As a computational mathematician, Rob Falgout of the Center for Applied Scientific Computing (CASC) is a solver of problems. Whether he’s navigating the challenges and hurdles of launching projects like *hypre* and XBraid or considering a lengthy formula on his office whiteboard, Falgout has made a career of finding solutions to some of the Lab’s heaviest headscratchers.

Falgout received his undergraduate degree from Nicholls State University (NSU) in his hometown of Thibodaux, Louisiana. There he was already majoring in mathematics when he decided on a whim to sign up for a computer science elective. While working the window at NSU’s data processing center as a student worker, Falgout eventually decided to pursue a double major. Falgout recalls students handing over their decks of punch cards for him to run through the machine which behaved a bit like a money counter, reading the cards and compiling the program from the lines of code on each card.

“I didn’t really know anything about computing when I started college, but for some reason, I really liked working in FORTRAN77 and writing programs on those punch cards, and it was only a few extra credits to pick up the double major,” recalls Falgout. “So I went for it.”

Falgout would go on to obtain a graduate degree in applied mathematics at the University of Virginia, and now, more than 30 years later, he’s still finding the fun in problem solving as project leader for two of CASC’s most cutting-edge multigrid method computing projects, *hypre *and XBraid. His team is developing codes to address challenges associated with parallelism, or the way supercomputers can run many, many functions at the same time.

“When I came to the Lab in 1991, we were working on a project for simulating groundwater flow by developing a code on what was at the time massively parallel computers with 1000-way parallelism,” said Falgout. “When El Capitan comes online, we will be working with about 1 billion-way parallelism!”

With such a huge jump in parallelism come ever larger and more complex problems to solve. Rob and his team are meeting these new challenges head-on by developing multigrid methods. The *hypre* project started in 1998 to solve large-scale linear systems (that are not time dependent) and is used by many codes at LLNL and around the world. The XBraid parallel-in-time project began more recently and looks to solve time-dependent nonlinear problems.

“Normally, we compute things sequentially in predetermined increments of time,” says Falgout. “Multigrid-in-time methods allow us to solve for many points of time simultaneously, both future and past, getting the solution much faster as a result.”

Falgout says that effective parallel-in-time methods are still being developed for solving some types of equations such as hyperbolic problems where, for example, fluids move rapidly with very little diffusion. Since hyperbolic problems are important in many physics applications, this is a major XBraid research area.

“It’s not yet been adopted by a lot of applications, but it’s on the horizon,” says Falgout about parallel-in-time methods. “We’re trying to solve the problems these applications will face before they even get there.”

Of all the problem solving Falgout has done in his decades with CASC, among the work he is most proud of is the ParFlow groundwater flow project in his early career. The ParFlow code developed by Falgout and his peers was originally designed as a massively parallel tool to aid with contaminant cleanup in the Lab's groundwater, and it is now used by organizations for continental-scale watershed modeling.

“I like to see the things I’ve worked on being used,” says Falgout. “When you do the math, you’re not just solving a problem in one specific area. The algorithms and codes you develop could end up having applications for all kinds of problems you may never have considered.”

As a member of CASC, Falgout has most enjoyed engaging with what he calls “a centralized group of people with a ton of expertise in math and computing.” Falgout also partners with researchers in academia on long-term fundamental research while simultaneously working to support deliverables for programs in-house at the Lab.

“Solving problems, writing code, working with others. I love that about my work with CASC,” says Falgout, who in 2018 was promoted to Distinguished Member of Technical Staff, the Lab’s highest technical job classification level.

Falgout also enjoys the opportunities he has to interact with graduate students (typically) in the Lab’s internship program. For the last few summers, Falgout has mentored four-person teams of undergraduates through a program at UCLA and is excited to do so again this year.

“It’s fun to watch them get excited about applying the math they’ve learned in the classroom to real-world problems at a major scientific institution like LLNL,” says Falgout. “And giving undergraduates the opportunity to work with us provides a great springboard into what could be a career here at the Lab.”

When he’s not scribbling on his office whiteboard in the name of problem solving, he’s trying to unwind with any number of hobbies including playing music, weightlifting, mountain biking, and scuba diving. These days you may find him out on a run simply lounging with one of the many books he reads in a year (48 in 2022!).

*—Amy Weldon*