## Obituaries: Paul Swarztrauber

**April 14, 2012**

Paul Swarztrauber, 1936-2011

During more than 40 years at the National Center for Atmospheric Research in Boulder, Paul made fundamental contributions to scientific computing in weather and climate research and parallel computing and communications. He provided algorithms, wrote many thousands of lines of useful software, which he shared with everyone, and brought insight into supercomputers as they evolved during these years. He worked with many scientists and researchers, and on many computers, and his software libraries remain in wide use today, more than 20 years after their development. His work shaped future software development and distribution, especially in the area of elliptic partial differential equations.

A career-long member of SIAM, Paul served as a conference organizer, lecturer, Council member, and as an editor for several journals.

Paul was born on November 2, 1936, in Zion, Illinois. He did his undergraduate study at the University of Illinois at Champaign–Urbana, switching his major in his sophomore year from physics to engineering physics. He was excited about the physics classes, but also about the attendant mathematics courses in advanced calculus, ordinary differential equations, and complex variables. In 1958, he enrolled in an elective computing course in the university's newly established computer science department, studying under Lloyd Fosdick and using the ILLIAC computer. After that experience, Paul said, "There was just simply no question as to which direction my career was going to go."

After his graduation in 1959, he spent three years in the U.S. Air Force at Kirtland Air Force Base in New Mexico, attracted by its IBM 704 computing environment. During this time he studied computational mathematics from the best available books, such as Robert Richtmyer's

*Difference Methods for Initial Value Problems*, solidifying choices he would make later.

Following the Bay of Pigs invasion in 1961, Paul's Air Force service was extended by three months. On his discharge in June 1962, he went to work for McAllister and Associates, a small company providing technical services in Albuquerque, moving to a branch office in Denver, Colorado, as part of the company's computer support for Colorado elections. When the service bureau folded in 1962, Paul's supervisor told him of a job opening at the newly created National Center for Atmospheric Research.

Despite an attractive job offer from the RAND Corporation in Santa Monica, California, Paul decided to interview at NCAR. The interview included a rigorous oral exam by the head of computing at NCAR, a mathematician named Glenn Edwin Lewis. Realizing that he would learn a lot working for Lewis, Paul accepted NCAR's offer and began work there in January 1963.

Of his early days at NCAR, Paul recalled: "Well, the big project was weather prediction, but there was a whole bunch of small projects." Virtually everybody was using the computer, he said: balloonists, experimentalists, and solar physicists, for work on aerosols, chemistry, and other topics. "I remember a lot of problems," Paul said. "In fact, that's one thing about atmospheric science. You name it, and there's a computational math application, everything including linear algebra, ordinary differential equations, partial differential equations, and statistics. You encounter just about everything. I remember computing the shape and loading of a high altitude balloon." The first computer he used at NCAR, an IBM 709, was later replaced with a 7090.

As he worked with NCAR scientists, Paul realized that he wanted to pursue an advanced degree---in particular, that he wished to augment his physics background with more mathematics. He enrolled in a PhD program at the University of Colorado, Boulder, in the fall of 1963. To his surprise, he enjoyed the required pure math classes (in later years, he would apply abstract algebra in some of his work). He also took all the applied math courses then available at the university. He considered himself "very, very fortunate" to have Robert Richtmyer as his major professor to guide him in computational mathematics and in physics, a rare combination of knowledge then as perhaps now. As he would do the rest of his life, Paul independently read books on computational mathematics and numerical analysis, because CU did not yet have a computer science department. He received a PhD in mathematics in 1970. His thesis, "A Study of the Time Dependent Free Boundary of an Ideal Fluid," yielded two publications [4,5], neither of which set the tone for his future work.

Paul admitted to being less than satisfied with his thesis: Though his numerical approach had yielded some results on the thesis problem, the basic result was the non-existence of a solution. He said this left him feeling a little bit insecure about his dissertation, and about his future in research. After receiving his PhD, he thus declined an invitation to do full-time research, agreeing to a 25–75 split between research and support; the latter included writing software for scientists. He eventually went into research full-time, but his early devotion to supporting NCAR scientists and the computing environment never left him.

At about this time, Paul recalled,

"A very interesting problem came through the door having to do with computing atmospheric pressure in certain atmospheric circulation models. Any solution method would have very broad application, say to computing electrostatic or magnetic fields. The underlying mathematical problem was the solution to what are called elliptic equations, which are common to all of these areas."

Paul and Roland Sweet, who held a joint appointment at CU and NCAR, were using iterative methods, then considered the methods of choice, in these solvers. One day a colleague brought to their attention a 1970 paper [1] by Golub, Buzbee, and Nielson on the method of cyclic-reduction. "We began looking at these new ‘fast' methods including the Fourier method of Hockney," Paul noted later. "It's also important to mention Oscar Buneman who stabilized cyclic-reduction and made it useful. While looking into these methods it became evident that cyclic-reduction could be generalized to solve a larger class of problems, which resulted in a paper [6] that marked the beginning of my research career." That paper presents a direct method for the discrete solution of separable elliptic equations. Paul, Sweet, and John Adams later incorporated this software into the Fishpack library.

SIAM played a significant role not only in Paul's early work on mathematical algorithms, but throughout his career. He attended SIAM meetings and gave talks on computational mathematics, and was grateful for that community, as well as for the collegial help he received in the form of letters supporting his promotion to the position of senior scientist at NCAR. Computational mathematicians, a driving force within SIAM, were very responsive to his algorithms for solving PDEs, and especially for his implementation of them in Fortran. Nearly 20% of Paul's 67 publications [3] appeared in SIAM journals. In 2005, Paul was interviewed by Thomas Haigh for SIAM's History of Numerical Analysis and Scientific Computing; the quotes herein, unless otherwise noted, are from that interview [2].

Nowhere is Paul's support of the computer environment at NCAR more evident than in his involvement with the acquisition of its first Cray-1 computer. By the mid-70s, Paul had experience with NCAR's CDC 6600 and 7600 computers, and he understood that the NCAR modeling and computing community would benefit greatly from the Cray, which had recently made its debut at Los Alamos. Because the Cray-1 had a relatively large memory and performed well on applications with short vectors, Paul felt that it would suit the NCAR models and applications very well. Paul vigorously recommended acquisition of a Cray-1, and NCAR purchased the Cray-1 Serial 3 in July 1977. It was an immediate success with the NCAR computing staff and scientists, including those from UCAR member universities.

Probably as a result of his interest in solving PDEs, but also from the viewpoint of general consulting on scientific computing problems, he was interested in the fast Fourier transform. "There were codes for the complex fast Fourier transform very early on," Paul noted. "But one of the problems was that if you gave those codes to somebody, they would come back the next day and ask, ‘How do I make use of the results?' So I would sit down. I would go through the process of telling them what they had. This usually amounted to expressing the complex transform in terms of the real trigonometric representation of their data. I did that a number of times, and finally decided to write both a program and documentation for this process." The FFT codes he wrote in the early 70s evolved into the FFTpack library, installed at NCAR in January 1980. The symmetric FFT routines are used primarily for solving elliptic PDEs.

In the late 70s, following the Fishpack and FFTpack libraries, Paul began to develop a library for spherical harmonic transforms. This time, a new goal for the software emerged:

"We wrote the harmonic transform, we vectorized the harmonic transform, and documented the harmonic transform. However there was always something to add. Graduate students and young faculty are constantly building models of geophysical processes, which require other quantities. They needed what are called ‘derived' quantities . . . such as divergence, gradient, or the Laplacian of these fields. So at first these would be provided from my private stock. However, after doing this a few times it was clear that I could save both myself and the user some time if these codes were documented and made available in a package. Eventually, this evolved into a ‘model development facility' that included most of the derived quantities required for models of geophysical processes. Graduate students and young faculty could build a model very efficiently and very rapidly just by incorporating these derived quantities into their program. That, basically, is how Spherepack was built."

John Adams of NCAR and Paul wrote many of the Spherepack routines.

In 1989, Paul's interest in parallel computational algorithms began to expand to algorithms for parallel communication. NCAR had recently acquired a Connection Machine 2, with 8192 processors. Paul, Jim Hack, Dick Sato, and Dave Williamson experimented, running models on the new machine. On hearing about this project, Bob Ward of Oak Ridge asked if he could take part. They began regular meetings, and soon not only ORNL, but also Argonne, Los Alamos, and Pacific Northwest Labs joined in. These labs offered a pool of different massively parallel computers on which performance of an atmospheric model or kernel could be compared. This effort evolved into the DOE Computer Hardware Applied Mathematics and Model Physics project. In Paul's words:

"Now connecting a bunch of floating point processors to increase compute power was what everybody had in mind at that time. This seemed like just a great idea. However, when it came down to it, the speed of those machines was really limited by the much slower speed of the communication channels. Indeed, in practice, communication could occupy over 90 percent of the total compute time. . . . The second thing that was realized, was that for every computation, there is an underlying communication algorithm. . . . There was a third realization. Schedules or algorithms exist that provide a sort of vector ‘like' performance across the processors. . . . Actually, it was this third realization that drove the first two. So I began putting these three observations together and designed the Multipipeline Multiprocessor, which was subsequently patented. The current version is called the Communication Machine."

Of his contributions, Paul considered that computer, described in [7], to have the potential to be the most far reaching.

Paul taught graduate computational mathematics for one year at Florida State University and for one semester at Stanford, and he was an adjoint professor in the Department of Computer Science at the University of Colorado. He often associated with graduating or early-career mathematicians at NCAR, serving as a mentor most recently to Natasha Flyer, Christiane Jablonowski, Bill Spotz, and Mark Taylor. Flyer spoke at Paul's memorial service: "Without a doubt, I would not be at NCAR working in the capacity of mathematician if it were not for Paul. He was very encouraging of my work." Jablonowski remembers him this way: "Paul and I had technical conversations, mostly about Spherepack and spherical harmonics. He was generous with his time, generous with his advice and generous with his ideas. The atmospheric science research community has lost a great personality and scientific leader."

Paul enjoyed his family immensely. He would take any opportunity to tell a humorous story about himself or his family. Often these stories would be about family vacations, and were a real treat to many of us. He loved cars. He owned a vintage VW bug on which he lavished attention, always tinkering to improve its appearance and gas mileage. It was an honor to be invited by Paul for a ride in that pristine, well-tuned machine. He also loved hiking. He estimated that he had hiked Table Mesa 4000 times in his 43 years at NCAR. That hill has an elevation gain of about 400 feet, and he could often be seen in the morning hiking up to work, deep in thought, hands clasped behind his back.

Paul was a quintessential humanitarian, offering encouragement to his colleagues and friends. His expression "Life is good!" still rings in the halls of NCAR and elsewhere, in the memories of those who had the good fortune to know him. He is survived by Suzanne, his wife of 51 years, his daughter, Karleen Swarztrauber, and his son, Ronald Swarztrauber.---

*Richard Valent, University Corporation for Atmospheric Research.*

**References**

[1] B.L. Buzbee, G.H. Golub, and C.W. Nielson,

*On direct methods for solving Poisson's equations*, SIAM J. Numer. Anal., 7 (1970), 627–656.

[2] http://history.siam.org/oralhistories.htm.

[3] http://www.cisl.ucar.edu/css/staff/pauls/papers/pubs.ps.

[4] P.N. Swarztrauber,

*On the numerical solution of the Dirichlet problem for a region of general shape*, SIAM J. Numer. Anal., 9 (1971), 300–306.

[5] P.N. Swarztrauber,

*A numerical model of the unsteady free-boundary of an ideal fluid*, Quart. Appl. Math., 31 (1973), 245–251.

[6] P.N. Swarztrauber,

*A direct method for the discrete solution of separable elliptic equations*, SIAM J. Numer. Anal., 11 (1974), 1136–1150.

[7] P.N. Swarztrauber,

*The communication machine*, Int. J. High Speed Comput., 12 (2004), 65–82.