论文标题
pargemslr：平行的多级Schur补充低级预处理和用于一般稀疏矩阵的解决方案套件
parGeMSLR: A Parallel Multilevel Schur Complement Low-Rank Preconditioning and Solution Package for General Sparse Matrices
论文作者
论文摘要
本文讨论了Pargemslr，这是一个C ++/MPI软件库，用于通过分布式内存计算环境中的预处理的Krylov子空间方法来解决线性代数方程的稀疏系统。 pargemslr中实现的预处理基于代数域的分解，并通过P-way顶点分离器将对称的邻接图递归地分配到几个非重叠的分区中，其中P是MPI过程总数的整数。从数值角度来看，Pargemslr构建了Schur补体近似反向预处理，作为接口耦合矩阵矩阵矩阵之间的总和与低级别校正项之间的总和。为了降低与近似矩阵的计算相关的成本，Pargemslr利用代数域的多级分区。 pargemslr库是在消息传递接口的顶部实现的，并且可以解决真实和复杂的线性系统。此外，Pargemslr可以利用与一个或多个图形处理单元内访问的混合计算环境。最后，pargemslr的平行效率（弱和强缩放）在因3D部分微分方程的离散化引起的一些模型问题上得到了证明。
This paper discusses parGeMSLR, a C++/MPI software library for the solution of sparse systems of linear algebraic equations via preconditioned Krylov subspace methods in distributed-memory computing environments. The preconditioner implemented in parGeMSLR is based on algebraic domain decomposition and partitions the symmetrized adjacency graph recursively into several non-overlapping partitions via a p-way vertex separator, where p is an integer multiple of the total number of MPI processes. From a numerical perspective, parGeMSLR builds a Schur complement approximate inverse preconditioner as the sum between the matrix inverse of the interface coupling matrix and a low-rank correction term. To reduce the cost associated with the computation of the approximate inverse matrices, parGeMSLR exploits a multilevel partitioning of the algebraic domain. The parGeMSLR library is implemented on top of the Message Passing Interface and can solve both real and complex linear systems. Furthermore, parGeMSLR can take advantage of hybrid computing environments with in-node access to one or more Graphics Processing Units. Finally, the parallel efficiency (weak and strong scaling) of parGeMSLR is demonstrated on a few model problems arising from discretizations of 3D Partial Differential Equations.
