arXiv subjects

David Keyes

Publications and source records attributed to David Keyes.

43 records · Page 3Linked to original sources

arXiv2014

Towards energy efficiency and maximum computational intensity for stencil algorithms using wavefront diamond temporal blocking

We study the impact of tunable parameters on computational intensity (i.e., inverse code balance) and energy consumption of multicore-optimized wavefront diamond temporal blocking (MWD) applied to different stencil-based update schemes. MWD combines the concepts of diamond tiling and multicore-aware wavefront blocking in order to achieve lower cache size requirements than standard single-core wavefront temporal blocking. We analyze the impact of the cache block size on the theoretical and observed code balance, introduce loop tiling in the leading dimension to widen the range of applicable diamond sizes, and show performance results on a contemporary Intel CPU. The impact of code balance on power dissipation on the CPU and in the DRAM is investigated and shows that DRAM power is a decisive factor for energy consumption, which is strongly influenced by the code balance. Furthermore we show that highest performance does not necessarily lead to lowest energy even if the clock speed is fixed.

cs.PF↗

arXiv2014

Multicore-optimized wavefront diamond blocking for optimizing stencil updates

The importance of stencil-based algorithms in computational science has focused attention on optimized parallel implementations for multilevel cache-based processors. Temporal blocking schemes leverage the large bandwidth and low latency of caches to accelerate stencil updates and approach theoretical peak performance. A key ingredient is the reduction of data traffic across slow data paths, especially the main memory interface. In this work we combine the ideas of multi-core wavefront temporal blocking and diamond tiling to arrive at stencil update schemes that show large reductions in memory pressure compared to existing approaches. The resulting schemes show performance advantages in bandwidth-starved situations, which are exacerbated by the high bytes per lattice update case of variable coefficients. Our thread groups concept provides a controllable trade-off between concurrency and memory usage, shifting the pressure between the memory interface and the CPU. We present performance results on a contemporary Intel processor.

cs.DC↗

arXiv2014

KBLAS: An Optimized Library for Dense Matrix-Vector Multiplication on GPU Accelerators

KBLAS is a new open source high performance library that provides optimized kernels for a subset of Level 2 BLAS functionalities on CUDA-enabled GPUs. Since performance of dense matrix-vector multiplication is hindered by the overhead of memory accesses, a double-buffering optimization technique is employed to overlap data motion with computation. After identifying a proper set of tuning parameters, KBLAS is able to efficiently run on various GPU architectures across different generations, avoiding the time-consuming step of code rewriting, while still being compliant with the standard BLAS API. Another advanced optimization technique allows to ensure coalesced memory access when dealing with submatrices, especially in the context of high level dense linear algebra algorithms. All four precisions KBLAS kernels have been leveraged to multi-GPUs environment, which requires the introduction of new APIs to ease users' experiences on these challenging systems. The KBLAS performance outperforms existing state-of-the-art implementations on all matrix sizes, achieves asymptotically up to 50% and 60% speedup on single GPU and multi-GPUs systems, respectively, and validates our performance model. A subset of KBLAS high performance kernels has been integrated into NVIDIA's standard BLAS implementation (cuBLAS) for larger dissemination, starting version 6.0.

cs.MS↗

arXiv2014

Communication Complexity of the Fast Multipole Method and its Algebraic Variants

A combination of hierarchical tree-like data structures and data access patterns from fast multipole methods and hierarchical low-rank approximation of linear operators from H-matrix methods appears to form an algorithmic path forward for efficient implementation of many linear algebraic operations of scientific computing at the exascale. The combination provides asymptotically optimal computational and communication complexity and applicability to large classes of operators that commonly arise in scientific computing applications. A convergence of the mathematical theories of the fast multipole and H-matrix methods has been underway for over a decade. We recap this mathematical unification and describe implementation aspects of a hybrid of these two compelling hierarchical algorithms on hierarchical distributed-shared memory architectures, which are likely to be the first to reach the exascale. We present a new communication complexity estimate for fast multipole methods on such architectures. We also show how the data structures and access patterns of H-matrices for low-rank operators map onto those of fast multipole, leading to an algebraically generalized form of fast multipole that compromises none of its architecturally ideal properties.

cs.DC↗

arXiv2014

Asynchronous Execution of the Fast Multipole Method Using Charm++

Fast multipole methods (FMM) on distributed mem- ory have traditionally used a bulk-synchronous model of com- municating the local essential tree (LET) and overlapping it with computation of the local data. This could be perceived as an extreme case of data aggregation, where the whole LET is communicated at once. Charm++ allows a much finer control over the granularity of communication, and has a asynchronous execution model that fits well with the structure of our FMM code. Unlike previous work on asynchronous fast N-body methods such as ChaNGa and PEPC, the present work performs a direct comparison against the traditional bulk-synchronous approach and the asynchronous approach using Charm++. Furthermore, the serial performance of our FMM code is over an order of magnitude better than these previous codes, so it is much more challenging to hide the overhead of Charm++.

cs.DC↗

arXiv2014

A Performance Model for the Communication in Fast Multipole Methods on HPC Platforms

Exascale systems are predicted to have approximately one billion cores, assuming Gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the current parallel programing model. Currently, there are many efforts to evaluate the hardware and software bottlenecks of exascale designs. There is therefore an urgent need to model application performance and to understand what changes need to be made to ensure extrapolated scalability. The fast multipole method (FMM) was originally developed for accelerating N-body problems in astrophysics and molecular dynamics, but has recently been extended to a wider range of problems, including preconditioners for sparse linear solvers. It's high arithmetic intensity combined with its linear complexity and asynchronous communication patterns makes it a promising algorithm for exascale systems. In this paper, we discuss the challenges for FMM on current parallel computers and future exascale architectures, with a focus on inter-node communication. We develop a performance model that considers the communication patterns of the FMM, and observe a good match between our model and the actual communication time, when latency, bandwidth, network topology, and multi-core penalties are all taken into account. To our knowledge, this is the first formal characterization of inter-node communication in FMM, which validates the model against actual measurements of communication time.

cs.DC↗

arXiv2008

Linear Augmented Slater-Type Orbital Method for Free Standing Clusters

We have developed a Scalable Linear Augmented Slater-Type Orbital (LASTO) method for electronic-structure calculations on free-standing atomic clusters. As with other linear methods we solve the Schrödinger equation using a mixed basis set consisting of numerical functions inside atom-centered spheres and matched onto tail functions outside. The tail functions are Slater-type orbitals, which are localized, exponentially decaying functions. To solve the Poisson equation between spheres, we use a finite difference method replacing the rapidly varying charge density inside the spheres with a smoothed density with the same multipole moments. We use multigrid techniques on the mesh, which yield the Coulomb potential on the spheres and in turn defines the potential inside via a Dirichlet problem. To solve the linear eigen-problem, we use ScaLAPACK, a well-developed package to solve large eigensystems with dense matrices. We have tested the method on small clusters of palladium.

cond-mat.mtrl-sci↗