3,292 research outputs found
Asynchronous and Multiprecision Linear Solvers - Scalable and Fault-Tolerant Numerics for Energy Efficient High Performance Computing
Asynchronous methods minimize idle times by removing synchronization barriers, and therefore allow the efficient usage of computer systems. The implied high tolerance with respect to communication latencies improves the fault tolerance. As asynchronous methods also enable the usage of the power and energy saving mechanisms provided by the hardware, they are suitable candidates for the highly parallel and heterogeneous hardware platforms that are expected for the near future
GPU-Accelerated Asynchronous Error Correction for Mixed Precision Iterative Refinement
In hardware-aware high performance computing, block-asynchronous iteration and mixed precision iterative refinement are two techniques that may be used to leverage the computing power of SIMD accelerators like GPUs in the iterative solution of linear equation systems. although they use a very different approach for this purpose, they share the basic idea of compensating the convergence properties of an inferior numerical algorithm by a more efficient usage of the provided computing power. In this paper, we analyze the potential of combining both techniques. Therefore, we derive a mixed precision iterative refinement algorithm using a block-asynchronous iteration as an error correction solver, and compare its performance with a pure implementation of a block-asynchronous iteration and an iterative refinement method using double precision for the error correction solver. For matrices from the University of Florida Matrix collection, we report the convergence behaviour and provide the total solver runtime using different GPU architectures
Parallel Tempering Simulation of the three-dimensional Edwards-Anderson Model with Compact Asynchronous Multispin Coding on GPU
Monte Carlo simulations of the Ising model play an important role in the
field of computational statistical physics, and they have revealed many
properties of the model over the past few decades. However, the effect of
frustration due to random disorder, in particular the possible spin glass
phase, remains a crucial but poorly understood problem. One of the obstacles in
the Monte Carlo simulation of random frustrated systems is their long
relaxation time making an efficient parallel implementation on state-of-the-art
computation platforms highly desirable. The Graphics Processing Unit (GPU) is
such a platform that provides an opportunity to significantly enhance the
computational performance and thus gain new insight into this problem. In this
paper, we present optimization and tuning approaches for the CUDA
implementation of the spin glass simulation on GPUs. We discuss the integration
of various design alternatives, such as GPU kernel construction with minimal
communication, memory tiling, and look-up tables. We present a binary data
format, Compact Asynchronous Multispin Coding (CAMSC), which provides an
additional speedup compared with the traditionally used Asynchronous
Multispin Coding (AMSC). Our overall design sustains a performance of 33.5
picoseconds per spin flip attempt for simulating the three-dimensional
Edwards-Anderson model with parallel tempering, which significantly improves
the performance over existing GPU implementations.Comment: 15 pages, 18 figure
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