A Tuned and Scalable Fast Multipole Method as a Preeminent Algorithm for Exascale Systems

Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (FMM) appears as a rising star. Our previous recent work showed scaling of an FMM on GPU clusters, with problem sizes in the order of billions of unknowns. That work led to an extremely parallel FMM, scaling to thousands of GPUs or tens of thousands of CPUs. This paper reports on a a campaign of performance tuning and scalability studies using multi-core CPUs, on the Kraken supercomputer. All kernels in the FMM were parallelized using OpenMP, and a test using 10^7 particles randomly distributed in a cube showed 78% efficiency on 8 threads. Tuning of the particle-to-particle kernel using SIMD instructions resulted in 4x speed-up of the overall algorithm on single-core tests with 10^3 - 10^7 particles. Parallel scalability was studied in both strong and weak scaling. The strong scaling test used 10^8 particles and resulted in 93% parallel efficiency on 2048 processes for the non-SIMD code and 54% for the SIMD-optimized code (which was still 2x faster). The weak scaling test used 10^6 particles per process, and resulted in 72% efficiency on 32,768 processes, with the largest calculation taking about 40 seconds to evaluate more than 32 billion unknowns. This work builds up evidence for our view that FMM is poised to play a leading role in exascale computing, and we end the paper with a discussion of the features that make it a particularly favorable algorithm for the emerging heterogeneous and massively parallel architectural landscape

Cross-Disciplinary Analysis of the On-Farm Transition from Conventional to Organic Vegetable Production

This farm-scale analysis of the three-year transition to organic from conventional vegetable production tracked the changes in crop, soil, pest and management on two ranches (40 and 47 ha) in the Salinas Valley, California. Many small plantings of a diverse set of cash crop and cover crop species were used, as compared to only a few species in large monocultures in conventional production. The general trends with time were: increase in soil biological indicators, low soil nitrate pools, adequate crop nutrients, minor disease and weed problems, and sporadic mild insect damage. Some crops and cultivars consistently produced higher yields than others, relative to the maximum yield for a given crop. Differences in insect and disease damage were also observed. These results support the value of initially using a biodiverse set of taxa to reduce risk, then later choosing the best-suited varieties for optimal production. The grower used some principles of organic farming (e.g., crop diversity, crop rotation, and organic matter management), but also relied on substitution-based management, such as fertigation with soluble nutrients, initially heavy applications of organic pesticides, and use of inputs derived from off-farm sources. The organic transition was conducive to both production goals and environmental quality

Computing the k-th Eigenvalue of Symmetric H2H^2-Matrices

The numerical solution of eigenvalue problems is essential in various application areas of scientific and engineering domains. In many problem classes, the practical interest is only a small subset of eigenvalues so it is unnecessary to compute all of the eigenvalues. Notable examples are the electronic structure problems where the $k$-th smallest eigenvalue is closely related to the electronic properties of materials. In this paper, we consider the $k$-th eigenvalue problems of symmetric dense matrices with low-rank off-diagonal blocks. We present a linear time generalized LDL decomposition of $\mathcal{H}^2$ matrices and combine it with the bisection eigenvalue algorithm to compute the $k$-th eigenvalue with controllable accuracy. In addition, if more than one eigenvalue is required, some of the previous computations can be reused to compute the other eigenvalues in parallel. Numerical experiments show that our method is more efficient than the state-of-the-art dense eigenvalue solver in LAPACK/ScaLAPACK and ELPA. Furthermore, tests on electronic state calculations of carbon nanomaterials demonstrate that our method outperforms the existing HSS-based bisection eigenvalue algorithm on 3D problems.Comment: 14 pages, 11 figure

Locking Local Oscillator Phase to the Atomic Phase via Weak Measurement

We propose a new method to reduce the frequency noise of a Local Oscillator (LO) to the level of white phase noise by maintaining (not destroying by projective measurement) the coherence of the ensemble pseudo-spin of atoms over many measurement cycles. This scheme uses weak measurement to monitor the phase in Ramsey method and repeat the cycle without initialization of phase and we call, "atomic phase lock (APL)" in this paper. APL will achieve white phase noise as long as the noise accumulated during dead time and the decoherence are smaller than the measurement noise. A numerical simulation confirms that with APL, Allan deviation is averaged down at a maximum rate that is proportional to the inverse of total measurement time, tau^-1. In contrast, the current atomic clocks that use projection measurement suppress the noise only down to the level of white frequency, in which case Allan deviation scales as tau^-1/2. Faraday rotation is one of the possible ways to realize weak measurement for APL. We evaluate the strength of Faraday rotation with 171Yb+ ions trapped in a linear rf-trap and discuss the performance of APL. The main source of the decoherence is a spontaneous emission induced by the probe beam for Faraday rotation measurement. One can repeat the Faraday rotation measurement until the decoherence become comparable to the SNR of measurement. We estimate this number of cycles to be ~100 cycles for a realistic experimental parameter.Comment: 18 pages, 7 figures, submitted to New Journal of Physic

Leaky Lamb Wave Along VCR Magnetic Tapes

High recording density with the home-use digital VCRs requires the use of narrow tracks, short recording wavelength, and thin magnetic tapes. Knowledge of Young’s modulus of the tape is essential for the precise positioning of the tape on the rotating drums and then a stable tape-to-head interface. The magnetic tapes usually show different Young’s moduli for the machine direction (MD) and the transverse direction (TD) [1]. The anisotropy develops mainly in the base film of polyethylene terephthalate (PET) through the partial crystallization and the crystallite orientation alignment during the stretching process on the tapes [2], while the original PET sheet, from which the tapes are cut, shows much less anisotropy. This situation requires the determination of Young’s moduli for both MD and TD of the tape. The tapes on play are straightened by tensile loads, which should be controlled with Young’s modulus for the MD. Too much load may distort the recorded tracks or damage the tape. Besides, the vertical load is applied onto both edges of the running tape by the guiding rollers. Again, too much load may induce the tape buckling. Critical load is proportional to the Young’s modulus in the TD. Large moduli are desirable for both directions

Ensiling Characteristics of Sudangrass Silage Treated with Green Tea Leaf Waste or Green Tea Polyphenols

Green tea waste (GTW), emitted from beverage companies manufacturing tea drinks, contains high crude protein (CP) and polyphenols. Kondo et al. (2004) showed that GTW addition to forage ensiling enhanced lactic acid fermentation and decreased pH value. Ishihara et al. (2001) showed that high counts of Lactobacillus species were maintained and the counts of clostridia were decreased in the intestinal microflora of animals fed the diet containing green tea polyphenols (GTP). It is hypothesised that GTP might activate lactic acid bacteria and enhance silage fermentation. This study was conducted to evaluate the potential of GTW and GTP as silage additives and explored the mechanisms of enhanced lactic acid fermentation by GTW