We leverage CUDA dynamic parallelism to reduce execution time while significantly reducing energy consumption of the Conjugate Gradient (CG) method for the iterative solution of sparse linear systems on graphics processing units (GPUs). Our new implementation of this solver is launched from the CPU in the form of a single "parent" CUDA kernel, which invokes other "child" CUDA kernels. The CPU can then continue with other work while the execution of the solver proceeds asynchronously on the GPU, or block until the execution is completed. Our experiments on a server equipped with an Intel Core i7-3770K CPU and an NVIDIA "Kepler" K20c GPU illustrate the benefits of the new CG solver.

We introduce a systematic analysis in order to fuse CUDA kernels arising in efficient iterative methods for the solution of sparse linear systems. Our procedure characterizes the input and output vectors of these methods, combining this information together with a dependency analysis, in order to decide which kernels to merge. The experiments on a recent NVIDIA "Kepler" GPU report significant gains, especially in energy consumption, for the fused implementations derived from the application of the methodology to three of the most popular Krylov subspace solvers with/without preconditioning.

SummaryIn this paper, we analyze the interactions occurring in the triangle performance‐power‐energy for the execution of a pivotal numerical algorithm, the iterative conjugate gradient (CG) method, on a diverse collection of parallel multithreaded architectures. This analysis is especially timely in a decade where the power wall has arisen as a major obstacle to build faster processors. Moreover, the CG method has recently been proposed as a complement to the LINPACK benchmark, as this iterative method is argued to be more archetypical of the performance of today's scientific and engineering applications. To gain insights about the benefits of hands‐on optimizations we include runtime and energy efficiency results for both out‐of‐the‐box usage relying exclusively on compiler optimizations, and implementations manually optimized for target architectures, that range from general‐purpose and digital signal multicore processors to manycore graphics processing units, all representative of current multithreaded systems. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper we investigate the performance-energy balance of a variety of concurrent architectures, from general-purpose and digital signal multicore systems to graphics processors (GPUs), representative of current technology. This analysis employs the conjugate gradient method, an important algorithm for the iterative solution of linear systems that is basically composed of the sparse matrix-vector product and other (minor) vector kernels. To allow a fair comparison, we leverage simple implementations of the numerical methods and underlying kernels, and rely only on those optimizations applied by the target compiler.

In this paper we introduce a redesign of the conjugate gradient method for the iterative solution of sparse linear systems on heterogeneous systems accelerated by graphics processing units (GPUs). Reshaping the GPU kernels induced by the classical formulation of the CG method into algorithm-specific routines results in a slight increase of performance and, more importantly, enables the efficient exploitation of power-saving techniques implicit in the hardware, like the processor C-states, that produce remarkable energy savings. Numerical experiments using data matrices from a popular sparse matrix collection show that the time overhead naturally associated with the application of these energy-aware techniques is no longer crucial to the overall runtime performance.