The first "Oscar Buneman" awards were presented for the most insightful visualization, with one prize in the still category and one in the animation category. The winners were:

still:          Takaya Hayashi, National Inst. for Fusion Science, Japan;
runner-up: Hideaki Miura, National Inst. for Fusion Science, Japan.

animation: Akira Kageyama, National Inst. for Fusion Science, Japan;
runner-up: Katsunoba Nishihara, Osaka Univ., Japan.

The award is a transparent plastic cube within which can be seen a second, smaller cube (due to internal reflection from the slightly coated walls).  This was chosen because Oscar used to carry a tesseract to illustrate the concept of a hypercube - the 4-dimensional analog of a cube.

oscar3m1.jpg (13732 bytes)

Remembrances of Oscar Buneman

by Bruce Langdon

This talk was presented by Bruce Langdon for the special session
organized by Bob Barker at the 1993 IEEE plasma meeting.

I'm glad that the organizers of this meeting kept this session Oscar's, as best we can keep it his.

With such an interesting and charming person as Oscar Buneman, it's hard to choose where to start. Of many thoughts, the one I'll choose is that Oscar made this field fun for us, through his enthusiasm, his ingenious and elegant numerical methods, and his physical insights.

Let's go way back to 1965. A fellow student showed me Hockney's JACM paper on fast direct Poisson solution and its application to plasma simulation. At that time I had been introduced to one-dimensional simulations in courses by John Dawson and Tom Stix. In particular, I knew of Buneman's theoretical and simulation results on collisionless dissipation of currents, his still-famous 1959 Physical Review paper. The mechanism is often called the Buneman instability, and is a pioneering example of anomalous resistivity or absorption, called anomalous because it doesn't depend on collisions.

The simulation work I knew about then used moving sheets of charge; you kept track of the spatial ordering of the sheets during the time integration, it was slow, and it didn't generalize to more than one dimension. Hockney's paper introduced me to the Stanford group's work with gridded methods, what many of us now generically call particle-in-cell methods, or PIC (not to be confused with Harlow's fluid PIC).

They had used a combination of cyclic reduction and something very close to Fast Fourier transforms to solve Poisson's equation quickly, to machine accuracy. This was a landmark. Equally important was Stanford's use of the mesh for the self-consistent electric field, and the time integration of the particles using that mesh field without explicit regard for nearby particles. This approach became prevalent for most applications in which long-range forces dominate. Also, it generalizes well to multi-dimensional electromagnetic codes, as Buneman may in fact have been the first to do, by 1968.

Oscar was a convincing advocate of the time-reversible integration schemes used at Stanford. Here, I won't take time to discuss the technical and aesthetic issues. Suffice it to say that these have been the usual algorithms of choice for 20 years, hard to improve on for many practical applications.

At the second conference on Numerical Simulation of Plasmas, in 1968, Oscar handed out small packets of punched cards carrying his new invention, a fast non-iterative two-dimensional Poisson solver that used cyclic reduction in both directions. Oscar called it 'fast' and 'compact', and it certainly was both. As I recall, his program was less than a page long, uncommented, and even more terse and mysterious than a fast Fourier transform program when you don't know the principle behind it. His multi-dimensional cyclic reduction has been heavily used. It was a real breakthrough, and illustrates Oscar's abilities and his habits: compact in realization, yet others hadn't thought of it, and Oscar seems never to have published it himself. It was left to others, such as Buzbee, Golub and Nielson, to publish papers explaining the algorithm, and why Oscar's form of it didn't suffer from the limitations of computer arithmetic.

Still at that meeting, on the bus one day, Oscar told me about his ideas for a multidimensional electromagnetic code in which the conservation laws of electromagnetism had algebraically exact analogues in the computer code. This included Gauss' law, which required a method to form a mesh current that preserved charge continuity. Oscar returned to this topic in recent years, and published an improved form last year with Villasenor.

In the 1970's, Oscar and his colleagues took on the task of pioneering 3D electromagnetic codes. Their code used fast Fourier transforms for the fields, which let them implement Oscar's new ideas on spatial accuracy. They wrote their code for the supercomputers of the day, like the CDC 7600 that had only a half-million words of memory, and the Cray 1 that had only a million words. In order to make interesting applications, they made the most of these machines. There's a 1980 paper in the Journal of Computational Physics that describes measures they took, like dividing up the spatial domain to process a piece at a time, as people do today with distributed memory parallel computers.

Oscar contributed so much to methods and applications of elliptic equation solvers and fast Fourier transforms, yet I think he may have preferred codes that didn't use those at all, but instead relied on the hyperbolic Maxwell's equations to propagate the correct field information at the speed of light as nature does, instead of instantaneously via elliptic equations or Fourier transforms. The TRISTAN code, used in much of his recent work, is of that type.

While I was at Berkeley with Ned Birdsall, the East-Bay simulation people and the Stanford group got together regularly. Later I saw Oscar mostly at meetings. Often he would tell me how to get a helicopter or small plane ride as part of the trip. Around 1971, coming back from somewhere, I was telling him about B splines for plasma simulation. The Stanford people in the 1960's used nearest-grid-point (NGP) weighting, which is fast but a bit bumpy. Other people like us used linear or bilinear weighting. That didn't seem to interest Oscar much. But splines, which leapfrog past bilinear in a hierarchy of accuracy, did catch his interest. Next I knew, Oscar had worked out many analytic results about using splines in PIC-type applications, and was using them in some codes.

There are other perspectives and historical information about Oscar in the recent SIMPO newsletter from Japan.

I can see Oscar clearly in my mind, smiling and listening or talking enthusiastically, or swimming laps in the hotel pool, or charging up a trail. There are many reminders of him; his ideas appear in so many places in my codes and writings. Oscar was a key figure for me from my beginnings in the field, and he still is.

Thank you.

References by Oscar mentioned in the above

O. Buneman, Dissipation of currents in ionized media, Phys. Rev. 115, 503 (1959).

O. Buneman, Time reversible difference procedures, J. Comput. Phys. 1, 517 (1967).

O. Buneman, A compact non-iterative poisson-solver, SUIPR report 294, Stanford University (1969).

O. Buneman, Fast numerical procedures for computer experiments on relativistic plasmas, in "Relativistic Plasmas (The Coral Gables Conference)", O. Buneman and W. Pardo editors (Benjamin, NY, 1968).

O. Buneman, Subgrid resolution of flow and force fields, J. Comput. Phys. 11, 250 (1973).

O. Buneman et al, Principles and capabilities of 3d EM particle simulations, J. Comput. Phys. 38, 1 (1980).

SIMPO Newsletter, STEP Simulation Promotion Office, H. Matsumoto, editor, Kyoto, Vol. 2, March 1993.

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