虚拟传输法：一种求解稀疏线性系统的新型分布式算法
Virtual Transmission Method, A New Distributed Algorithm to Solve Sparse Linear System
AI总结：
提出虚拟传输法（VTM），通过插入无损传输线实现分布式计算，并证明其收敛性，数值实验表明该方法高效、精确且稳定。
摘要：
本文提出了一种新的并行算法，该算法可自然地在具有任意数量处理器的并行计算机上工作。该算法被命名为虚拟传输法（VTM）。其物理背景是无损传输线和微波网络。VTM的基本思想是将无损传输线插入稀疏线性系统中以实现分布式计算。 证明了VTM在求解SPD线性系统时是收敛的。给出了预处理方法和性能模型。数值实验表明VTM高效、精确且稳定。 伴随VTM，我们引入了一种新的对称线性系统划分技术，称为广义节点与支路撕裂（GNBT）。它基于电路理论中的基尔霍夫电流定律。我们证明了GNBT对于划分任何SPD线性系统是可行的。
英文摘要：
In this paper, we propose a new parallel algorithm which could work naturally on the parallel computer with arbitrary number of processors. This algorithm is named Virtual Transmission Method (VTM). Its physical backgroud is the lossless transmission line and microwave network. The basic idea of VTM is to insert lossless transmission lines into the sparse linear system to achieve distributed computing. VTM is proved to be convergent to solve SPD linear system. Preconditioning method and performance model are presented. Numerical experiments show that VTM is efficient, accurate and stable. Accompanied with VTM, we bring in a new technique to partition the symmetric linear system, which is named Generalized Node & Branch Tearing (GNBT). It is based on Kirchhoff's Current Law from circuit theory. We proved that GNBT is feasible to partition any SPD linear system.
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