A Block Version of the SPAI Preconditioner
A Block Version of the SPAI Preconditioner
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发表时间：
1999
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通讯作者：
S. Barnard;M. Grote
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作者：
S. Barnard;M. Grote
我们提出了一个块版本的SPAI算法，并测试其性能在大型非对称矩阵的并行环境。SPAI算法最初由Grote和Huckle [1]提出，计算SParse近似逆，用作稀疏线性方程组迭代解的预条件。它已被证明是一个强大的和通用的预处理在许多应用。由于其固有的并行性，它不suuer从通常的缺点不完全因式分解方法时，在并行环境中使用。事实上，Barnard 8] 9]的SPAI并行实现证明了该算法在各种并行架构上的高性能和出色的缩放行为。Block-SPAI算法在标准测试矩阵上进行评估，这些测试矩阵来自流体动力学的有限元离散化，这些矩阵往往是相对密集和非对称的。它大大减少了计算近似逆所需的时间，同时保持了原始SPAI算法的鲁棒性，完全并行性和优良的缩放特性。
We present a block version of the SPAI algorithm and test its performance on large nonsymmetric matrices in a parallel environment. The SPAI algorithm, initially proposed by Grote and Huckle 1], computes a SParse Approximate Inverse for use as a preconditioner for the iterative solution of a sparse linear system of equations. It has proved to be a robust and versatile preconditioner in numerous applications. Due to its inherent parallelism it does not suuer from the usual drawbacks of incomplete factorization methods when used in a parallel environment. Indeed, the parallel implementation of SPAI by Barnard 8] 9] demonstrated the high performance and excellent scaling behavior of the algorithm across various parallel architectures. The Block-SPAI algorithm is evaluated on standard test matrices which result from nite element discretizations of uid dynamics, which tend to be relatively dense and nonsymmetric. It greatly reduces the time required to compute the approximate inverse, while maintaining the robustness, full parallelism, and excellent scaling property of the original SPAI algorithm.