No Arabic abstract
Like time complexity models that have significantly contributed to the analysis and development of fast algorithms, energy complexity models for parallel algorithms are desired as crucial means to develop energy efficient algorithms for ubiquitous multicore platforms. Ideal energy complexity models should be validated on real multicore platforms and applicable to a wide range of parallel algorithms. However, existing energy complexity models for parallel algorithms are either theoretical without model validation or algorithm-specific without ability to analyze energy complexity for a wide-range of parallel algorithms. This paper presents a new general validated energy complexity model for parallel (multithreaded) algorithms. The new model abstracts away possible multicore platforms by their static and dynamic energy of computational operations and data access, and derives the energy complexity of a given algorithm from its work, span and I/O complexity. The new model is validated by different sparse matrix vector multiplication (SpMV) algorithms and dense matrix multiplication (matmul) algorithms running on high performance computing (HPC) platforms (e.g., Intel Xeon and Xeon Phi). The new energy complexity model is able to characterize and compare the energy consumption of SpMV and matmul kernels according to three aspects: different algorithms, different input matrix types and different platforms. The prediction of the new model regarding which algorithm consumes more energy with different inputs on different platforms, is confirmed by the experimental results. In order to improve the usability and accuracy of the new model for a wide range of platforms, the platform parameters of ICE model are provided for eleven platforms including HPC, accelerator and embedded platforms.
We show how to quantify scalability with the Universal Scalability Law (USL) by applying it to performance measurements of memcached, J2EE, and Weblogic on multi-core platforms. Since commercial multicores are essentially black-boxes, the accessible performance gains are primarily available at the application level. We also demonstrate how our methodology can identify the most significant performance tuning opportunities to optimize application scalability, as well as providing an easy means for exploring other aspects of the multi-core system design space.
A parallel and nested version of a frequency filtering preconditioner is proposed for linear systems corresponding to diffusion equation on a structured grid. The proposed preconditioner is found to be robust with respect to jumps in the diffusion coefficients. The storage requirement for the preconditioner is O(N),where N is number of rows of matrix, hence, a fairly large problem of size more than 42 million unknowns has been solved on a quad core machine with 64GB RAM. The parallelism is achieved using twisted factorization and SIMD operations. The preconditioner achieves a speedup of 3.3 times on a quad core processor clocked at 4.2 GHz, and compared to a well known algebraic multigrid method, it is significantly faster in both setup and solve times for diffusion equations with jumps.
In this paper, we use multithreaded fast Fourier transforms provided in three highly optimized packages, FFTW-2.1.5, FFTW-3.3.7, and Intel MKL FFT, to present a novel model-based parallel computing technique as a very effective and portable method for optimization of scientific multithreaded routines for performance, especially in the current multicore era where the processors have abundant number of cores. We propose two optimization methods, PFFT-FPM and PFFT-FPM-PAD, based on this technique. They compute 2D-DFT of a complex signal matrix of size NxN using p abstract processors. Both algorithms take as inputs, discrete 3D functions of performance against problem size of the processors and output the transformed signal matrix. Based on our experiments on a modern Intel Haswell multicore server consisting of 36 physical cores, the average and maximum speedups observed for PFFT-FPM using FFTW-3.3.7 are 1.9x and 6.8x respectively and the average and maximum speedups observed using Intel MKL FFT are 1.3x and 2x respectively. The average and maximum speedups observed for PFFT-FPM-PAD using FFTW-3.3.7 are 2x and 9.4x respectively and the average and maximum speedups observed using Intel MKL FFT are 1.4x and 5.9x respectively.
Fine particle suspensions (such as cornstarch mixed with water) exhibit dramatic changes in viscosity when sheared, producing fascinating behaviors that captivate children and rheologists alike. Recent examination of these mixtures in simple flow geometries suggests inter-granular repulsion is central to this effect --- for mixtures at rest or shearing slowly, repulsion prevents frictional contacts from forming between particles, whereas, when sheared more forcefully, granular stresses overcome the repulsion allowing particles to interact frictionally and form microscopic structures that resist flow. Previous constitutive studies of these mixtures have focused on particular cases, typically limited to two-dimensional, steady, simple shearing flows. In this work, we introduce a predictive and general, three-dimensional continuum model for this material, using mixture theory to couple the fluid and particle phases. Playing a central role in the model, we introduce a micro-structural state variable, whose evolution is deduced from small-scale physical arguments and checked with existing data. Our space- and time-dependent model is implemented numerically in a variety of unsteady, non-uniform flow configurations where it is shown to accurately capture a variety of key behaviors: (i) the continuous shear thickening (CST) and discontinuous shear thickening (DST) behavior observed in steady flows, (ii) the time-dependent propagation of `shear jamming fronts, (iii) the time-dependent propagation of `impact activated jamming fronts, and (iv) the non-Newtonian, `running on oobleck effect wherein fast locomotors stay afloat while slow ones sink.
This deliverable reports our early energy models for data structures and algorithms based on both micro-benchmarks and concurrent algorithms. It reports the early results of Task 2.1 on investigating and modeling the trade-off between energy and performance in concurrent data structures and algorithms, which forms the basis for the whole work package 2 (WP2). The work has been conducted on the two main EXCESS platforms: (1) Intel platform with recent Intel multi-core CPUs and (2) Movidius embedded platform.