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Sam Webster is quite literally ‘at home’ around numbers. “I was surrounded by math from a young age," chuckles the fifth-year applied mathematics Ph.D. candidate and graduate instructor. Coming from the home of two math lovers--his mother is a university statistics professor and his father is a university finance department chairperson, Webster was instilled with an early appreciation for mathematics.

Webster earned his B.S. in Mathematics from Villanova University. With plans to become a math professor, Webster turned to graduate school. Along with its strong academic reputation, the personal interest and attention he received from UMBC's Department of Mathematics and Statistics attracted him to the university. “I got a call from Dr. Neerchal, head of the applied mathematics graduate program at the time, and we got together to discuss the program. That went a long way,” he explains.

Webster’s mentor, associate professor Dr. Matthias Gobbert , has provided him with a new source of support and inspiration. “He looked out for me from day one and pointed me in the right direction,” he says. “He believed in me, and I’m grateful for the opportunities he’s given me.”

"I immensely enjoy teaching. If you can reach a few people, that makes it all worth it,” says Webster. Named Outstanding Graduate Instructor in 2002 for his teaching excellence in his department, Webster has clearly reached more than just a few of his students. A graduate instructor since summer ‘00, Webster has taught four algebra and calculus-based courses for his department: Math 106,151, 155 and 221. Bringing math to life for his students is paramount. He explains, “If you can show that math doesn’t just exist in a vacuum, that it can solve real-life problems, then people can easily see its true importance. The application is what gives it real meaning."

Indeed, Webster’s current research experience has reinforced this truth for him. “It’s been great—I’ve really enjoyed seeing it all come together,” he says of his Ph.D. dissertation work, which is applied to the computer industry. Webster is involved in optimizing semiconductor, i.e. computer chip, manufacturing. His research is part of a collaborative effort established between Dr. Gobbert and chemical engineers at Rensselaer Polytechnic Institute (RPI) in Troy, N.Y.

Very simply put, semiconductor production involves feeding a gas over a silicon wafer. The two react, and a very fine layer of conductive material is deposited on the surface of a wafer. For reasons of cost and quality control, chip manufacturers would like to more precisely determine the amount and uniformity of this conductive material being deposited. In order to derive this information, one must first determine the gas flow properties.

This is where Webster’s work comes into play, and, where things become a little tricky. The equation that models this gas flow the Boltzmann Transport Equation (BTE), has one slightly inconvenient attribute. Webster explains, “The BTE has no true analytic solution. So we try to approximate it as best we can. This is done by applying our numerical method, to the BTE, which transforms it into a solvable system of equations.” Because this approximate solution is only as good as its numerical method, Webster’s challenge has been to improve the numerical method in order to reach the most accurate possible approximate solution. The closer the numerical solution is to reality, the better manufacturers can optimize the chip-making process.

Webster has created computer models simulating several of the processes related to the gas flow in chip manufacturing. He is using parallel computing to simulate these processes efficiently. “We solve the problem ‘in parallel’,” explains Webster, "meaning we use a cluster of connected computers that work simultaneously on the same problem to speed up our simulations. The processing speed is increased by the number of computers used." Thanks to a recent NSF grant, the mathematics department just acquired a 64-processor cluster (shown in background of photograph of Webster and Gobbert), so Webster can now solve for the BTE 64 times faster. This translates into a significant savings of time. "A computer simulation that once took approximately 3 hours running in serial now takes about 5 minutes running in parallel,”explains Webster.

To learn more about their research, visit the following websites:
www.math.umbc.edu/~swebst1/research/boltzmann.html
www.math.umbc.edu/~gobbert/boltzmann.html