ICNSP'98 

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; animation: Akira Kageyama,
National Inst. for Fusion Science, 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 4dimensional analog of a cube. Remembrances of Oscar Buneman by Bruce Langdon This talk was presented by Bruce Langdon for
the special session
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 onedimensional 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 stillfamous 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 particleincell 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
selfconsistent 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 longrange forces dominate. Also, it generalizes well to
multidimensional electromagnetic codes, as Buneman may in fact have been the first to do,
by 1968. Oscar was a convincing advocate of the timereversible
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
noniterative twodimensional 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
multidimensional 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 halfmillion
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 EastBay
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 nearestgridpoint (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 PICtype 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.
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 noniterative poissonsolver, 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. Program General Information Registrants Abstracts Tom Thompson Tel:(310)8259531 Fax(310)8254057 thompson@physics.ucla.edu 
