Boundary Values

April 25, 2006

Talk of the Society
James Crowley

Attending the recent SIAM Conference on Parallel Processing (San Francisco, February 2224), I was struck anew by how many of SIAM's activities are interdisciplinary. SIAM is often referred to as a "math society" (it's in our name, after all), but the real picture is far more complicated and interesting. SIAM often operates on boundaries between disciplines, which can raise some difficult issues as cultural differences emerge.

Parallel processing is a case in point. The SIAM Conference on Parallel Processing for Scientific Computing, sponsored by the SIAM Activity Group on Supercomputing, has been held every other year (with a single missed year) since 1983. The focus has shifted somewhat over the years and may have sharpened recently with the advent of a related biennial conference: the SIAM Conference on Computational Science and Engineering.

Whereas both the CS&E and the parallel processing conferences focus on computational methods to solve problems in science and engineering, parallel processing has also extended to include sessions on platforms, environments, and tools as they affect scientific computing. This is not to discount the significant place of computational methods in the parallel processing programs, but rather to emphasize the simultaneous attention to areas more closely associated with computer science---topics like MPI, compilers, benchmarking, and aspects of hardware that affect algorithm design. The programs include discussions of new and emerging machines and their use as well.

The 2006 parallel processing conference, with an organizing committee co-chaired by Charbel Farhat of Stanford University and William Gropp of Argonne National Lab, straddled the interface where applied mathematics and numerical methods meet computer science. Such a mix can lead to interesting contrasts in expectations.

An example of a talk at the numerical methods/hardware interface---with the emphasis on the numerical methods side---is Barry Smith's invited address on sparse matrix methods. This sounds like a topic for a traditional numerical analysis talk, on solvers for matrix systems arising in PDE approximations, but in this case the motivation came from the hardware side: the oft-cited memory bandwidth bottleneck. In certain circumstances, the efficiency of Newton/multigrid methods is very low (about 10%) because of limited memory bandwidth; much of the CPU time is spent in the wait for delivery of the sparse matrix entries. Smith's proposed solution is to look back to some older classes of algorithms, such as the full approximation scheme developed by Achi Brandt. This is an interesting illustration of the observation that minimizing the number of FLOPs, depending on the computer architecture, does not always lead to the fastest solution.

Another speaker whose talk fell at the boundary of numerical methods and computer environments is Katherine Yelick, who discussed partitioned global address space languages. Considering some novel alternatives to message passing (MPI) for certain computational problems, such as adaptive mesh refinement for an elliptic solver, she argued that such languages can provide improvements in performance as well as programmer productivity.

A mix of modeling and computing, hardware and numerics, emerged in several sessions on new, high-end, massively parallel computing platforms. There has been an upsurge in interest in high-end computing, as evidenced by these talks, as well as by the promise of additional resources for the area in the U.S. research budget for fiscal year 2007.

Several minisymposia and an invited talk considered new computing platforms, along with results of computational simulations on challenging problems. Nearly all high-end systems---those found at or near the top of the most recent Top500 list---were represented. One talk, for example, covered "the unprecedented levels of performance achieved on BlueGene/L," the IBM machine developed in partnership with DOE's Advanced Simulation and Computing Program; the speaker presented results for challenging applications like molecular dynamics. The Cray XT3 at Oak Ridge National Lab was the focus of another talk, with benchmark as well as performance results in such application areas as climate and fusion.

Joining these talks on the program were applications sessions of the type people have come to expect at SIAM conferences: cell modeling, ab initio simulations of electrons in a field, processing of massive amounts of genomic data, and multiphysics models that capture physical phenomena with increasing accuracy---to name a few examples.


Simulation-Based Engineering Science (SBES), a new report commissioned by the National Science Foundation, makes a strong case for the value of multidisciplinary research, especially that between the engineering disciplines and computational simulation. It complements other recent reports, such as the SCaLeS report (commissioned by the Department of Energy), that have begun to develop a framework for computational science and engineering. SBES, prepared from an engineering perspective, calls for changes in the ways in which engineering research is conducted and engineers are educated.

J. Tinsley Oden chaired the blue-ribbon panel assembled by NSF to produce the report, which is now available at Other members of the panel are Ted Belytschko, Jacob Fish, Thomas J.R. Hughes, Chris Johnson, David Keyes, Alan Laub, Linda Petzold, David Srolovitz, and Sidney Yip.

The report presents findings and recommendations for advancing SBES as a discipline within engineering. It discusses applications of computational simulation in a variety of areas, including medicine, national security, the environment, materials, and industry and defense. It also describes research opportunities in, for example, multiscale modeling and simulation, verification and validation, uncertainty quantification, and data-driven simulations.

The panel made four major recommendations. The first is that NSF change its organizational structure to support SBES activities. The second is a call for a major (six-fold) funding increase over the 2005 baseline for SBES-related disciplines. The third calls for a program in high-risk long-term research "to exploit the considerable promise of SBES."

The fourth and final recommendation would bring about sweeping changes in the educational system to recognize the multidisciplinary nature of modern engineering research and "to help students acquire the necessary modeling and simulation skills."

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This brings me back to the cultural differences mentioned earlier. One interesting aspect of the business meetings (usually a misnomer!) held at some of our activity group conferences is the chance to hear the views of people from the various disciplines represented at the meeting. At the parallel processing conference, for example, ideas expressed by people associated with computer science departments were in interesting juxtaposition with those of people from (applied) mathematics departments. The cultural differences reflected by the comments were sometimes striking, and serve to point up difficulties with multidisciplinary research.

In the case of parallel processing, and other SIAM groups as well, the different traditions and expectations of researchers from math and computer science, especially in the area of conferences, can leave SIAM facing some difficult choices. Two areas in which attitudes differ significantly are poster presentations and proceedings.

Computer scientists have come to rely on conference proceedings for dissemination of research results, and CS departments consequently consider an individual's publications in such volumes when making tenure and promotion decisions. Math departments do not tend to put such a high value on proceedings. The two groups therefore have quite different needs when it comes to proceedings---one counts on them, the other may not even want them.

This particular difference was the subject of an interesting exchange at the parallel processing business meeting, one that had no final resolution. SIAM, with a membership in which both disciplines are well represented, publishes proceedings of activity group conferences if the organizing committee so recommends and if the papers are selected in advance of the meeting.

Another thought from the business meeting relates SIAM's multidisciplinary activities to a very important group: students. Several people at the meeting asked whether SIAM student chapters could be formed in computer science departments. It's an interesting question. Most of our student chapters originate in math/applied math departments, but this is not a requirement; in fact, the variety of departments represented in SIAM chapters is probably very close to that of the regular membership. SIAM student chapters are intended for students in all departments, regardless of where the chapter is based.

Collaborations between applied mathematicians, researchers in numerical methods, and scientists in application domains like physics and biology are now common. Many would say that much of the most exciting research now occurs at such boundaries. SIAM is dedicated to the idea of multidisciplinary research and welcomes readers' suggestions for addressing the difficult issues that can arise.

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