High Performance Parallel Linear Solver for Peta-scale Simulation

对用于Peta尺度模拟的线性求解器进行了研究。研究了一种改进病态问题(包括超大规模问题)的收敛速度的技术和一种在求解器中获得较高并行加速比的并行化技术。采用隐式修正多重网格法和EEC/IEC方法有效地处理了病态问题。我和我的同事开发了一种技术，使开发各种多级求解器变得容易，并在一个实际的模拟领域(计算电磁学)提出了一种收敛加速技术。在对开发的求解器进行的性能评估测试中，我们在不到250个S的时间内，用1024个处理器核成功地解决了大约8亿自由度的问题。

The research work for a linear solver for peta-scale simulation has been conducted. A technique to improve convergence for ill-conditioned problems including very large-scale problems and a parallelization technique getting high parallel speedups in the solver have been investigated. An implicit correction multigrid method and EEC/IEC methods were efficiently utilized to deal with the ill-conditioned problem. I and my co-workers have developed a technique which makes it easy to develop various multilevel solvers, and also proposed a convergence acceleration technique in a practical simulation area(computational electromagnetism). In a performance evaluation test for developed solvers, we successfully solved an about 800 million DOF problem by 1024 processor cores in less than 250 s.