The Math-Supercomputing Connection
The Berkeley Lab website recently published a short “five-question” interview with David Brown, the director of the Computational Research Division at Lawrence Berkeley National Laboratory (Berkeley Lab) since August 2011. Mathematics, according to Brown, is the foundation of modern computational science.
When Brown got a post-doc position at Los Alamos National Laboratory after earning his PhD in applied mathematics from California Institute of Technology in 1982, he thought he would only stay a couple of years, before accepting a teaching position elsewhere. Best laid plans, and all that because that 2-year plan evolved into a 31-year tenure with US Department of Energy (DOE) national laboratories, including 14 years at Los Alamos National Laboratory and 13 years at Lawrence Livermore National Laboratory.
Brown explains that when he made the move to Lawrence Livermore National Lab, he was able to “apply his knowledge of math and science to the development and oversight of new research opportunities for scientists and mathematicians at that lab and throughout the DOE.” Brown’s passion for the field made him an ideal candidate to lead the extensive research program in applied mathematics at Berkeley Lab.
Brown refers to mathematics as the language of science, and says this language is what allows science to be put on computers. From there, it’s not a huge jump to see why the DOE invests in math research.
“New and better mathematical theories, models and algorithms…allow us to model and analyze physical and engineered systems that are important to DOE’s mission,” notes Brown. “Often math is used to make a very difficult problem tractable on computers.”
Brown cites a notable example from 30 years ago. Mathematician James Sethian’s work with asymptotic methods set the stage for breakthroughs in combustion simulation techniques. That discovery undergirds modern supercomputing codes used in everything from combustion to astrophysics to atmospheric flow.
Asked how math applies to supercomputers, Brown responds:
The scientific performance of big applications on supercomputers is as much a result of better mathematical models and algorithms as it is of increases in computer performance. In fact, the increases in performance of many scientific applications resulting from these better models and algorithms has often exceeded the performance increases due to Moore’s Law . And Moore’s Law, which predicts of doubling of performance every 18 months, offers a pretty impressive increase on its own. These improvements in performance help scientists make much more efficient use of supercomputers and study problems in greater detail.
An applied mathematician by training, Brown is especially interested in the development and analysis of algorithms for solving partial differential equations (PDEs). In 2001, the Overture project, which Brown led, was selected as one of the 100 “most important discoveries in the past 25 years” by the DOE Office of Science.