A class of parallel implicit Runge-Kutta formulas is constructed for multiprocessor system. A family of parallel implicit two-stage fourth order Runge-Kutta formulas is given. For these formulas, the convergence is pr...A class of parallel implicit Runge-Kutta formulas is constructed for multiprocessor system. A family of parallel implicit two-stage fourth order Runge-Kutta formulas is given. For these formulas, the convergence is proved and the stability analysis is given. The numerical examples demonstrate that these formulas can solve an extensive class of initial value problems for the ordinary differential equations.展开更多
在机电暂态仿真计算中,常用的稀疏三角分解存在分解效率不高、并行度低等问题。基于隐式梯形积分法,首先根据雅克比矩阵的特点,将雅可比矩阵分裂,然后利用扩展的Sherrman-Morrison求逆公式递推求解,从而避免了稀疏三角分解,得到了一类...在机电暂态仿真计算中,常用的稀疏三角分解存在分解效率不高、并行度低等问题。基于隐式梯形积分法,首先根据雅克比矩阵的特点,将雅可比矩阵分裂,然后利用扩展的Sherrman-Morrison求逆公式递推求解,从而避免了稀疏三角分解,得到了一类新的机电暂态仿真算法。利用高性能的图形处理器(Graphics Processing Unit, GPU)对大规模合成系统进行仿真测试。结果分析表明,所提出的并行算法可以获得较好的加速比和良好的扩展性。展开更多
基金Project supported by the National Natural Science Foundation of China
文摘A class of parallel implicit Runge-Kutta formulas is constructed for multiprocessor system. A family of parallel implicit two-stage fourth order Runge-Kutta formulas is given. For these formulas, the convergence is proved and the stability analysis is given. The numerical examples demonstrate that these formulas can solve an extensive class of initial value problems for the ordinary differential equations.
文摘在机电暂态仿真计算中,常用的稀疏三角分解存在分解效率不高、并行度低等问题。基于隐式梯形积分法,首先根据雅克比矩阵的特点,将雅可比矩阵分裂,然后利用扩展的Sherrman-Morrison求逆公式递推求解,从而避免了稀疏三角分解,得到了一类新的机电暂态仿真算法。利用高性能的图形处理器(Graphics Processing Unit, GPU)对大规模合成系统进行仿真测试。结果分析表明,所提出的并行算法可以获得较好的加速比和良好的扩展性。
