A Cholesky preconditioned conjugate gradient algorithm on GPU for the 3D parabolic equation
A Cholesky preconditioned conjugate gradient algorithm on GPU for the 3D parabolic equation
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DOI：
10.1504/ijcse.2015.073493
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发表时间：
2015-12
期刊：
影响因子：
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通讯作者：
Jiaquan Gao;Bo Li
中科院分区：
文献类型：
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作者：
Jiaquan Gao;Bo Li
针对三维抛物型方程数值解所导致的大型稀疏线性方程组的求解问题，提出了一种基于GPU MICPCGA的改进的不完全Cholesky MIC预条件子的并行预条件共轭梯度算法.在我们提出的方法中，对于这种情况下，我们克服了MIC预处理器通常难以在GPU上并行化的缺点，由于向前/向后替换，从而提出了一种有效的并行实现方法在GPU GPUFBS上。此外，通过将多个向量操作分组到单个核中来优化向量操作，并且建议使用内积核，并且采用了RIPARSE库中用于稀疏矩阵向量乘法的核。数值结果表明，本文提出的GPUFBS和MICPCGA都能获得显著的加速比，与近似逆SSOR预条件共轭梯度算法SSORPCGA相比，本文提出的MICPCGA不仅获得了更大的加速比，而且在求解三维抛物方程时具有更高的精度.
For solving the large sparse linear systems to which numerical solution of the three-dimensional 3D parabolic equation leads, an efficient parallel preconditioned conjugate gradient algorithm with the modified incomplete Cholesky MIC preconditioner on the GPU MICPCGA is proposed. In our proposed method, for this case, we overcome the drawback that the MIC preconditioner is generally difficult to parallelise on the GPU owing to the forward/backward substitutions, and thus present an efficient parallel implementation method on the GPU GPUFBS. In addition, the vector operations are optimised by grouping several vector operations into a single kernel, and an inner-product kernel is suggested, and a kernel for the sparse matrix-vector multiplication in the CUSPARSE library is adopted. Numerical results show that our proposed GPUFBS and MICPCGA both can achieve a significant speedup, and compared to an approximate inverse SSOR preconditioned conjugate gradient algorithm SSORPCGA, our proposed MICPCGA not only obtains a bigger speedup, but also has higher precision in solving the 3D parabolic equation.