并行J-变量块Cholesky分解算法的仿真研究

该文提出一个针对大型实对称正定稠密方程组或复对称非Hermitian稠密方程组线性求解器的并行分布式算法。它使用了不同于ScaLAPACK的J-变量块Cholesky分解算法和一维块循环列数据分配。该算法以MPI作为消息传递库，在最多可达16个处理器的集群上针对实对称正定稠密方程组可提供与ScaLAPACK近似的浮点操作性能，并可解决一些涉及复对称非Hermitian稠密方程组的电磁场散射问题。该算法的优点是执行Cholesky分解所需的存储量只是标准并行库ScaLAPACK的一半。仿真的数值结果表明该算法是正确、有效的。

Simulation of a Parallel J-variant Block Cholesky Factorization Algorithm

In this paper the parallel distributed algorithm of a linear solver involving large scale real symmetric positive definite or complex symmetric non - Hermitian dense systems is presented. The algorithm uses a J - variant block Cholesky algorithm and a one dimensional block - cyclic column data distribution that are different from the library ScaLAPACK. The algorithm uses MPI as message passing library and gives similar float operations performance involving real symmetric positive definite dense systems compared with ScaLAPACK when applied to electromagnetic scattering problems involving complex symmetric non - Hermitian dense systems that can be solved on a moderately cluster with up to 16 processors. The advantage of the algorithm is that it performs a Cholesky factorization by requiring only half the storage needed by the standard parallel library ScaLAPACK . The numerical results of simulations show the correctness and validity of the algorithm.