Obituaries: A.R. Mitchell

January 6, 2008

A.R. Mitchell, 1921-2007

Andrew Ronald Mitchell was born in Dundee, Scotland, on June 21, 1921, and died in Dundee on November 22, 2007. Ron, as he was known to almost everyone, was an only child; his father was a blacksmith.

Ron went to Morgan Academy in Dundee and in 1938 won a scholarship through the school to do a mathematics degree in University College, Dundee (then a college of St Andrews University). After graduating with First Class Honours in 1942, he was called up and sent to the wartime Ministry of Aircraft Production in London, where he remained until after the end of the war. His duties included the interrogation of captured Luftwaffe pilots, in an attempt to get information about their aircraft; some years later he met one of the pilots at a conference. Ron had shown great promise as a footballer at school, and while in Dundee had played for Dundee North End Junior Football Club; he continued to play during the war, turning out a few times for Chelsea.

In October 1946, Ron was appointed to an assistant lectureship at St Andrews University and started work on a PhD with D.E. Rutherford. In 1950, Ron received his PhD (with a thesis on relaxation methods in compressible flow) and stayed on at St Andrews as a lecturer. He did some work with Rutherford; in particular, they discovered an early form of successive overrelaxation (before the method appeared in the famous 1954 paper of David Young), although the work was never published. His first PhD student was J.D. Murray, who started in 1953 with research on a topic in boundary layer fluid dynamics. Around this time, Ron developed an interest in numerical analysis, initially as a means of tackling fluid dynamics problems using Southwell's relaxation methods.

Ron continued to play football while at St Andrews, signing on as a part-time professional with a number of Scottish League clubs. During the period from 1946 to 1955, he played with St Johnstone, East Fife, Brechin City, and Berwick Rangers. While with Brechin City, he won a Scottish Qualifying Cup South Runners Up Medal (1949–50) and Scottish Qualifying Cup South Winners Medal (1950–51).

In 1959, Ron married Ann Craig, and took up a one-year post as a senior research fellow in the Mathematics Department at the California Institute of Technology. Jack Lambert, appointed a lecturer at St Andrews in the same year, became Ron's third PhD student, working on numerical methods for ODEs. Other PhD students who worked with Ron at the time were Graeme Fairweather and Sandy Gourlay; important contributions to finite difference methods for PDEs came from work with these students in particular.

A joint paper with Graeme Fairweather, published in Numerische Mathematik in 1964, was the first in a series on high-order alternating-direction finite difference methods for elliptic PDEs. The paper caused surprise in some quarters, in which such higher-order methods were not believed to exist. Not completely reliable, the method came with some loss of accuracy. Ron believed that there was an error in the program, but it turned out that the problem was in the handling of the boundary conditions. An elegant way around the problem, obtained by Ron and Graeme Fairweather in 1966, was published the following year. This paper also described how to deal with problems in L-shaped regions. In earlier joint work, published in 1966, the same authors had used a difference scheme based on the Schwarz alternating procedure; this paper may have been the first to give numerical results obtained with a domain decomposition method.

By 1965, St Andrews was home to a thriving numerical analysis group. Mike Osborne, in Edinburgh, was head of another such group. Believing that there should be more interaction, Ron and Mike Osborne agreed to hold a conference, with St Andrews chosen as the venue, and Ron and Jack Lambert as the main organisers. Of course, no one knew at the time that this would be the first in a biennial series of conferences on numerical analysis, which continued in Dundee, and became the longest-running series of its kind in the world. The 22nd conference in the series was held in Dundee in June 2007.

Around 1965–66, Ron enrolled in evening classes in Dundee to learn Russian. During Graeme Fairweather's thesis work, it had become clear that some Russians, in particular Samarskii, Andreyev, and D'Yakonov, were also working on high-order difference methods for PDEs. Indeed, a method, essentially that of the 1964 Numerische Mathematik paper, had been published in Russian at about the same time, and D'Yakonov had also discovered the loss of accuracy referred to earlier.

Knowledge of Russian not only allowed Ron to keep up with the Russian literature as soon as it appeared, but was invaluable when he attended the International Congress of Mathematicians in Moscow in 1966. There he met D'Yakonov, who, as a result, visited Ron in the late sixties. A by-product was that people in the West became much more aware of the activity in the USSR on split operator techniques. The work with Graeme Fairweather lay somewhere between the classical ADI approach of Douglas, Peaceman, Rachford, and Gunn, and that of D'Yakonov. The former would not handle the loss of accuracy at the boundary, and the latter, although it would, was cumbersome.

In Moscow Ron played football for The Rest of the World against the USSR in a match held in the stadium of Moscow Dynamo. The home team, which had been in training for several weeks, won 5–2.

In 1967, Queen's College Dundee (as University College had been renamed in 1954) separated from St Andrews to become the University of Dundee. Ron's growing reputation and influence were recognised when he was appointed to a newly established Chair of Numerical Analysis. Over the next few years, Ron's leadership and vision built up numerical analysis in Dundee, attracting some excellent staff and students. He obtained Research Council money for a numerical analysis year in 1970–71, as a result of which five conferences were held, and visits for periods up to a year were arranged for about 34 of the world's leading numerical analysts. Indeed, his efforts really put Dundee on the numerical analysis map.

Ron's interests changed in the late 1960s, from finite differences to finite elements. This was virgin territory for numerical analysts, and Ron did much pioneering work during the next few years with others, in-cluding George Phillips, Gene Wachspress, and Bob Barnhill, and with his students Dick Wait, Robin McLeod, and Jim Marshall. This work focussed mainly on the treatment of boundaries---the approximation of curved boundaries and the exact matching of boundary data using blending interpolants.

The next change of direction occurred as a consequence of a lecture given by Olec Zienkiewicz at a conference at Brunel University in 1975. In this talk Zienkiewicz described instabilities experienced by his group in converting their successful finite element codes for structural problems into codes for solving the Navier–Stokes and related equations in fluid dynamics. Finite difference practitioners had known for many years that the instability could be overcome by the use of "upwind differencing," and Ron was immediately intrigued by the question of how such stabilization could be applied to the finite element situation.

On his return to Dundee, he and David Griffiths attacked this problem with some gusto over the next few weeks. The end results were upwind-biased test functions and what is now known as the Petrov–Galerkin finite element method (a term apparently coined in a joint paper by Ron and Bob Anderssen). In the several fruitful years that followed, Ron worked on convection–diffusion problems until, through his interest in diffusion and dispersion effects and his collaboration with Brian Sleeman, he became interested in nonlinear effects in the early 1980s. Some of the problems arose from mathematical biology, but Ron was also interested in solitons, particularly those arising from the Korteweg–de Vries and Schrödinger equations. He was instrumental in bringing the subject of spurious solutions to the fore.

During his research career, Ron always had the uncanny knack of alighting on fundamental issues that, through his many papers and conference talks, drew others to the subject. He has a long and illustrious list of publications, but equally if not more impressive is the list of his 27 PhD students, many of whom have gone on to successful research careers. One of Ron's great strengths was the way he was able to motivate and encourage his students; he had a truly outstanding talent for getting the best out of research students and for instilling self-confidence in them.

Ron's many contributions to numerical analysis, both at a national and an international level, through his books, his conference talks, his visits, his supervision of students and research fellows, his encouragement of young people, are only a part of the story. No attempt to paint a picture of Ron would be complete without mention of his human qualities, the immense personal magnetism, the marvellous sense of humour. He was a wonderful companion, a friendly, warm and entertaining person, who had no airs and graces and who made everyone feel comfortable in his presence. He was able to combine a serious side as far as his work was concerned with the ability to poke fun at people and things, and find humour in just about anything.

His last few years were plagued by ill health. As someone who had been very active, both physically and mentally, it was frustrating for him to experience a diminution of those powers. But he never lost his sense of humour, or his love of football and mathematics. Ron was a major figure in numerical analysis who had a significant impact on the subject. Because of his human qualities, he was also regarded with huge affection by a great many friends and colleagues from all over the world. He will be greatly missed.---Alistair Watson, University of Dundee.

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