探讨聚合物流体分子模型的应力计算问题,给出了基于Euler格式随机Brown轨道的多层蒙特卡罗(multilevel Monte Carlo,MLMC)方法。该方法利用多尺度时间步长思想优化尺度样本数,提高计算效率。Hooke和FENE模型的数值结果表明:在低Wi(Weiss...探讨聚合物流体分子模型的应力计算问题,给出了基于Euler格式随机Brown轨道的多层蒙特卡罗(multilevel Monte Carlo,MLMC)方法。该方法利用多尺度时间步长思想优化尺度样本数,提高计算效率。Hooke和FENE模型的数值结果表明:在低Wi(Weissenberg)数情况下,MLMC方法比标准蒙特卡罗(StdMC)方法的计算成本更低,随机误差更小;而且目标精度越高,MLMC方法的计算效率提升越明显。进一步研究发现,由于在W i数较小时随机系统的Brown力比弹性力占优,应力的样本方差对MLMC层数的变化较敏感。因此,MLMC方法可以有效的降低随机误差。展开更多
This paper discusses a class of discretized Newton methods for solving systems of nonlinear equations. The number of function evaluations requred by the new discretized algorithm is about half of the classical discret...This paper discusses a class of discretized Newton methods for solving systems of nonlinear equations. The number of function evaluations requred by the new discretized algorithm is about half of the classical discretized Newton method as Brown and Brent methods. The approximation given by the algorithms to F’(x) is strongly consistent. The algorithms can reduce to the Newton method when the difference stepsize h approaches to zeros but Brown and Brent methods can’t do it. Numerical results show the algorithms are efficient.展开更多
文摘探讨聚合物流体分子模型的应力计算问题,给出了基于Euler格式随机Brown轨道的多层蒙特卡罗(multilevel Monte Carlo,MLMC)方法。该方法利用多尺度时间步长思想优化尺度样本数,提高计算效率。Hooke和FENE模型的数值结果表明:在低Wi(Weissenberg)数情况下,MLMC方法比标准蒙特卡罗(StdMC)方法的计算成本更低,随机误差更小;而且目标精度越高,MLMC方法的计算效率提升越明显。进一步研究发现,由于在W i数较小时随机系统的Brown力比弹性力占优,应力的样本方差对MLMC层数的变化较敏感。因此,MLMC方法可以有效的降低随机误差。
文摘This paper discusses a class of discretized Newton methods for solving systems of nonlinear equations. The number of function evaluations requred by the new discretized algorithm is about half of the classical discretized Newton method as Brown and Brent methods. The approximation given by the algorithms to F’(x) is strongly consistent. The algorithms can reduce to the Newton method when the difference stepsize h approaches to zeros but Brown and Brent methods can’t do it. Numerical results show the algorithms are efficient.
