Linear algebra operators for GPU implementation of numerical algorithms
Linear algebra operators for GPU implementation of numerical algorithms
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DOI：
10.1145/1201775.882363
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发表时间：
2003-07
期刊：
影响因子：
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通讯作者：
J. Krüger;R. Westermann
中科院分区：
文献类型：
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作者：
J. Krüger;R. Westermann
在这项工作中，重点是在图形芯片上实现数值计算技术的策略的发展。特别是，重点是加速技术解决代数方程组，因为它们发生在数值模拟。我们介绍了一个框架，用于实现线性代数运算符的可编程图形处理器（GPU），从而提供了更复杂的数值算法的设计积木。特别是，我们提出了一个流模型的向量和矩阵的算术运算，利用现代GPU的内在并行性和有效的通信。除了由于改进的数值计算而获得的性能增益之外，图形算法还受益于该模型，因为避免了将计算结果传送到图形处理器以用于显示。我们证明了我们的方法的有效性，通过实施稀疏矩阵的直接求解器，并通过将这些求解器应用到多维有限差分方程，即二维波动方程和不可压缩Navier-Stokes方程。
In this work, the emphasis is on the development of strategies to realize techniques of numerical computing on the graphics chip. In particular, the focus is on the acceleration of techniques for solving sets of algebraic equations as they occur in numerical simulation. We introduce a framework for the implementation of linear algebra operators on programmable graphics processors (GPUs), thus providing the building blocks for the design of more complex numerical algorithms. In particular, we propose a stream model for arithmetic operations on vectors and matrices that exploits the intrinsic parallelism and efficient communication on modern GPUs. Besides performance gains due to improved numerical computations, graphics algorithms benefit from this model in that the transfer of computation results to the graphics processor for display is avoided. We demonstrate the effectiveness of our approach by implementing direct solvers for sparse matrices, and by applying these solvers to multi-dimensional finite difference equations, i.e. the 2D wave equation and the incompressible Navier-Stokes equations.