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Parallel Multiprojection Preconditioned Methods Based on Subspace Compression

机译：基于子空间压缩的并行多投影预处理方法

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摘要

During the last decades, the continuous expansion of supercomputing infrastructures necessitates the design of scalable and robust parallel numerical methods for solving large sparse linear systems. A new approach for the additive projection parallel preconditioned iterative method based on semiaggregation and a subspace compression technique, for general sparse linear systems, is presented. The subspace compression technique utilizes a subdomain adjacency matrix and breadth first search to discover and aggregate subdomains to limit the average size of the local linear systems, resulting in reduced memory requirements. The depth of aggregation is controlled by a user defined parameter. The local coefficient matrices use the aggregates computed during the formation of the subdomain adjacency matrix in order to avoid recomputation and improve performance. Moreover, the rows and columns corresponding to the newly formed aggregates are ordered last to further reduce fill-in during the factorization of the local coefficient matrices. Furthermore, the method is based on nonoverlapping domain decomposition in conjunction with algebraic graph partitioning techniques for separating the subdomains. Finally, the applicability and implementation issues are discussed and numerical results along with comparative results are presented.
机译：在过去的几十年中，超级计算基础设施的不断扩展，需要设计可扩展且健壮的并行数值方法来解决大型稀疏线性系统。针对一般的稀疏线性系统，提出了一种基于半聚合和子空间压缩技术的加法投影并行预处理迭代方法。子空间压缩技术利用子域邻接矩阵和广度优先搜索来发现和聚集子域，以限制局部线性系统的平均大小，从而降低了内存需求。聚合深度由用户定义的参数控制。局部系数矩阵使用在子域邻接矩阵形成期间计算的聚合，以避免重新计算并提高性能。此外，与新形成的集合相对应的行和列最后被排序，以在局部系数矩阵的因式分解期间进一步减少填充。此外，该方法基于非重叠域分解以及用于分离子域的代数图划分技术。最后，讨论了适用性和实施​​问题，并给出了数值结果和比较结果。

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  • 来源
    《Mathematical Problems in Engineering》 |2017年第7期|2580820.1-2580820.11|共11页
  • 作者

    Moutafis Byron E.; Filelis-Papadopoulos Christos K.; Gravvanis George A.;

  • 作者单位

    Democritus Univ Thrace, Dept Elect & Comp Engn, Sch Engn, Univ Campus, GR-67100 Xanthi, Greece;

    Democritus Univ Thrace, Dept Elect & Comp Engn, Sch Engn, Univ Campus, GR-67100 Xanthi, Greece;

    Democritus Univ Thrace, Dept Elect & Comp Engn, Sch Engn, Univ Campus, GR-67100 Xanthi, Greece;

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