Celebrating Bjorn Engquist: Pushing Boundaries with Numerical Analysis

Bjorn Engquist says that if you ask a mathematician to categorize Bjorn’s work, she will say that it is applied. Her rationale is that the differential equations he’s studied over the years are used to describe phenomena like seismic wave propagation or the flow of air around an object.

But Engquist, recently elected to the American Academy of Arts and Sciences, says that if you ask an engineer the same question, he will respond that Bjorn’s work is theoretical. Although Engquist has developed mathematics that have found their way into engineering software used by geophysicists, telecommunication experts, and aerospace engineers, he’s not interested in parsing company numbers.

Engquist, director of the ICES Center for Numerical Analysis, straddles the domain of theoretical and applied through his research in numerical analysis. His field searches for methods that can be used to derive quantitative answers for phenomena that mathematics defines as continuous, or infinite.

“It’s a great area if you want to connect with the real world and play with math,” Engquist said.

Engquist’s early research in the 1980s centered on boundary conditions and played an important role in defining the sphere of direct influence of phenomena on an object. That finding has been incorporated into various forms of engineering and mathematical simulation software today. And his current work at ICES is helping to improve multiscale modeling by finding ways to efficiently couple mathematics that govern behavior at various spatial and temporal scales.

Over the years, Engquist has been honored with a multitude of national and international awards honoring his contributions to mathematics and science. Engquist is a member of the Royal Swedish Academy of Sciences, the Royal Swedish Academy of Engineering Sciences, and the Norwegian Academy of Science and Letters. In 2015 alone, he’s been honored with SIAMS’s Pioneer Prize, an award for “long-lasting impacts” in science, engineering, and industry, as well as his recent election to the American Academy of Arts and Sciences.

But his latest honor comes from a more local and personal level. The Institute is dedicating its annual KI-Net conference in multiscale methods to the celebration of Engquist’s 70th birthday.

Engquist’s ICES colleague, Irene Gamba, serves as the principal investigator for Ki-Net, a National Science Foundation-sponsored network with goals in both theoretical and applied areas. The group seeks to develop, analyze, and compute novel kinetic descriptions of quantum dynamics with applications to chemistry; network dynamics with applications to social sciences; and kinetic models of biological processes. KI-Net fosters work between mathematicians and those in other scientific disciplines and is centered around three hubs: ICES, the Center for Scientific Computation & Math Modeling at the University of Maryland, and the Department of Mathematics at the University of Wisconsin-Madison.

“Interdisciplinary work allows you to change between different scientific fields and look at fields all at once,” Engquist said. “But my home is in mathematics.”

His perspective as a mathematician has helped lead to developments that are not only useful to the different applied projects at hand, but to the basic science of applied and computational mathematics.

Looking back on his illustrious career, shows more than 40 of his 70 years have been spent in numerical analysis, counting when Engquist received his Ph.D. on the subject from the University of Uppsala, in Sweden, in 1975. His work has resulted in collaborations with imaging experts, materials engineers, and physicists.

He says his three most well known contributions are likely his work on setting boundary conditions, developing methods that can account for the presence of shock-waves in high velocity flows, and multiscale modeling. With the advent of high-performance computing, he says the scenarios and simulations where they’re applied are becoming more and more precise models of reality.

“The computer has increased numerical analysis’ connection to the real world. Without it we could not have sophisticated models that allow the deeper part of mathematics to be connected to the applied world,” Engquist said.

However, he says his most important research contribution may be in the development of Ph.D. students, with whom he’s been working since the early 1980s, when he joined the faculty of the University of California, Los Angeles. It’s a job he’s continued since arriving at ICES from Princeton in 2004.

“To work with young people and develop the excitement they show is a rewarding thing,” Engquist said.

He is currently working to bring numerical analysis to students beyond his own also as the editor-in-chief of an encyclopedia for applied and computational mechanics to be distributed by Springer Publishing. The encyclopedia, expected to be released by the end of 2015, is planned to appear in a digital format that can be easily updated as the field evolves. In addition, printed books with new editions published every few years, will ensure a solid record of science and provide an unchanging text suitable for citation.

While Engquist is in charge of the encyclopedia, he’s not the only ICES researcher involved. Among them is ICES Director Tinsley J. Oden, who is the field editor of computational mechanics, which gives the encyclopedia its name. Both have created long and successful careers in categories of their own.