Graphics processing unit acceleration of the red/black SOR method

Abstract

SUMMARYThis work presents our strategy, applied optimizations and results in our effort to exploit the computational capabilities of graphics processing units (GPUs) under the CUDA environment in order to solve the Laplacian PDE. The parallelizable red/black successive over-relaxation (SOR) method was used. Additionally, a program for the CPU was developed as a performance reference. Various performance improvements were achieved by using optimization methods, which proved to provide significant speedup. Memory access patterns prove to be a critical factor in efficient program execution on GPUs and it is, therefore, appropriate to follow data reorganization to achieve the highest feasible memory throughput. The same approach exhibits performance benefits on the CPU version, as well. Eventually, a direct comparison of optimal versions' performance was realized. A 10 speedup was measured for the CUDA version on an NVidia GTX480 GPU (NVidia Corp, Sta. Clara, CA, USA), exceeding 142 GB/s bandwidth, over the single threaded CPU version when run on an Intel Core i7 2600K CPU. The results prove that the global memory cache added on recent GPU architectures assist achieving high performance without requiring to employ the special memory types provided by the GPU (i.e. shared, texture or constant memory).

Numerical Solution of BVP on GPU with Application to Path Planning

“…As already stated, the SOR method uses the values from the previous iteration and the values from the current iteration to compute the current point, similarly as the Gauss-Seidel method, see (16.2). The parallel GPU implementation of the SOR method is enabled using the Red-Black ordering [15]. Updated values of the black points, i.e., values of the current iteration, are used to compute the red points.…”

Graphics processing unit computing and exploitation of hardware accelerators

“…In , the authors present GPU and CPU implementations of the red/black successive over‐relaxation method, comparing them for a variety of problem sizes. Five GPU kernels are implemented, tuned, and compared.…”

A GPU performance estimation model based on micro-benchmarks and black-box kernel profiling

“…Other contributions that have been used in this thesis include an implementation of a redblack SOR stencil computation method [44,45] which has been utilized in the experiments and it poses as a proof of concept case study in this thesis. A theoretical performance analysis of the algorithm was provided and the implementations included various kernels, each utilizing a different memory caching approach.…”

“…The method is E. Konstantinidis described in detail in the next chapter (5.1.1) accompanied with a wide range of experimental results. Furthermore, related work has also been published by the author of this thesis [44,45] and can be referred for more information. After running 4 iterations of the computation on the GTX-480, the accumulated metrics were captured with the nvprof tool for all iterations of the red elements' computation as shown in table 4.4.…”

“…One of the first experiments that had been developed in the endeavor on the accomplishment of this thesis was the experimentation and analysis of the red/black SOR stencil computation [44,45]. Specific methods for stencil computations provide large scale of parallelism and can be therefore applied on GPUs.…”