John Bell, A Pioneering Mathematician Continues to Shape the Future

John Bell has been part of the U.S. Department of Energy’s National Laboratories for a long time. Thirty-eight years to be exact, 28 of them at Lawrence Berkeley National Laboratory (Berkeley Lab). But his storied career in mathematics goes back even further. In fact, his fascination with math began when he was quite young, spurred on by some key influencers along the way.

“There was a famous guy who was asked, ‘Why did you become a mathematician?’ His answer was ‘I couldn’t imagine being anything else,’” said Bell, a senior scientist in the Center for Computational Sciences and Engineering (CCSE) at Berkeley Lab and formerly chief scientist in the Lab’s Applied Mathematics and Computational Research (AMCR) Division. “I really resonated with that.  Even at the middle school level, math was the thing I really enjoyed. My mother wanted me to be a doctor and my father wanted me to be a lawyer. Neither of those would have worked.”

Bell’s family moved a lot when he was growing up; he was born in Texas, then they moved to California, then back to Texas, then Nebraska, and finally to the Maryland suburbs of Washington, DC. 

“When we got to Maryland, I had two math teachers who really helped push me forward,” Bell said. As a result of their support, he went on to earn his B.S. in mathematics from the Massachusetts Institute of Technology (1975) before heading on to grad school. “I ended up at MIT because those two teachers looked at me and said ‘you’re one of the best students in math we’ve ever had at this high school so you should go to MIT.’ I applied and got in and that was that.” 

After MIT, Bell went on to earn his master's (1977) and Ph.D. (1979) at Cornell University, also in mathematics. He then worked as a researcher at the Naval Surface Weapons Center and Exxon Production Research Company before joining Lawrence Livermore National Laboratory (LLNL) in 1986.

“I didn’t really enjoy the corporate research environment,” he said. “So when LLNL started making a big push to build up its applied math area, I got recruited and went for it.” 

In 1993, while at LLNL, Bell became founding director of the CCSE, which today is widely recognized as a leader in the field of adaptive mesh refinement (AMR): algorithms developed to focus the power of a supercomputer on the most interesting parts of a scientific problem, leading to more detailed studies and more efficient use of computing resources. In 1996, he and 22 other members of the CCSE moved to Berkeley Lab, where – as part of what was then CRD and is now AMCR – they remained focused on the development and application of computer simulations for complex physics problems in areas ranging from combustion to atmospheric and astrophysical flows.

Research Path

Along the way, Bell’s journey in applied mathematics has taken a number of interesting twists and turns. Today he is internationally recognized as a leader in the development and analysis of numerical methods for partial differential equations (PDEs) in science and engineering, but his work with PDEs originally began during his time as a summer student at the Naval Surface Weapons Center. What started as a summer job turned into an intermittent full-time gig that helped supplement his graduate student income. It also fueled his interest in numerics.

“When I went to work at the Navy Lab, the researchers there were developing numerical methods for PDEs, which was new to me but something I really enjoyed,” Bell said. “My Ph.D. thesis was basically about proving a bunch of theorems. Once I finished my Ph.D., I shifted to numerics.”

As Bell’s career has evolved, so has his research focus. His research has always centered around the development and analysis of numerical methods for PDEs that arise in science and engineering.   Within that broad framework, he has made contributions in the areas of finite difference and finite volume methods, numerical methods for low Mach number flows, adaptive mesh refinement, time-stepping algorithms, interface tracking, and parallel computing. He has also worked on the application of these numerical methods to problems in a broad range of fields, including combustion, shock physics, seismology, flow in porous media, and astrophysics.

“For most of my career, I focused on classical numerical methods for modeling physical systems. However, about 15 years ago I became interested in how fluids behave at very small scales. At microscopic scales the behavior of fluids is inherently random,” he said. “Developing models and algorithms for these types of probabilistic systems has opened up new avenues of research.”

Teamwork and Collaborations

John Bell (left) receives the Berkeley Lab Prize—Lifetime Achievement Award from Computational Research Division Director David Brown (right) during Berkeley Lab's 2018 Director's Achievement Awards Ceremony.

This shift is reflected in Bell’s long-running collaborations with multiple colleagues in both mathematics and science applications. His nearly 30-year friendship with physicist Alejandro Garcia, a professor at San Jose State University, is a great example. Much of their research has focused on the intersection of applied math and physics in fluid mechanics, using unconventional math to better understand fluids at the microscopic level.

“Unconventional,” Garcia explained, “in that we use the math of random processes, which up until a few years ago was almost unheard of in computational fluid dynamics.”

He and Bell have always had a good collaboration and synergy, Garcia added. “We play to each other’s strengths. He is extremely hands-on with the programs and coding and all that, but also with the theory and pencil/paper calculations and proofs and derivations. It’s been a good and productive relationship, with quite a few publications and things we are known for that we are very proud of. And we’ve had a lot of fun along the way.”

He credits Bell’s natural curiosity and willingness to dive into something he doesn’t understand with making his research partnerships so successful. There are even stories of algorithms scribbled on napkins that turned out to be central to addressing problems that had previously been unsolvable. “He's Interested in all aspects of the science,” Garcia said.

Another long-time collaborator, Andy Nonaka, joined Berkeley Lab’s Computing Sciences Area as a postdoc in 2007 and now leads the CCSE group, working closely with Bell and Ann Almgren, head of AMCR’s Applied Mathematics Department, alongside application scientists on projects in HPC, modeling, simulation, and applied math for fundamental algorithm development. Nonaka points to Bell’s interactive approach to working with colleagues and collaborators as key to CCSE’s success and longevity.

“Over his career, John has been a world-class researcher in fundamental algorithm development for PDEs, most notably for fluids but now extending to a wider range of applications,” Nonaka said. “He’s also world-class at collaborating with domain scientists and is very happy to work with people who have specific expertise that he can learn from. And he is quick to give credit to others, always acknowledging his collaborators for making things happen.”

To this day, Nonaka said, “we still work together on a long-standing (15+ year) project involving the use of stochastic techniques for nanoscale flows.”

That Bell served as director of the Exascale Computing Project’s (ECP’s) AMReX Co-Design Center since its inception in 2016 is another testament to his long-standing career, Nonaka added. 

Bell says his work with the ECP AMReX Center has been the only opportunity he’s had “to focus on turning what we’ve done on the research side into really usable, ‘professional quality’ software. And to me that is very important because it provides a mechanism for some of the stuff I’ve worked on to continue on after I retire. We believe AMReX is successful enough and has enough users all across the world that it will continue.”

Jonathan Carter, associate laboratory director for Computing Sciences, picked up on this thread: “While I’ve known since joining Berkeley Lab that John is a world-class scientist who boldly moves into new and unexplored application areas, his work with ECP was another aspect to his many contributions – bringing his innovations into a software framework that would enable scientists to use them across the latest generation of high-performance computing platforms.”

The Next Generation

Mentoring junior researchers to build a strong community of mathematicians at Berkeley Lab and beyond has long been important to Bell. Sean Carney, who has a Ph.D. in mathematics from the University of Texas at Austin, worked in CCSE in 2018 and 2019 as a summer intern. He is currently a postdoctoral researcher in the Center for Mathematics and Artificial Intelligence at George Mason University, where he is focusing on solving optimization problems constrained by differential equations. Carney, who will start a faculty position this fall at Union College in Schenectady, NY, says his time in CCSE and his resulting friendship with Bell have had an enormous influence on his career.

“The ability to spend those two summers in Berkeley and the Bay Area was really special. Scientifically, I learned so much about the physics of microscale fluid systems and statistical mechanics that I was previously totally ignorant of. And John liked to talk about the different aspects of the problems we were working on, sometimes likening them to different styles of martial arts. He would stress that to make progress on these problems, you had to be a master of physics, mathematics, and different areas of math that are close to computer science. I learned so much during my time at CCSE about all of these applied and computational math ‘muscles.’ John has also been really generous with his time mentoring me even after I left the Lab. His experience enabled him to give very good advice as I was advancing from a grad student to a postdoc and then to a career in academia.”

For Bell, it’s long been about team science. 

“One of the things I’ve really enjoyed about my laboratory career is the ability to put together a group of people to focus on a project or problem,” he said. “Years ago people who did what I do worked as individual researchers, writing short programs for simple problems that you typed onto punch cards, and fed the cards into a card reader. We’ve come a long way, both in terms of the problems we look at and the computers we use. Working in teams at the Lab has allowed us to build much more sophisticated algorithms and tackle much more complex problems.”

This evolution has, in turn, opened up new avenues of scientific research. “There are so many science areas that I enjoy working in, and because what we do is applicable in a variety of different contexts, I’m able to interact with people from many different disciplines who teach me things about what they know. That’s been a great aspect of my career. Some people really dig in and focus on one thing, but I like to work on a variety of different problems and learn new things. That’s what’s really fun.”

“I’ve known John as a colleague and friend for over 30 years,” said David Brown, senior advisor to Berkeley Lab’s Computing Sciences Area and former director of the Computing Research Division (now the AMCR and Scientific Data Divisions). “His contributions to the field of numerical PDEs have been truly impressive, both because of the high technical quality of his research and because of the measurable impact these contributions have had on many fields of science. One thing that has always impressed me has been his willingness to push the boundaries of his research outside his comfort zone. I think this is one of the reasons he has been so successful in so many scientific areas.”

Looking ahead, Bell—an avid hiker, golfer, scuba diver, and fiction reader, among other things—plans to continue being involved in many ongoing projects at the Lab as a rehired affiliate researcher. “This is what I like to do,” he adds.