a feat that won them a 2002 Gordon Bell Prize from the Institute of Electrical and Electronics Engineers. “Now we ran on 22,000,” hoping for a bigger award and recognition in the field.

Computing engineers have been harnessing multiple computer processors to calculate and resolve many technological problems, including in the fields of solid mechanics, fluid dynamics, heat transfer and signal processing.

Theoretically, multiple computers can confront, digest and solve complex equations faster than a single computer but coordination among the processors is as difficult as it is among people, Farhat said. Just as adding 10 people to a task doesn’t necessarily improve skill lvels in the same level, so is the complexity of interactions among the computers, he said.

“When you connect 100 computers and tell them to solve a system of equations, I need to break it into 100 pieces and ship each piece to a computer, and then they need to talk to each other,” Farhat said.

Farhat and his team – led by Jari Toivanen, Radek Tezaur and Philip Avery – collaborated with the ARL DSRC to craft algorithms to divide these calculations among thousands of computers and worked round the clock for three weeks to prepare their software for the test on Excalibur.

On the day of experiment, they used 101,184 processors to divide up slices of their equations, share information and solve the problem. A mere three minutes later, those thousands of processors had solved over 10 billion calculations accurately.

Though such enormous access won’t be available again, Farhat said he believes this new scalable algorithm will be tremendously useful on smaller computing systems.

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