Dynamic Sparsing in Stiff Extrapolation Methods
Dynamic Sparsing in Stiff Extrapolation Methods
复制标题
刚性外推方法中的动态稀疏
DOI：
10.1006/icse.1993.1003
复制
发表时间：
1993
期刊：
影响因子：
--
通讯作者：
U. Nowak
中科院分区：
文献类型：
--
作者：
U. Nowak
摘要基于半图表Euler离散化的简单稳定性分析，得出了一种新的动态稀疏程序。此过程自动消除了Jacobian矩阵的“小”元素。结果，可以大幅度降低在半插图外推积分子内处理线性代数所需的工作量。在整合过程中，决定“小”含义的稀疏标准是动态适应的，以确保离散方案的稳定性。因此，可以避免由于不稳定而产生的步骤限制。关于完全不同问题的数值实验表明了这种动态稀疏技术的鲁棒性和效率。原则上，在僵硬的外推积分子的背景下，这里开发的技术可以应用于W方法，在那里，确切的Jacobians可以用“足够好”的近似值代替。
Abstract Based on a simple stability analysis for the semi-implicit Euler discretization, a new dynamic sparsing procedure is derived. This procedure automatically eliminates "small" elements of the Jacobian matrix. As a consequence, the amount of work needed to handle the linear algebra within a semi-implicit extrapolation integrator can be reduced drastically. Within the course of integration the sparsing criterion, which decides what "small" means, is dynamically adapted to ensure stability of the discretization scheme. Thus, stepsize restrictions due to instability can be avoided. Numerical experiments for quite different problems show the robustness and efficiency of this dynamic sparsing technique. The techniques developed here in the context of stiff extrapolation integrators can, in principle, be applied to W-methods, where exact Jacobians may be replaced by "sufficiently good" approximations.