Abstract:

We study the use of a GPU for the numerical approximation of the curvature dependent flows of graphs – the mean-curvature flow and the Willmore flow. Both problems are often applied in image processing where fast solvers are required. We approximate these problems using the complementary finite volume method combined with the method of lines. We obtain a system of ordinary differential equations which we solve by the Runge–Kutta–Merson solver. It is a robust solver with an automatic choice of the integration time step. We implement this solver on CPU but also on GPU using the CUDA toolkit.  We demonstrate that the mean-curvature flow can be successfully approximated in single precision arithmetic with the speed-up almost 17 on the Nvidia GeForce GTX 280 card compared to Intel Core 2 Quad CPU. On the same card, we obtain the speed-up 7 in double precision arithmetic which is necessary for the fourth order problem – the Willmore flow of graphs. Both speed-ups were achieved without affecting the accuracy of the approximation. The article is structured in such way that the reader interested only in the implementation of the Runge–Kutta–Merson solver on the GPU can skip the sections containing the mathematical formulation of the problems.

(Oberhuber T., Suzuki A., Žabka V.: “The CUDA implementation of the method of lines for the curvature dependent flows”, Kybernetika 47(2):251–272, 2011. [PDF])

Abstract:

The emergence of Graphics Processing Units (GPUs) as a potential alternative to conventional general-purpose processors has led to significant interest in these architectures by both the academic community and the High Performance Computing (HPC) industry. While GPUs look likely to deliver unparalleled levels of performance, the publication of studies claiming performance improvements in excess of 30,000x are misleading. Significant on-node performance improvements have been demonstrated for code kernels and algorithms amenable to GPU acceleration; studies demonstrating comparable results for full scientific applications requiring multiple-GPU architectures are rare.

In this paper we present an analysis of a port of the NAS LU benchmark to NVIDIA’s Compute Unified Device Architecture (CUDA) – the most stable GPU programming model currently available. Our solution is also extended to multiple nodes and multiple GPU devices.

Runtime performance on several GPUs is presented, ranging from low-end, consumer-grade cards such as the 8400GS to NVIDIA’s flagship Fermi HPC processor found in the recently released C2050. We compare the runtimes of these devices to several processors including those from Intel, AMD and IBM.

In addition to this we utilise a recently developed performance model of LU. With this we predict the runtime performance of LU on large-scale distributed GPU clusters, which are predicted to become commonplace in future high-end HPC architectural solutions.

(S.J. Pennycook, S.D. Harmond, S.A. Jarvis and G.R. Mudalige: “Implementation of the NAS-LU Benchmark”, 1st International Workshop on Performance Modeling, Benchmarking and Simulation of High Performance Computing Systems (PMBS 10), held as part of Supercomputing 2010 (SC’10), New Orleans, LA, USA. [PDF])

Abstract:

Heterogeneous systems, systems with multiple processors tailored for specialized tasks, are challenging programming environments. While it may be possible for domain experts to optimize a high performance application for a very specific and well documented system, it may not perform as well or even function on a different system. Developers who have less experience with either the application domain or the system architecture may devote a significant effort to writing a program that merely functions correctly. We believe that a comprehensive analysis and modeling framework is necessary to ease application development and automate program optimization on heterogeneous platforms.

This paper reports on an empirical evaluation of 25 CUDA applications on four GPUs and three CPUs, leveraging the Ocelot dynamic compiler infrastructure which can execute and instrument the same CUDA applications on either target. Using a combination of instrumentation and statistical analysis, we record 37 different metrics for each application and use them to derive relationships between program behavior and performance on heterogeneous processors. These relationships are then fed into a modeling framework that attempts to predict the performance of similar classes of applications on different processors. Most significantly, this study identifies several non-intuitive relationships between program characteristics and demonstrates that it is possible to accurately model CUDA kernel performance using only metrics that are available before a kernel is executed.

(Andrew Kerr, Gregory Diamos and Sudakhar Yalamanchili: “Modeling GPU-CPU Workloads and Systems”. Proceedings of the Third Workshop on General-Purpose Computation on Graphics Processing Units (GPGPU-3), Pittsburgh, PA. Apr. 2010. PDF Link.)