William J. Camp

Massively parallel methods for engineering and science problems

Scientific research and engineering development are relying increasingly on computational simulation to augment theoretical analysis, experimentation, and testing. Many of todays problems are far too complex to yield to mathematical analyses. Likewise, large-scale experimental testing is often infeasible for a variety of economic, political, or environmental reasons. At the very least, testing adds to the time and expense of product development

Architectural specification for massively parallel computers: an experience and measurement‐based approach

In this paper, we describe the hardware and software architecture of the Red Storm system developed at Sandia National Laboratories. We discuss the evolution of this architecture and provide reasons for the different choices that have been made. We contrast our approach of leveraging high‐volume, mass‐market commodity processors to that taken for the Earth Simulator. We present a comparison of benchmarks and application performance that support our approach. We also project the performance of Red Storm and the Earth Simulator. This projection indicates that the Red Storm architecture is a much more cost‐effective approach to massively parallel computing. Published in 2005 by John Wiley & Sons, Ltd.

Creating science-driven computer architecture: A new patch to scientific leadership

We believe that it is critical for the future of high end computing in the United States to bring into existence a new class of computational capability that is optimal for science. In recent years scientific computing has increasingly become dependent on hardware that is designed and optimized for commercial applications. Science in this country has greatly benefited from the improvements in computers that derive from advances in microprocessors following Moores Law, and a strategy of relying on machines optimized primarily for business applications. However within the last several years, in part because of the challenge presented by the appearance of the Japanese Earth Simulator, the sense has been growing in the scientific community that a new strategy is needed. A more aggressive strategy than reliance only on market forces driven by business applications is necessary in order to achieve a better alignment between the needs of scientific computing and the platforms available. The United States should undertake a program that will result in scientific computing capability that durably returns the advantage to American science, because doing so is crucial to the countrys future. Such a strategy must also be sustainable. New classes of computer designs will not only revolutionize the power of supercomputing for science, but will also affect scientific computing at all scales. What is called for is the opening of a new frontier of scientific capability that will ensure that American science is greatly enabled in its pursuit of research in critical areas such as nanoscience, climate prediction, combustion, modeling in the life sciences, and fusion energy, as well as in meeting essential needs for national security. In this white paper we propose a strategy for accomplishing this mission, pursuing different directions of hardware development and deployment, and establishing a highly capable networking and grid infrastructure connecting these platforms to the broad research community.

The Red Storm Architecture and Early Experiences with Multi-Core Processors

The Red Storm architecture, which was conceived by Sandia National Laboratories and implemented by Cray, Inc., has become the basis for most successful line of commercial supercomputers in history. The success of the Red Storm architecture is due largely to the ability to effectively and efficiently solve a wide range of science and engineering problems. The Cray XT series of machines that embody the Red Storm architecture have allowed for unprecedented scaling and performance of parallel applications spanning many areas of scientific computing. This paper describes the fundamental characteristics of the architecture and its implementation that have enabled this success, even through successive generations of hardware and software.

Confluent corrections to scaling in the isotropic Heisenberg model

Confluent corrections to scaling are explicitly incorporated in the analysis of high-temperature series for the S=1/2 (quantum-mechanical) and S= infinity (classical) isotropic Heisenberg models on the FCC lattice. For S= infinity , strong confluent corrections are found in the susceptibility, the second moment of the correlation function, as well as the anisotropy crossover function. No evidence for confluent, non-analytic corrections to scaling is found in the analysis of the S=1/2 susceptibility. The best value for the S= infinity susceptibility exponent is gamma ( infinity )=1.42-0.01+0.02, which-taken with the best previous estimate gamma (1/2)=1.43-is consistent with universality. However, for S=1/2, it is felt that (because of apparent non-confluent singularities) gamma is known no better than gamma (1/2) approximately=1.41-1.51. The S= infinity correlation-length exponent is estimated to be nu =0.725+or-0.015, and the crossover exponent is estimated to be phi =1.30+or-0.03. Finally, the S= infinity correction-to-scaling exponent is found to be Delta 1=0.54+or-0.10.

High‐temperature series studies of Ising‐like Wilson models in three dimensions

We have studied the susceptibility of continuous‐spin Landau‐Wilson models on the FCC lattice using exact series expansions through 10‐th order in the inverse temperature. Both order‐disorder (double‐well) and displacive (single‐well) models have been considered. The exponent γ of the dominant singularity is found to be 1.25 for both types of model. The confluent singularity arising from corrections to scaling is found to have the universal value δ=0.5. We discuss in detail the crossover from Gaussian to Ising constant, and find a crossover exponent o/=1 in all dimensions.

Series studies of critical exponents in continuous dimensions

Using results we have previously derived for the high‐temperature susceptibility expansion of classical models as a closed‐form function of lattice dimension, we study the dimensional dependence of the critical exponent γ and critical temperature, as well as the correction‐to‐scaling exponent Δ1, for Ising‐like (n=1) models. The numerical results are obtained by extrapolation of 10‐th order series on loose‐packed hypercubical lattices, and 8‐th order series on close‐packed hypertriangular lattices. The critical exponent γ increases monotonically with decreasing dimension, d, for d<4, and apparently tends to infinity at d=1; while the critical temperature decreases monotonically and smoothly to zero at d=1. Detailed contact is made with the e‐expansion estimates for critical exponents obtained in the context of renormalization group theory.

High Temperature Series, Universality And Scaling Corrections+

The evidence for universality of critical behavior is reviewed from a series expansion viewpoint. The necessity of incorporating non-analytic corrections to dominant scaling-theory singularities is pointed out, and the outlook for the verification of hyperscaling is discussed.

High‐Temperature Expansions for Classical Systems

We have derived series in powers of K to 8‐th order for the two‐point function, susceptibility and free energy of the model Hamiltonian, ΣR⇒ {W[Q(R⇒)] + K/2 Σδ⇒ Q(R⇒)·Q(R⇒+δ⇒)}, where Q is a real tensor, and W is an arbitrary, even function of Q. Special cases include the spin‐S Ising model and the classical Heisenberg model, for both of which W = 0. Additional applications include models for structural phase transitions, tricritical points, He3‐He4 mixtures, liquid crystals, and the class of models employed in renormalization — group studies of critical phenomena. Detailed evaluation of susceptibility series have been carried out on the standard 2, 3, and 4‐dimensional lattices. The series for the scalar case on the triangular net is presented herein.